spc & msa presentation
DESCRIPTION
aTRANSCRIPT
WELCOME TO TRAINING ON
STATISTICAL PROCESS CONTROL (SPC)
amp
MEASUREMENT SYSTEM ANALYSIS (MSA)
1
CONTENTS
Statistical Process Control (SPC)
SPC ndash Description
Variations amp types of variations
Data amp Types of Data
Control charts amp types
Process Capability
Measurement System Analysis(MSA)
Measurement System Analysis ndash Description
Measurement System Variations amp Descriptions
Gauge R amp R study
2
WHAT IS SPC
SPC - Statistical Process Control is a
process that was designed to describe the
changes in process variation from a standard
It can be used for both attribute and variable
data
3
WHAT IS SPC
Statistical - The collection of data and the arrangement of those data in clear pattern to allow predictions to be made on performance
Process ndash A process is considered as an any activity involving combination of people equipment and materials working together to produce an output
Control ndash Comparing actual performance against a target and identifiying when and what corrective action is necessary to achieve the target
4
STATISTICAL PROCESS CONTROL
In statistics when we look at groups of numbers they are centered in three different ways Mode Median Mean
Mode Mode is the number that occurs the most frequently in a group of numbers
7 9 11 6 13 6 6 311 Put them in order 3 6 6 6 7 9 11 11 13
The mode is 6
5
Median Median is like the geographical center it would be the middle number
7 9 11 6 13 6 6 311 Put them in order 3 6 6 6 7 9 11 11 13 7 is the median
Mean Mean is the average of all the numbers The mean is derived by adding all the numbers and then dividing by the quantity of numbers
X1 + X2 + X3 + X4 + X5 + X6 + X7 +hellip+Xn
n
STATISTICAL PROCESS CONTROL
6
1 2 3 6 8
VARIATION
No two products or characteristics are exactly alike because any process contains many sources of variability
The differences among products may be large or may be immeasurably small but they are present
For instance the diameter of a machined shaft would be susceptible to potential variation from
Machine - Clerancesbearing wear
Tool - Strength rate of wear
Material - Hardness strength
Operator - Part feed accuracy of centering
Maintenance - Lubrication replacement of worn out parts
Environment - Temperature consistency of power supply
The numbers that were not exactly on the mean are considered ldquovariationrdquo
7
TYPES OF VARIATION
There are two types of variation
Common cause variation
Special cause variation
8
COMMON CAUSES
Common cause variation is that normal variation that exists in a process when it is running exactly as it should
Eg In the production of that Shaft variation even
When the operator is running the machine properly
When the machine is running properly
When the material is correct
When the method is correct
When the environment is correct
When the original measurements are correct
9
As we have just reviewed common cause variation cannot be defined by one particular characteristic
It is the inherent variation of all the parts of the operation together
Eg
Voltage fluctuation
Looseness or tightness of machine bearings
Common cause variation must be optimized and run at a reasonable cost
If only common causes of variation are present the output of a process is predictable
COMMON CAUSES
10
SPECIAL CAUSES
Special cause is when one or more of the process specificationsconditions change
Temperatures
Tools dull
Voltage drops drastically
Material change
Bearings are failing
Special cause variations are the variations that need to be corrected immediately since it affect the process output in unpredictable ways
11
WHY DO WE NEED DATA
Assessment
Assessing the effectiveness of specific process or corrective actions
Evaluation
Determine the quality of a process or product
Improvement
Help us understand where improvement is needed
Control
To help control a process and to ensure it does not move out of control
Prediction
Provide information and trends that enables us to predict when an activity will fail in the future
12
TYPES OF DATA
Data can be grouped into two major categories
Attributes data
Variable data
13
TYPES OF DATA ndash ATTRIBUTE DATA
Attributes data Non-measurable characteristics Can be very subjective
Blush Scratched Color etc
Observations are counted YesNo PresentAbsent MeetsDoesnrsquot meet
Visually inspected Gono-go gauges
If color happens to be an attribute that is being inspected for Typically meet the expected color sample is given Maybe a light and dark compared to sample given The acceptable range is in between A reject is not measured just counted as one
14
Collected through measurement
Is very objective
Can be temperature length width weight force volts amps etc
Uses a measuring tool
Scale
Meters
Inspection should not be done to sort but for data collection and correction of the process
This will allow for quick response and rapid correction minimizing defect quantities
TYPES OF DATA ndash VARIABLE DATA
15
PARETO CHARTS
Vilfredo Pareto
Italyrsquos wealth
80 held by 20 of people
Used when analyzing attributes
Based on results of tally numbers in specific categories
What is a Pareto Chart used for
To display the relative importance of data
To direct efforts to the biggest improvement opportunity by highlighting the vital few in contrast to the useful many
16
CONSTRUCTING A PARETO CHART
Determine the categories and the units for comparison of the data such as frequency cost or time
Total the raw data in each category then determine the grand total by adding the totals of each category
Re-order the categories from largest to smallest
Determine the cumulative percent of each category (ie the sum of each category plus all categories that precede it in the rank order divided by the grand total and multiplied by 100)
17
CONSTRUCTING A PARETO CHART
Draw and label the left-hand vertical axis with the unit of comparison such as frequency cost or time
Draw and label the horizontal axis with the categories List from left to right in rank order
Draw and label the right-hand vertical axis from 0 to 100 percent The 100 percent should line up with the grand total on the left-hand vertical axis
Beginning with the largest category draw in bars for each category representing the total for that category
18
CONSTRUCTING A PARETO CHART
Draw a line graph beginning at the right-hand
corner of the first bar to represent the
cumulative percent for each category as
measured on the right-hand axis
Analyze the chart Usually the top 20 of the
categories will comprise roughly 80 of the
cumulative total
19
PARETO CHART - EXAMPLE
Lets assume we are listing all the rejected products that are removed from a candy manufacturing line in one week
First we put the rejects in specific categories
No wrapper - 10
No center - 37
Wrong shape - 53
Short shot - 6
Wrapper open - 132
Underweight - 4
Overweight ndash 17
Get the total rejects - 259
20
Develop a percentage for each category
No wrapper ndash 10259 = 39
No center ndash 37259 = 143
Wrong shape ndash 53259 = 205
Short shot ndash 6259 = 23
Wrapper open ndash 132259 = 51
Underweight ndash 4259 = 15
Overweight ndash 17259 = 66
PARETO CHART - EXAMPLE
21
Now place the counts in a histogram largest to smallest
0
10
20
30
40
50
60
Wrapper
Open
No Center No Wrapper Underweight
70
80
90
100
51
205
143
66 39
23 15
22
Finally add up each and plot as a line diagram
0
10
20
30
40
50
60
Wrapper
Open
No Center No Wrapper Underweight
70
80
90
100
715
51
205
143
858
66
924
39
963
23
986
15
1001
23
0
10
20
30
40
50
60
Wrapper
Open
No Center No Wrapper Underweight
70
80
90
100
715
51
205
143
858
66
924
39
963
23
986
15
1001
24
CONTROL CHARTS
Control charts are one of the most commonly used methods of Statistical Process Control (SPC) which
monitors the stability of a process
The main features of a control chart include the data points a centreline (mean value) and upper and
lower limits (bounds to indicate where a process output is considered out of control)They visually
display the fluctuations of a particular process variable that easily determine whether these variations
fall within the specified process limits
Control charts
a graphical method for detecting if the underlying distribution of variation of some measurable
characteristic of the product seems to have undergone a shift
monitor a process in real time
Map the output of a production process over time
A control chart always has a central line for the average an upper line for the upper control limit and a
lower line for the lower control limit These lines are determined from historical data
By comparing current data to these lines you can draw conclusions about whether the process
variation is consistent (in control) or is unpredictable
25
CONTROL CHART - PURPOSE
The main purpose of using a control chart is to monitor control and improve
process performance over time by studying variation and its source There are
several functions of a control chart
It centres attention on detecting and monitoring process variation over time
It provides a tool for on-going control of a process
It differentiates special from common causes of variation in order to be a guide for
local or management action
It helps improve a process to perform consistently and predictably to achieve higher
quality lower cost and higher effective capacity
It serves as a common language for discussing process performance
26
TYPES OF CONTROL CHARTS
The basic tool used in SPC is the control chart
There are various types of control charts
Variable Control Chart
Averages and range chart (X-Bar and R Bar Chart)
X bar and s chart
Moving Range Chart
Moving AveragendashMoving Range chart (also called MAndashMR chart)
p chart (also called proportion chart)
c chart (also called count chart)
np chart
u chart
27
POPULARITY OF CONTROL CHARTS
Control charts are a proven technique for improving productivity
Control charts are effective in defect prevention
Control charts prevent unnecessary process
adjustment
Control charts provide diagnostic information
Control charts provide information about process
capability
28
PROCEDURE FOR X ndashBAR AND R BAR CHART
1 Randomly sample ldquonrdquo units throughout the day (can be every 5
minutes every 30 minutes etc - whatever is appropriate for your
case)
2 For each sample calculate ldquoX-BARrdquo to estimate the mean and ldquoR
(range)rdquo to estimate variability NOTE THE RANGE CAN BE USED TO
ESTIMATE THE STANDARD DEVIATION
3 After collecting the 20-25 samples calculate X-BAR-BAR (the
average of all the X-BARs) and R-BAR (the average of all the ranges)
4 Using X-BAR-BAR and R-BAR calculate the control limits for your X-
BAR and R Control Charts
29
X-BAR CONTROL LIMITS
Upper Control Limit (UCL) = (X-BAR-BAR) + A2 (R-BAR)
Lower Control Limit(LCL) = (X-BAR-BAR) - A2 (R-BAR)
R CONTROL LIMITS
Upper Control Limit - D3 (R-BAR)
Lower Control Limit - D4 (R-BAR)
PROCEDURE FOR X ndashBAR AND R BAR CHART
30
CONTROL CHART CONSTANTS
sample size constant constant constant constant constant constant constant
n d2 A2 A3 B3 B4 D3 D4
2 1128 188 2659 0 3267 0 3267
3 1693 1023 1954 0 2568 0 2574
4 2059 0729 1628 0 2266 0 2282
5 2326 0577 1427 0 2089 0 2114
6 2534 0483 1287 003 197 0 2004
7 2704 0419 1182 0118 1882 0076 1924
8 2847 0373 1099 0185 1815 0136 1864
9 297 0337 1032 0239 1761 0184 1816
10 3078 0308 0975 0284 1716 0223 1777
31
5 For the R Control Chart plot all R values on the R Control Chart
to see if all the Ranges are ldquobetween the control limitsrdquo If they are
then your process is considered to be in a state of statistical control
(as far as the variability of the process is concerned)
6 For the X-BAR Control Chart plot all the X-BARs on the X-BAR
control chart to see if all the X-BARs are ldquobetween the control
limitsrdquo If they are then your process is considered in a state of
statistical control (as far as the average of the process is
concerned)
PROCEDURE FOR X ndashBAR AND R BAR CHART
32
SAMPLE DATA FOR X BAR ndashR CHART
Sub Group 1 2 3 4 5 X -Bar Range reg
1 1195 1191 1211 1203 1198 1200 02
2 1201 1198 1198 1197 12 1199 004
3 1193 1206 1198 1196 1202 1199 013
4 1205 1198 1205 1206 1198 1202 008
5 1198 1203 1206 1201 1199 1201 008
6 1202 1205 1196 1201 1195 1200 01
7 1199 1206 1201 1204 1201 1202 007
8 1201 1197 1198 1204 1198 1200 007
9 1198 1204 1198 1204 1204 1202 006
10 1205 1195 1198 1204 1196 1200 01
` X Bar-Bar 1200 009
X Bar Chart
UCL = X BAR-BAR + A2 R Bar
1200 +(0577009) 1205
LCL= X BAR-BAR - A2 R Bar
1200 - (0577009) 1195
R Chart
UCL = D4R Bar 211 009 021
LCL = D3 R Bar 0009 0
33
PLOT DATA ON CONTROL CHARTS
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1 2 3 4 5 6 7 8 9 10
Ave
rage
(X
ba
r)
X Bar Chart
UCL
LCL
X Bar
34
PLOT DATA ON CONTROL CHARTS
001
003
005
007
009
011
013
015
017
019
021
023
025
1 2 3 4 5 6 7 8 9 10
R Chart
UCL
LCL
35
PROCEDURE TO DETERMINE IF PROCESS IS IN A STATE OF
STATISTICAL CONTROL
7 If process is determined to be ldquoNOT STABLErdquo then stop and find out what
an assignable cause might be fix and then repeat the complete process of
collecting new data
8 If the process is determined to be ldquoSTABLErdquo then you may use the
control charts you developed to monitor future production to ensure that the
process REMAINS stable
More Samples for Control charts
36
READING OF CONTROL CHART
Control charts can determine whether a process is behaving in an unusual way The quality of the individual points of a subset is determined unstable if any of the
following occurs
Rule 1 Any point falls beyond 3σ from the centreline(this is represented by the upper and
lower control limits)
Rule 2 Two out of three consecutive points fall beyond 2σ on the same side of the
centreline
Rule 3 Four out of five consecutive points fall beyond 1σ on the same side of the
centreline
Rule 4 Nine or more consecutive points fall on the same side of the centreline
(Ref Next page for sample)
37
READING THE CONTROL CHART
38
CONTROL CHARTS FOR ATTRIBUTES ndashP-CHARTS amp C-CHARTS
Attributes are discrete events yesno or passfail
Use P-Charts for quality characteristics that are discrete and involve yesno or goodbad decisions
Eg
Number of leaking caulking tubes in a box of 48
Number of broken eggs in a carton
Use C-Charts for discrete defects when there can be more than one defect per unit
Eg
Number of stains in a carpet sample cut from a production run
Number of complaints per customer at a hotel
39
P-CHART EXAMPLE A PRODUCTION MANAGER FOR A TIRE COMPANY HAS INSPECTED THE NUMBER OF
DEFECTIVE TIRES IN FIVE RANDOM SAMPLES WITH 20 TIRES IN EACH SAMPLE THE TABLE BELOW SHOWS THE
NUMBER OF DEFECTIVE TIRES IN EACH SAMPLE OF 20 TIRES CALCULATE THE CONTROL LIMITS
Sample Number of
Defective Tires
Number of Tires in each
Sample
Proportion Defective
1 3 20 15
2 2 20 10
3 1 20 05
4 2 20 10
5 2 20 05
Total 9 100 09
01023(064)09σzpLCL
2823(064)09σzpUCL
06420
(09)(91)
n
)p(1pσ
09100
9
Inspected Total
DefectivespCL
p
p
p
Solution
40
P- CONTROL CHART
41
C-CHART EXAMPLE THE NUMBER OF WEEKLY CUSTOMER COMPLAINTS ARE MONITORED IN A LARGE HOTEL USING A C-CHART DEVELOP THREE SIGMA CONTROL LIMITS USING THE DATA TABLE BELOW
Week Number of Complaints
1 3
2 2
3 3
4 1
5 3
6 3
7 2
8 1
9 3
10 1
Total 22
022522322ccLCL
66522322ccUCL
2210
22
samples of
complaintsc
c
c
z
z
Solution
42
C- CONTROL CHART
43
The ability of a process to meet product designtechnical specifications
Assessing capability involves evaluating process variability relative to preset product or service specifications
Process Capability ndash Cp and Cpk
Cp assumes that the process is centered in the specification range
Cpk helps to address a possible lack of centering of the process
PROCESS CAPABILITY
6σ
LSLUSL
width process
width ionspecificatCp
3σ
LSLμ
3σ
μUSLminCpk
44
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
45
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
46
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
47
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
--and an individual part is measured at 520rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
48
GRAPHING THE TOLERANCE AND MEASUREMENTS
Suppose we made and measured several more
units and they were all EXACTLY the same
We wouldnrsquot have very many part problems
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
X
X
X
49
GRAPHING THE TOLERANCE AND MEASUREMENTS
In the real world units are NOT EXACTLY the same
Everything VARIES
The question isnrsquot IF units vary
Itrsquos how much when and why
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
XX
XXX
XXXXX
XXXXXXX
50
The ldquonormal bell curverdquo
Widths heights depths thicknesses weights speeds strengths
and many other types of measurements when charted as a
histogram often form the shape of a bell
A ldquoperfect bellrdquo like a ldquoperfect circlerdquo doesnrsquot occur in nature but
many processes are close enough to make the bell curve useful
(A number of common industrial measurements such as flatness and straightness do NOT tend to distribute in a bell shape their proper statistical analysis is performed using models other than the bell curve)
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
51
What is a ldquostandard deviationrdquo
If we measure the DISTANCE from the CENTER of the bell
to each individual measurement that makes up the bell curve
we can find a TYPICAL DISTANCE
The most commonly used statistic to estimate this distance is the
Standard Deviation (also called ldquoSigmardquo)
Because of the natural shape of the bell curve the area of +1 to ndash1
standard deviations includes about 68 of the curve
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
Typical distance
from the center +1
standard deviation
Typical distance
from the center -1
standard deviation
52
How much of the curve is included in how many standard
deviations
From ndash1 to +1 is about 68 of the bell curve
From ndash2 to +2 is about 95
From ndash3 to +3 is about 9973
From ndash4 to +4 is about 9999
(NOTE We usually show the bell from ndash3 to +3 to make it easier to draw but in concept the ldquotailsrdquo of the bell get very thin and go on forever)
-6 -5 -4 -3 -2 -1 +1 +2 +3 +4 +5 +6 0
53
A
B
What is Cpk It is a measure of how well a process is within a specification
Cpk = A divided by B
A = Distance from process mean to closest spec limit
B = 3 Standard Deviations (also called ldquo3 Sigmardquo)
A bigger Cpk is better because fewer units will be beyond spec
(A bigger ldquoArdquo and a smaller ldquoBrdquo are better)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
54
A
B
ldquoProcess Capabilityrdquo is the ability of a process
to fit its output within the tolerances
hellipa LARGER ldquoArdquo
hellipand a SMALLER ldquoBrdquo
hellipmeans BETTER ldquoProcess Capabilityrdquo
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
55
A
B
An Analogy
Analogy
The bell curve is your automobile
The spec limits are the edges of your garage door
If A = B you are hitting the frame of your garage door with your car
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
56
A
B
How can we make Cpk (A divided by B) better
1 Design the product so a wider tolerance is functional (ldquorobust designrdquo)
2 Choose equipment and methods for a good safety margin (ldquoprocess capabilityrdquo)
3 Correctly adjust but only when needed (ldquocontrolrdquo)
4 Discover ways to narrow the natural variation (ldquoimprovementrdquo)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
57
A
B
What does a very good Cpk do for us
This process is producing good units with a good safety margin
Note that when Cpk = 2 our process mean is 6 standard deviations from
the nearest spec so we say it has ldquo6 Sigma Capabilityrdquo
Specification
Limit
Specification
Limit
This Cpk is
about 2
Very good
Mean
58
A
B
What does a problem Cpk look like
This process is in danger of producing some defects
It is too close to the specification limits
(Remember the bell curve tail goes further than Bhellip hellipwe only show the bell to 3-sigma to make it easier to draw)
Specification
Limit
Specification
Limit
This Cpk is just
slightly greater
than 1 Not good
59
A
B
What does a very bad Cpk look like
A significant part of the ldquotailrdquo is hanging out beyond the spec limits
This process is producing scrap rework and customer rejects
Notice that if distance ldquoArdquo approaches zerohellip
hellipthe Cpk would approach zero andhellip
hellipthe process would become 50 defective
Specification
Limit
Specification
Limit
This Cpk is less
than 1 We desire
a minimum of 133
and ultimately we
want 2 or more
60
-
Q amp A
61
MEASUREMENT SYSTEM ANALYSIS (MSA)
An MSA is a statistical tool used to determine if a measurement system is capable of precise measurement
What is It
Objective or Purpose
bull To determine how much error is in the measurement due to the measurement process itself
bull Quantifies the variability added by the measurement system
bull Applicable to attribute data and variable data
When to Use It
bull On the critical inputs and outputs prior to collecting data for analysis
bull For any new or modified process in order to ensure the quality of the data
Measurement System Analysis is an analysis of the measurement process not an analysis of the people
IMPORTANT
Who Should be Involved
Everyone that measures and makes decisions about these measurements should be involved in the MSA
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The observed variation in process output measurements is not simply the variation in the process itself it is the variation in the process plus the variation in measurement that results from an inadequate measurement system
Conducting an MSA reduces the likelihood of passing a bad part or rejecting a good part
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The output of the process measured by bull Cycle time bull Dimensional data bull Number of defects and others
Observed Variation
Process Variation
Measurement System
Variation
Reproducibility
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Accuracy (Central Location)
OBSERVED VARIATION
Calibration addresses accuracy
Measurement System Analysis (MSA)
MEASUREMENT SYSTEM ERRORS
Accuracy difference between the observed measurement and the actual measurement
Precision variation that occurs when measuring the same part with the same instrument
MEASUREMENT SYSTEM ERROR
Precise but not
accurate
Accurate but not
precise
Not accurate or
precise
Accurate and
precise
ACCURACY OF MEASUREMENT
Broken down into three components
aStability
The consistency of measurements over time
bBias
A measure of the amount of partiality in the system
cLinearity
A measure of the bias values through the expected
range of measurements
OBSERVED VARIATION
Observed Variation
Process Variation
Measurement System
Variation
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Reproducibility
Accuracy (Central Location)
Calibration Addresses Accuracy
Letrsquos take a closer look at Precision
Measurement System Analysis (MSA)
Measurement System Analysis (MSA)
Error in Resolution The inability to detect small changes
Possible Cause
Wrong measurement device selected - divisions on scale not fine enough to detect changes
Resolution
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Repeatability The inability to get the same answer from repeated measurements made of the same item under absolutely identical conditions
Possible Cause
Lack of standard operating procedures (SOP) lack of training measuring system variablilty
Repeatability
Equipment Variation
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Reproducibility The inability to get the same answer from repeated measurements made under various conditions from different inspectors
Possible Cause
Lack of SOP lack of training
Reproducibility
Appraiser Variation
VARIABLE MSA ndash GAGE RampR STUDY
bull Gage RampR is the combined estimate of
measurement system Repeatability and
Reproducibility
bull Typically a 3-person study is performed Each person randomly measures 10 marked parts per trial
Each person can perform up to 3 trials
bull There are 3 key indicators EV or Equipment Variation
AV or Appraiser Variation
Overall GRR
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
CONTENTS
Statistical Process Control (SPC)
SPC ndash Description
Variations amp types of variations
Data amp Types of Data
Control charts amp types
Process Capability
Measurement System Analysis(MSA)
Measurement System Analysis ndash Description
Measurement System Variations amp Descriptions
Gauge R amp R study
2
WHAT IS SPC
SPC - Statistical Process Control is a
process that was designed to describe the
changes in process variation from a standard
It can be used for both attribute and variable
data
3
WHAT IS SPC
Statistical - The collection of data and the arrangement of those data in clear pattern to allow predictions to be made on performance
Process ndash A process is considered as an any activity involving combination of people equipment and materials working together to produce an output
Control ndash Comparing actual performance against a target and identifiying when and what corrective action is necessary to achieve the target
4
STATISTICAL PROCESS CONTROL
In statistics when we look at groups of numbers they are centered in three different ways Mode Median Mean
Mode Mode is the number that occurs the most frequently in a group of numbers
7 9 11 6 13 6 6 311 Put them in order 3 6 6 6 7 9 11 11 13
The mode is 6
5
Median Median is like the geographical center it would be the middle number
7 9 11 6 13 6 6 311 Put them in order 3 6 6 6 7 9 11 11 13 7 is the median
Mean Mean is the average of all the numbers The mean is derived by adding all the numbers and then dividing by the quantity of numbers
X1 + X2 + X3 + X4 + X5 + X6 + X7 +hellip+Xn
n
STATISTICAL PROCESS CONTROL
6
1 2 3 6 8
VARIATION
No two products or characteristics are exactly alike because any process contains many sources of variability
The differences among products may be large or may be immeasurably small but they are present
For instance the diameter of a machined shaft would be susceptible to potential variation from
Machine - Clerancesbearing wear
Tool - Strength rate of wear
Material - Hardness strength
Operator - Part feed accuracy of centering
Maintenance - Lubrication replacement of worn out parts
Environment - Temperature consistency of power supply
The numbers that were not exactly on the mean are considered ldquovariationrdquo
7
TYPES OF VARIATION
There are two types of variation
Common cause variation
Special cause variation
8
COMMON CAUSES
Common cause variation is that normal variation that exists in a process when it is running exactly as it should
Eg In the production of that Shaft variation even
When the operator is running the machine properly
When the machine is running properly
When the material is correct
When the method is correct
When the environment is correct
When the original measurements are correct
9
As we have just reviewed common cause variation cannot be defined by one particular characteristic
It is the inherent variation of all the parts of the operation together
Eg
Voltage fluctuation
Looseness or tightness of machine bearings
Common cause variation must be optimized and run at a reasonable cost
If only common causes of variation are present the output of a process is predictable
COMMON CAUSES
10
SPECIAL CAUSES
Special cause is when one or more of the process specificationsconditions change
Temperatures
Tools dull
Voltage drops drastically
Material change
Bearings are failing
Special cause variations are the variations that need to be corrected immediately since it affect the process output in unpredictable ways
11
WHY DO WE NEED DATA
Assessment
Assessing the effectiveness of specific process or corrective actions
Evaluation
Determine the quality of a process or product
Improvement
Help us understand where improvement is needed
Control
To help control a process and to ensure it does not move out of control
Prediction
Provide information and trends that enables us to predict when an activity will fail in the future
12
TYPES OF DATA
Data can be grouped into two major categories
Attributes data
Variable data
13
TYPES OF DATA ndash ATTRIBUTE DATA
Attributes data Non-measurable characteristics Can be very subjective
Blush Scratched Color etc
Observations are counted YesNo PresentAbsent MeetsDoesnrsquot meet
Visually inspected Gono-go gauges
If color happens to be an attribute that is being inspected for Typically meet the expected color sample is given Maybe a light and dark compared to sample given The acceptable range is in between A reject is not measured just counted as one
14
Collected through measurement
Is very objective
Can be temperature length width weight force volts amps etc
Uses a measuring tool
Scale
Meters
Inspection should not be done to sort but for data collection and correction of the process
This will allow for quick response and rapid correction minimizing defect quantities
TYPES OF DATA ndash VARIABLE DATA
15
PARETO CHARTS
Vilfredo Pareto
Italyrsquos wealth
80 held by 20 of people
Used when analyzing attributes
Based on results of tally numbers in specific categories
What is a Pareto Chart used for
To display the relative importance of data
To direct efforts to the biggest improvement opportunity by highlighting the vital few in contrast to the useful many
16
CONSTRUCTING A PARETO CHART
Determine the categories and the units for comparison of the data such as frequency cost or time
Total the raw data in each category then determine the grand total by adding the totals of each category
Re-order the categories from largest to smallest
Determine the cumulative percent of each category (ie the sum of each category plus all categories that precede it in the rank order divided by the grand total and multiplied by 100)
17
CONSTRUCTING A PARETO CHART
Draw and label the left-hand vertical axis with the unit of comparison such as frequency cost or time
Draw and label the horizontal axis with the categories List from left to right in rank order
Draw and label the right-hand vertical axis from 0 to 100 percent The 100 percent should line up with the grand total on the left-hand vertical axis
Beginning with the largest category draw in bars for each category representing the total for that category
18
CONSTRUCTING A PARETO CHART
Draw a line graph beginning at the right-hand
corner of the first bar to represent the
cumulative percent for each category as
measured on the right-hand axis
Analyze the chart Usually the top 20 of the
categories will comprise roughly 80 of the
cumulative total
19
PARETO CHART - EXAMPLE
Lets assume we are listing all the rejected products that are removed from a candy manufacturing line in one week
First we put the rejects in specific categories
No wrapper - 10
No center - 37
Wrong shape - 53
Short shot - 6
Wrapper open - 132
Underweight - 4
Overweight ndash 17
Get the total rejects - 259
20
Develop a percentage for each category
No wrapper ndash 10259 = 39
No center ndash 37259 = 143
Wrong shape ndash 53259 = 205
Short shot ndash 6259 = 23
Wrapper open ndash 132259 = 51
Underweight ndash 4259 = 15
Overweight ndash 17259 = 66
PARETO CHART - EXAMPLE
21
Now place the counts in a histogram largest to smallest
0
10
20
30
40
50
60
Wrapper
Open
No Center No Wrapper Underweight
70
80
90
100
51
205
143
66 39
23 15
22
Finally add up each and plot as a line diagram
0
10
20
30
40
50
60
Wrapper
Open
No Center No Wrapper Underweight
70
80
90
100
715
51
205
143
858
66
924
39
963
23
986
15
1001
23
0
10
20
30
40
50
60
Wrapper
Open
No Center No Wrapper Underweight
70
80
90
100
715
51
205
143
858
66
924
39
963
23
986
15
1001
24
CONTROL CHARTS
Control charts are one of the most commonly used methods of Statistical Process Control (SPC) which
monitors the stability of a process
The main features of a control chart include the data points a centreline (mean value) and upper and
lower limits (bounds to indicate where a process output is considered out of control)They visually
display the fluctuations of a particular process variable that easily determine whether these variations
fall within the specified process limits
Control charts
a graphical method for detecting if the underlying distribution of variation of some measurable
characteristic of the product seems to have undergone a shift
monitor a process in real time
Map the output of a production process over time
A control chart always has a central line for the average an upper line for the upper control limit and a
lower line for the lower control limit These lines are determined from historical data
By comparing current data to these lines you can draw conclusions about whether the process
variation is consistent (in control) or is unpredictable
25
CONTROL CHART - PURPOSE
The main purpose of using a control chart is to monitor control and improve
process performance over time by studying variation and its source There are
several functions of a control chart
It centres attention on detecting and monitoring process variation over time
It provides a tool for on-going control of a process
It differentiates special from common causes of variation in order to be a guide for
local or management action
It helps improve a process to perform consistently and predictably to achieve higher
quality lower cost and higher effective capacity
It serves as a common language for discussing process performance
26
TYPES OF CONTROL CHARTS
The basic tool used in SPC is the control chart
There are various types of control charts
Variable Control Chart
Averages and range chart (X-Bar and R Bar Chart)
X bar and s chart
Moving Range Chart
Moving AveragendashMoving Range chart (also called MAndashMR chart)
p chart (also called proportion chart)
c chart (also called count chart)
np chart
u chart
27
POPULARITY OF CONTROL CHARTS
Control charts are a proven technique for improving productivity
Control charts are effective in defect prevention
Control charts prevent unnecessary process
adjustment
Control charts provide diagnostic information
Control charts provide information about process
capability
28
PROCEDURE FOR X ndashBAR AND R BAR CHART
1 Randomly sample ldquonrdquo units throughout the day (can be every 5
minutes every 30 minutes etc - whatever is appropriate for your
case)
2 For each sample calculate ldquoX-BARrdquo to estimate the mean and ldquoR
(range)rdquo to estimate variability NOTE THE RANGE CAN BE USED TO
ESTIMATE THE STANDARD DEVIATION
3 After collecting the 20-25 samples calculate X-BAR-BAR (the
average of all the X-BARs) and R-BAR (the average of all the ranges)
4 Using X-BAR-BAR and R-BAR calculate the control limits for your X-
BAR and R Control Charts
29
X-BAR CONTROL LIMITS
Upper Control Limit (UCL) = (X-BAR-BAR) + A2 (R-BAR)
Lower Control Limit(LCL) = (X-BAR-BAR) - A2 (R-BAR)
R CONTROL LIMITS
Upper Control Limit - D3 (R-BAR)
Lower Control Limit - D4 (R-BAR)
PROCEDURE FOR X ndashBAR AND R BAR CHART
30
CONTROL CHART CONSTANTS
sample size constant constant constant constant constant constant constant
n d2 A2 A3 B3 B4 D3 D4
2 1128 188 2659 0 3267 0 3267
3 1693 1023 1954 0 2568 0 2574
4 2059 0729 1628 0 2266 0 2282
5 2326 0577 1427 0 2089 0 2114
6 2534 0483 1287 003 197 0 2004
7 2704 0419 1182 0118 1882 0076 1924
8 2847 0373 1099 0185 1815 0136 1864
9 297 0337 1032 0239 1761 0184 1816
10 3078 0308 0975 0284 1716 0223 1777
31
5 For the R Control Chart plot all R values on the R Control Chart
to see if all the Ranges are ldquobetween the control limitsrdquo If they are
then your process is considered to be in a state of statistical control
(as far as the variability of the process is concerned)
6 For the X-BAR Control Chart plot all the X-BARs on the X-BAR
control chart to see if all the X-BARs are ldquobetween the control
limitsrdquo If they are then your process is considered in a state of
statistical control (as far as the average of the process is
concerned)
PROCEDURE FOR X ndashBAR AND R BAR CHART
32
SAMPLE DATA FOR X BAR ndashR CHART
Sub Group 1 2 3 4 5 X -Bar Range reg
1 1195 1191 1211 1203 1198 1200 02
2 1201 1198 1198 1197 12 1199 004
3 1193 1206 1198 1196 1202 1199 013
4 1205 1198 1205 1206 1198 1202 008
5 1198 1203 1206 1201 1199 1201 008
6 1202 1205 1196 1201 1195 1200 01
7 1199 1206 1201 1204 1201 1202 007
8 1201 1197 1198 1204 1198 1200 007
9 1198 1204 1198 1204 1204 1202 006
10 1205 1195 1198 1204 1196 1200 01
` X Bar-Bar 1200 009
X Bar Chart
UCL = X BAR-BAR + A2 R Bar
1200 +(0577009) 1205
LCL= X BAR-BAR - A2 R Bar
1200 - (0577009) 1195
R Chart
UCL = D4R Bar 211 009 021
LCL = D3 R Bar 0009 0
33
PLOT DATA ON CONTROL CHARTS
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1 2 3 4 5 6 7 8 9 10
Ave
rage
(X
ba
r)
X Bar Chart
UCL
LCL
X Bar
34
PLOT DATA ON CONTROL CHARTS
001
003
005
007
009
011
013
015
017
019
021
023
025
1 2 3 4 5 6 7 8 9 10
R Chart
UCL
LCL
35
PROCEDURE TO DETERMINE IF PROCESS IS IN A STATE OF
STATISTICAL CONTROL
7 If process is determined to be ldquoNOT STABLErdquo then stop and find out what
an assignable cause might be fix and then repeat the complete process of
collecting new data
8 If the process is determined to be ldquoSTABLErdquo then you may use the
control charts you developed to monitor future production to ensure that the
process REMAINS stable
More Samples for Control charts
36
READING OF CONTROL CHART
Control charts can determine whether a process is behaving in an unusual way The quality of the individual points of a subset is determined unstable if any of the
following occurs
Rule 1 Any point falls beyond 3σ from the centreline(this is represented by the upper and
lower control limits)
Rule 2 Two out of three consecutive points fall beyond 2σ on the same side of the
centreline
Rule 3 Four out of five consecutive points fall beyond 1σ on the same side of the
centreline
Rule 4 Nine or more consecutive points fall on the same side of the centreline
(Ref Next page for sample)
37
READING THE CONTROL CHART
38
CONTROL CHARTS FOR ATTRIBUTES ndashP-CHARTS amp C-CHARTS
Attributes are discrete events yesno or passfail
Use P-Charts for quality characteristics that are discrete and involve yesno or goodbad decisions
Eg
Number of leaking caulking tubes in a box of 48
Number of broken eggs in a carton
Use C-Charts for discrete defects when there can be more than one defect per unit
Eg
Number of stains in a carpet sample cut from a production run
Number of complaints per customer at a hotel
39
P-CHART EXAMPLE A PRODUCTION MANAGER FOR A TIRE COMPANY HAS INSPECTED THE NUMBER OF
DEFECTIVE TIRES IN FIVE RANDOM SAMPLES WITH 20 TIRES IN EACH SAMPLE THE TABLE BELOW SHOWS THE
NUMBER OF DEFECTIVE TIRES IN EACH SAMPLE OF 20 TIRES CALCULATE THE CONTROL LIMITS
Sample Number of
Defective Tires
Number of Tires in each
Sample
Proportion Defective
1 3 20 15
2 2 20 10
3 1 20 05
4 2 20 10
5 2 20 05
Total 9 100 09
01023(064)09σzpLCL
2823(064)09σzpUCL
06420
(09)(91)
n
)p(1pσ
09100
9
Inspected Total
DefectivespCL
p
p
p
Solution
40
P- CONTROL CHART
41
C-CHART EXAMPLE THE NUMBER OF WEEKLY CUSTOMER COMPLAINTS ARE MONITORED IN A LARGE HOTEL USING A C-CHART DEVELOP THREE SIGMA CONTROL LIMITS USING THE DATA TABLE BELOW
Week Number of Complaints
1 3
2 2
3 3
4 1
5 3
6 3
7 2
8 1
9 3
10 1
Total 22
022522322ccLCL
66522322ccUCL
2210
22
samples of
complaintsc
c
c
z
z
Solution
42
C- CONTROL CHART
43
The ability of a process to meet product designtechnical specifications
Assessing capability involves evaluating process variability relative to preset product or service specifications
Process Capability ndash Cp and Cpk
Cp assumes that the process is centered in the specification range
Cpk helps to address a possible lack of centering of the process
PROCESS CAPABILITY
6σ
LSLUSL
width process
width ionspecificatCp
3σ
LSLμ
3σ
μUSLminCpk
44
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
45
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
46
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
47
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
--and an individual part is measured at 520rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
48
GRAPHING THE TOLERANCE AND MEASUREMENTS
Suppose we made and measured several more
units and they were all EXACTLY the same
We wouldnrsquot have very many part problems
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
X
X
X
49
GRAPHING THE TOLERANCE AND MEASUREMENTS
In the real world units are NOT EXACTLY the same
Everything VARIES
The question isnrsquot IF units vary
Itrsquos how much when and why
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
XX
XXX
XXXXX
XXXXXXX
50
The ldquonormal bell curverdquo
Widths heights depths thicknesses weights speeds strengths
and many other types of measurements when charted as a
histogram often form the shape of a bell
A ldquoperfect bellrdquo like a ldquoperfect circlerdquo doesnrsquot occur in nature but
many processes are close enough to make the bell curve useful
(A number of common industrial measurements such as flatness and straightness do NOT tend to distribute in a bell shape their proper statistical analysis is performed using models other than the bell curve)
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
51
What is a ldquostandard deviationrdquo
If we measure the DISTANCE from the CENTER of the bell
to each individual measurement that makes up the bell curve
we can find a TYPICAL DISTANCE
The most commonly used statistic to estimate this distance is the
Standard Deviation (also called ldquoSigmardquo)
Because of the natural shape of the bell curve the area of +1 to ndash1
standard deviations includes about 68 of the curve
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
Typical distance
from the center +1
standard deviation
Typical distance
from the center -1
standard deviation
52
How much of the curve is included in how many standard
deviations
From ndash1 to +1 is about 68 of the bell curve
From ndash2 to +2 is about 95
From ndash3 to +3 is about 9973
From ndash4 to +4 is about 9999
(NOTE We usually show the bell from ndash3 to +3 to make it easier to draw but in concept the ldquotailsrdquo of the bell get very thin and go on forever)
-6 -5 -4 -3 -2 -1 +1 +2 +3 +4 +5 +6 0
53
A
B
What is Cpk It is a measure of how well a process is within a specification
Cpk = A divided by B
A = Distance from process mean to closest spec limit
B = 3 Standard Deviations (also called ldquo3 Sigmardquo)
A bigger Cpk is better because fewer units will be beyond spec
(A bigger ldquoArdquo and a smaller ldquoBrdquo are better)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
54
A
B
ldquoProcess Capabilityrdquo is the ability of a process
to fit its output within the tolerances
hellipa LARGER ldquoArdquo
hellipand a SMALLER ldquoBrdquo
hellipmeans BETTER ldquoProcess Capabilityrdquo
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
55
A
B
An Analogy
Analogy
The bell curve is your automobile
The spec limits are the edges of your garage door
If A = B you are hitting the frame of your garage door with your car
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
56
A
B
How can we make Cpk (A divided by B) better
1 Design the product so a wider tolerance is functional (ldquorobust designrdquo)
2 Choose equipment and methods for a good safety margin (ldquoprocess capabilityrdquo)
3 Correctly adjust but only when needed (ldquocontrolrdquo)
4 Discover ways to narrow the natural variation (ldquoimprovementrdquo)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
57
A
B
What does a very good Cpk do for us
This process is producing good units with a good safety margin
Note that when Cpk = 2 our process mean is 6 standard deviations from
the nearest spec so we say it has ldquo6 Sigma Capabilityrdquo
Specification
Limit
Specification
Limit
This Cpk is
about 2
Very good
Mean
58
A
B
What does a problem Cpk look like
This process is in danger of producing some defects
It is too close to the specification limits
(Remember the bell curve tail goes further than Bhellip hellipwe only show the bell to 3-sigma to make it easier to draw)
Specification
Limit
Specification
Limit
This Cpk is just
slightly greater
than 1 Not good
59
A
B
What does a very bad Cpk look like
A significant part of the ldquotailrdquo is hanging out beyond the spec limits
This process is producing scrap rework and customer rejects
Notice that if distance ldquoArdquo approaches zerohellip
hellipthe Cpk would approach zero andhellip
hellipthe process would become 50 defective
Specification
Limit
Specification
Limit
This Cpk is less
than 1 We desire
a minimum of 133
and ultimately we
want 2 or more
60
-
Q amp A
61
MEASUREMENT SYSTEM ANALYSIS (MSA)
An MSA is a statistical tool used to determine if a measurement system is capable of precise measurement
What is It
Objective or Purpose
bull To determine how much error is in the measurement due to the measurement process itself
bull Quantifies the variability added by the measurement system
bull Applicable to attribute data and variable data
When to Use It
bull On the critical inputs and outputs prior to collecting data for analysis
bull For any new or modified process in order to ensure the quality of the data
Measurement System Analysis is an analysis of the measurement process not an analysis of the people
IMPORTANT
Who Should be Involved
Everyone that measures and makes decisions about these measurements should be involved in the MSA
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The observed variation in process output measurements is not simply the variation in the process itself it is the variation in the process plus the variation in measurement that results from an inadequate measurement system
Conducting an MSA reduces the likelihood of passing a bad part or rejecting a good part
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The output of the process measured by bull Cycle time bull Dimensional data bull Number of defects and others
Observed Variation
Process Variation
Measurement System
Variation
Reproducibility
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Accuracy (Central Location)
OBSERVED VARIATION
Calibration addresses accuracy
Measurement System Analysis (MSA)
MEASUREMENT SYSTEM ERRORS
Accuracy difference between the observed measurement and the actual measurement
Precision variation that occurs when measuring the same part with the same instrument
MEASUREMENT SYSTEM ERROR
Precise but not
accurate
Accurate but not
precise
Not accurate or
precise
Accurate and
precise
ACCURACY OF MEASUREMENT
Broken down into three components
aStability
The consistency of measurements over time
bBias
A measure of the amount of partiality in the system
cLinearity
A measure of the bias values through the expected
range of measurements
OBSERVED VARIATION
Observed Variation
Process Variation
Measurement System
Variation
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Reproducibility
Accuracy (Central Location)
Calibration Addresses Accuracy
Letrsquos take a closer look at Precision
Measurement System Analysis (MSA)
Measurement System Analysis (MSA)
Error in Resolution The inability to detect small changes
Possible Cause
Wrong measurement device selected - divisions on scale not fine enough to detect changes
Resolution
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Repeatability The inability to get the same answer from repeated measurements made of the same item under absolutely identical conditions
Possible Cause
Lack of standard operating procedures (SOP) lack of training measuring system variablilty
Repeatability
Equipment Variation
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Reproducibility The inability to get the same answer from repeated measurements made under various conditions from different inspectors
Possible Cause
Lack of SOP lack of training
Reproducibility
Appraiser Variation
VARIABLE MSA ndash GAGE RampR STUDY
bull Gage RampR is the combined estimate of
measurement system Repeatability and
Reproducibility
bull Typically a 3-person study is performed Each person randomly measures 10 marked parts per trial
Each person can perform up to 3 trials
bull There are 3 key indicators EV or Equipment Variation
AV or Appraiser Variation
Overall GRR
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
WHAT IS SPC
SPC - Statistical Process Control is a
process that was designed to describe the
changes in process variation from a standard
It can be used for both attribute and variable
data
3
WHAT IS SPC
Statistical - The collection of data and the arrangement of those data in clear pattern to allow predictions to be made on performance
Process ndash A process is considered as an any activity involving combination of people equipment and materials working together to produce an output
Control ndash Comparing actual performance against a target and identifiying when and what corrective action is necessary to achieve the target
4
STATISTICAL PROCESS CONTROL
In statistics when we look at groups of numbers they are centered in three different ways Mode Median Mean
Mode Mode is the number that occurs the most frequently in a group of numbers
7 9 11 6 13 6 6 311 Put them in order 3 6 6 6 7 9 11 11 13
The mode is 6
5
Median Median is like the geographical center it would be the middle number
7 9 11 6 13 6 6 311 Put them in order 3 6 6 6 7 9 11 11 13 7 is the median
Mean Mean is the average of all the numbers The mean is derived by adding all the numbers and then dividing by the quantity of numbers
X1 + X2 + X3 + X4 + X5 + X6 + X7 +hellip+Xn
n
STATISTICAL PROCESS CONTROL
6
1 2 3 6 8
VARIATION
No two products or characteristics are exactly alike because any process contains many sources of variability
The differences among products may be large or may be immeasurably small but they are present
For instance the diameter of a machined shaft would be susceptible to potential variation from
Machine - Clerancesbearing wear
Tool - Strength rate of wear
Material - Hardness strength
Operator - Part feed accuracy of centering
Maintenance - Lubrication replacement of worn out parts
Environment - Temperature consistency of power supply
The numbers that were not exactly on the mean are considered ldquovariationrdquo
7
TYPES OF VARIATION
There are two types of variation
Common cause variation
Special cause variation
8
COMMON CAUSES
Common cause variation is that normal variation that exists in a process when it is running exactly as it should
Eg In the production of that Shaft variation even
When the operator is running the machine properly
When the machine is running properly
When the material is correct
When the method is correct
When the environment is correct
When the original measurements are correct
9
As we have just reviewed common cause variation cannot be defined by one particular characteristic
It is the inherent variation of all the parts of the operation together
Eg
Voltage fluctuation
Looseness or tightness of machine bearings
Common cause variation must be optimized and run at a reasonable cost
If only common causes of variation are present the output of a process is predictable
COMMON CAUSES
10
SPECIAL CAUSES
Special cause is when one or more of the process specificationsconditions change
Temperatures
Tools dull
Voltage drops drastically
Material change
Bearings are failing
Special cause variations are the variations that need to be corrected immediately since it affect the process output in unpredictable ways
11
WHY DO WE NEED DATA
Assessment
Assessing the effectiveness of specific process or corrective actions
Evaluation
Determine the quality of a process or product
Improvement
Help us understand where improvement is needed
Control
To help control a process and to ensure it does not move out of control
Prediction
Provide information and trends that enables us to predict when an activity will fail in the future
12
TYPES OF DATA
Data can be grouped into two major categories
Attributes data
Variable data
13
TYPES OF DATA ndash ATTRIBUTE DATA
Attributes data Non-measurable characteristics Can be very subjective
Blush Scratched Color etc
Observations are counted YesNo PresentAbsent MeetsDoesnrsquot meet
Visually inspected Gono-go gauges
If color happens to be an attribute that is being inspected for Typically meet the expected color sample is given Maybe a light and dark compared to sample given The acceptable range is in between A reject is not measured just counted as one
14
Collected through measurement
Is very objective
Can be temperature length width weight force volts amps etc
Uses a measuring tool
Scale
Meters
Inspection should not be done to sort but for data collection and correction of the process
This will allow for quick response and rapid correction minimizing defect quantities
TYPES OF DATA ndash VARIABLE DATA
15
PARETO CHARTS
Vilfredo Pareto
Italyrsquos wealth
80 held by 20 of people
Used when analyzing attributes
Based on results of tally numbers in specific categories
What is a Pareto Chart used for
To display the relative importance of data
To direct efforts to the biggest improvement opportunity by highlighting the vital few in contrast to the useful many
16
CONSTRUCTING A PARETO CHART
Determine the categories and the units for comparison of the data such as frequency cost or time
Total the raw data in each category then determine the grand total by adding the totals of each category
Re-order the categories from largest to smallest
Determine the cumulative percent of each category (ie the sum of each category plus all categories that precede it in the rank order divided by the grand total and multiplied by 100)
17
CONSTRUCTING A PARETO CHART
Draw and label the left-hand vertical axis with the unit of comparison such as frequency cost or time
Draw and label the horizontal axis with the categories List from left to right in rank order
Draw and label the right-hand vertical axis from 0 to 100 percent The 100 percent should line up with the grand total on the left-hand vertical axis
Beginning with the largest category draw in bars for each category representing the total for that category
18
CONSTRUCTING A PARETO CHART
Draw a line graph beginning at the right-hand
corner of the first bar to represent the
cumulative percent for each category as
measured on the right-hand axis
Analyze the chart Usually the top 20 of the
categories will comprise roughly 80 of the
cumulative total
19
PARETO CHART - EXAMPLE
Lets assume we are listing all the rejected products that are removed from a candy manufacturing line in one week
First we put the rejects in specific categories
No wrapper - 10
No center - 37
Wrong shape - 53
Short shot - 6
Wrapper open - 132
Underweight - 4
Overweight ndash 17
Get the total rejects - 259
20
Develop a percentage for each category
No wrapper ndash 10259 = 39
No center ndash 37259 = 143
Wrong shape ndash 53259 = 205
Short shot ndash 6259 = 23
Wrapper open ndash 132259 = 51
Underweight ndash 4259 = 15
Overweight ndash 17259 = 66
PARETO CHART - EXAMPLE
21
Now place the counts in a histogram largest to smallest
0
10
20
30
40
50
60
Wrapper
Open
No Center No Wrapper Underweight
70
80
90
100
51
205
143
66 39
23 15
22
Finally add up each and plot as a line diagram
0
10
20
30
40
50
60
Wrapper
Open
No Center No Wrapper Underweight
70
80
90
100
715
51
205
143
858
66
924
39
963
23
986
15
1001
23
0
10
20
30
40
50
60
Wrapper
Open
No Center No Wrapper Underweight
70
80
90
100
715
51
205
143
858
66
924
39
963
23
986
15
1001
24
CONTROL CHARTS
Control charts are one of the most commonly used methods of Statistical Process Control (SPC) which
monitors the stability of a process
The main features of a control chart include the data points a centreline (mean value) and upper and
lower limits (bounds to indicate where a process output is considered out of control)They visually
display the fluctuations of a particular process variable that easily determine whether these variations
fall within the specified process limits
Control charts
a graphical method for detecting if the underlying distribution of variation of some measurable
characteristic of the product seems to have undergone a shift
monitor a process in real time
Map the output of a production process over time
A control chart always has a central line for the average an upper line for the upper control limit and a
lower line for the lower control limit These lines are determined from historical data
By comparing current data to these lines you can draw conclusions about whether the process
variation is consistent (in control) or is unpredictable
25
CONTROL CHART - PURPOSE
The main purpose of using a control chart is to monitor control and improve
process performance over time by studying variation and its source There are
several functions of a control chart
It centres attention on detecting and monitoring process variation over time
It provides a tool for on-going control of a process
It differentiates special from common causes of variation in order to be a guide for
local or management action
It helps improve a process to perform consistently and predictably to achieve higher
quality lower cost and higher effective capacity
It serves as a common language for discussing process performance
26
TYPES OF CONTROL CHARTS
The basic tool used in SPC is the control chart
There are various types of control charts
Variable Control Chart
Averages and range chart (X-Bar and R Bar Chart)
X bar and s chart
Moving Range Chart
Moving AveragendashMoving Range chart (also called MAndashMR chart)
p chart (also called proportion chart)
c chart (also called count chart)
np chart
u chart
27
POPULARITY OF CONTROL CHARTS
Control charts are a proven technique for improving productivity
Control charts are effective in defect prevention
Control charts prevent unnecessary process
adjustment
Control charts provide diagnostic information
Control charts provide information about process
capability
28
PROCEDURE FOR X ndashBAR AND R BAR CHART
1 Randomly sample ldquonrdquo units throughout the day (can be every 5
minutes every 30 minutes etc - whatever is appropriate for your
case)
2 For each sample calculate ldquoX-BARrdquo to estimate the mean and ldquoR
(range)rdquo to estimate variability NOTE THE RANGE CAN BE USED TO
ESTIMATE THE STANDARD DEVIATION
3 After collecting the 20-25 samples calculate X-BAR-BAR (the
average of all the X-BARs) and R-BAR (the average of all the ranges)
4 Using X-BAR-BAR and R-BAR calculate the control limits for your X-
BAR and R Control Charts
29
X-BAR CONTROL LIMITS
Upper Control Limit (UCL) = (X-BAR-BAR) + A2 (R-BAR)
Lower Control Limit(LCL) = (X-BAR-BAR) - A2 (R-BAR)
R CONTROL LIMITS
Upper Control Limit - D3 (R-BAR)
Lower Control Limit - D4 (R-BAR)
PROCEDURE FOR X ndashBAR AND R BAR CHART
30
CONTROL CHART CONSTANTS
sample size constant constant constant constant constant constant constant
n d2 A2 A3 B3 B4 D3 D4
2 1128 188 2659 0 3267 0 3267
3 1693 1023 1954 0 2568 0 2574
4 2059 0729 1628 0 2266 0 2282
5 2326 0577 1427 0 2089 0 2114
6 2534 0483 1287 003 197 0 2004
7 2704 0419 1182 0118 1882 0076 1924
8 2847 0373 1099 0185 1815 0136 1864
9 297 0337 1032 0239 1761 0184 1816
10 3078 0308 0975 0284 1716 0223 1777
31
5 For the R Control Chart plot all R values on the R Control Chart
to see if all the Ranges are ldquobetween the control limitsrdquo If they are
then your process is considered to be in a state of statistical control
(as far as the variability of the process is concerned)
6 For the X-BAR Control Chart plot all the X-BARs on the X-BAR
control chart to see if all the X-BARs are ldquobetween the control
limitsrdquo If they are then your process is considered in a state of
statistical control (as far as the average of the process is
concerned)
PROCEDURE FOR X ndashBAR AND R BAR CHART
32
SAMPLE DATA FOR X BAR ndashR CHART
Sub Group 1 2 3 4 5 X -Bar Range reg
1 1195 1191 1211 1203 1198 1200 02
2 1201 1198 1198 1197 12 1199 004
3 1193 1206 1198 1196 1202 1199 013
4 1205 1198 1205 1206 1198 1202 008
5 1198 1203 1206 1201 1199 1201 008
6 1202 1205 1196 1201 1195 1200 01
7 1199 1206 1201 1204 1201 1202 007
8 1201 1197 1198 1204 1198 1200 007
9 1198 1204 1198 1204 1204 1202 006
10 1205 1195 1198 1204 1196 1200 01
` X Bar-Bar 1200 009
X Bar Chart
UCL = X BAR-BAR + A2 R Bar
1200 +(0577009) 1205
LCL= X BAR-BAR - A2 R Bar
1200 - (0577009) 1195
R Chart
UCL = D4R Bar 211 009 021
LCL = D3 R Bar 0009 0
33
PLOT DATA ON CONTROL CHARTS
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1 2 3 4 5 6 7 8 9 10
Ave
rage
(X
ba
r)
X Bar Chart
UCL
LCL
X Bar
34
PLOT DATA ON CONTROL CHARTS
001
003
005
007
009
011
013
015
017
019
021
023
025
1 2 3 4 5 6 7 8 9 10
R Chart
UCL
LCL
35
PROCEDURE TO DETERMINE IF PROCESS IS IN A STATE OF
STATISTICAL CONTROL
7 If process is determined to be ldquoNOT STABLErdquo then stop and find out what
an assignable cause might be fix and then repeat the complete process of
collecting new data
8 If the process is determined to be ldquoSTABLErdquo then you may use the
control charts you developed to monitor future production to ensure that the
process REMAINS stable
More Samples for Control charts
36
READING OF CONTROL CHART
Control charts can determine whether a process is behaving in an unusual way The quality of the individual points of a subset is determined unstable if any of the
following occurs
Rule 1 Any point falls beyond 3σ from the centreline(this is represented by the upper and
lower control limits)
Rule 2 Two out of three consecutive points fall beyond 2σ on the same side of the
centreline
Rule 3 Four out of five consecutive points fall beyond 1σ on the same side of the
centreline
Rule 4 Nine or more consecutive points fall on the same side of the centreline
(Ref Next page for sample)
37
READING THE CONTROL CHART
38
CONTROL CHARTS FOR ATTRIBUTES ndashP-CHARTS amp C-CHARTS
Attributes are discrete events yesno or passfail
Use P-Charts for quality characteristics that are discrete and involve yesno or goodbad decisions
Eg
Number of leaking caulking tubes in a box of 48
Number of broken eggs in a carton
Use C-Charts for discrete defects when there can be more than one defect per unit
Eg
Number of stains in a carpet sample cut from a production run
Number of complaints per customer at a hotel
39
P-CHART EXAMPLE A PRODUCTION MANAGER FOR A TIRE COMPANY HAS INSPECTED THE NUMBER OF
DEFECTIVE TIRES IN FIVE RANDOM SAMPLES WITH 20 TIRES IN EACH SAMPLE THE TABLE BELOW SHOWS THE
NUMBER OF DEFECTIVE TIRES IN EACH SAMPLE OF 20 TIRES CALCULATE THE CONTROL LIMITS
Sample Number of
Defective Tires
Number of Tires in each
Sample
Proportion Defective
1 3 20 15
2 2 20 10
3 1 20 05
4 2 20 10
5 2 20 05
Total 9 100 09
01023(064)09σzpLCL
2823(064)09σzpUCL
06420
(09)(91)
n
)p(1pσ
09100
9
Inspected Total
DefectivespCL
p
p
p
Solution
40
P- CONTROL CHART
41
C-CHART EXAMPLE THE NUMBER OF WEEKLY CUSTOMER COMPLAINTS ARE MONITORED IN A LARGE HOTEL USING A C-CHART DEVELOP THREE SIGMA CONTROL LIMITS USING THE DATA TABLE BELOW
Week Number of Complaints
1 3
2 2
3 3
4 1
5 3
6 3
7 2
8 1
9 3
10 1
Total 22
022522322ccLCL
66522322ccUCL
2210
22
samples of
complaintsc
c
c
z
z
Solution
42
C- CONTROL CHART
43
The ability of a process to meet product designtechnical specifications
Assessing capability involves evaluating process variability relative to preset product or service specifications
Process Capability ndash Cp and Cpk
Cp assumes that the process is centered in the specification range
Cpk helps to address a possible lack of centering of the process
PROCESS CAPABILITY
6σ
LSLUSL
width process
width ionspecificatCp
3σ
LSLμ
3σ
μUSLminCpk
44
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
45
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
46
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
47
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
--and an individual part is measured at 520rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
48
GRAPHING THE TOLERANCE AND MEASUREMENTS
Suppose we made and measured several more
units and they were all EXACTLY the same
We wouldnrsquot have very many part problems
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
X
X
X
49
GRAPHING THE TOLERANCE AND MEASUREMENTS
In the real world units are NOT EXACTLY the same
Everything VARIES
The question isnrsquot IF units vary
Itrsquos how much when and why
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
XX
XXX
XXXXX
XXXXXXX
50
The ldquonormal bell curverdquo
Widths heights depths thicknesses weights speeds strengths
and many other types of measurements when charted as a
histogram often form the shape of a bell
A ldquoperfect bellrdquo like a ldquoperfect circlerdquo doesnrsquot occur in nature but
many processes are close enough to make the bell curve useful
(A number of common industrial measurements such as flatness and straightness do NOT tend to distribute in a bell shape their proper statistical analysis is performed using models other than the bell curve)
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
51
What is a ldquostandard deviationrdquo
If we measure the DISTANCE from the CENTER of the bell
to each individual measurement that makes up the bell curve
we can find a TYPICAL DISTANCE
The most commonly used statistic to estimate this distance is the
Standard Deviation (also called ldquoSigmardquo)
Because of the natural shape of the bell curve the area of +1 to ndash1
standard deviations includes about 68 of the curve
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
Typical distance
from the center +1
standard deviation
Typical distance
from the center -1
standard deviation
52
How much of the curve is included in how many standard
deviations
From ndash1 to +1 is about 68 of the bell curve
From ndash2 to +2 is about 95
From ndash3 to +3 is about 9973
From ndash4 to +4 is about 9999
(NOTE We usually show the bell from ndash3 to +3 to make it easier to draw but in concept the ldquotailsrdquo of the bell get very thin and go on forever)
-6 -5 -4 -3 -2 -1 +1 +2 +3 +4 +5 +6 0
53
A
B
What is Cpk It is a measure of how well a process is within a specification
Cpk = A divided by B
A = Distance from process mean to closest spec limit
B = 3 Standard Deviations (also called ldquo3 Sigmardquo)
A bigger Cpk is better because fewer units will be beyond spec
(A bigger ldquoArdquo and a smaller ldquoBrdquo are better)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
54
A
B
ldquoProcess Capabilityrdquo is the ability of a process
to fit its output within the tolerances
hellipa LARGER ldquoArdquo
hellipand a SMALLER ldquoBrdquo
hellipmeans BETTER ldquoProcess Capabilityrdquo
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
55
A
B
An Analogy
Analogy
The bell curve is your automobile
The spec limits are the edges of your garage door
If A = B you are hitting the frame of your garage door with your car
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
56
A
B
How can we make Cpk (A divided by B) better
1 Design the product so a wider tolerance is functional (ldquorobust designrdquo)
2 Choose equipment and methods for a good safety margin (ldquoprocess capabilityrdquo)
3 Correctly adjust but only when needed (ldquocontrolrdquo)
4 Discover ways to narrow the natural variation (ldquoimprovementrdquo)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
57
A
B
What does a very good Cpk do for us
This process is producing good units with a good safety margin
Note that when Cpk = 2 our process mean is 6 standard deviations from
the nearest spec so we say it has ldquo6 Sigma Capabilityrdquo
Specification
Limit
Specification
Limit
This Cpk is
about 2
Very good
Mean
58
A
B
What does a problem Cpk look like
This process is in danger of producing some defects
It is too close to the specification limits
(Remember the bell curve tail goes further than Bhellip hellipwe only show the bell to 3-sigma to make it easier to draw)
Specification
Limit
Specification
Limit
This Cpk is just
slightly greater
than 1 Not good
59
A
B
What does a very bad Cpk look like
A significant part of the ldquotailrdquo is hanging out beyond the spec limits
This process is producing scrap rework and customer rejects
Notice that if distance ldquoArdquo approaches zerohellip
hellipthe Cpk would approach zero andhellip
hellipthe process would become 50 defective
Specification
Limit
Specification
Limit
This Cpk is less
than 1 We desire
a minimum of 133
and ultimately we
want 2 or more
60
-
Q amp A
61
MEASUREMENT SYSTEM ANALYSIS (MSA)
An MSA is a statistical tool used to determine if a measurement system is capable of precise measurement
What is It
Objective or Purpose
bull To determine how much error is in the measurement due to the measurement process itself
bull Quantifies the variability added by the measurement system
bull Applicable to attribute data and variable data
When to Use It
bull On the critical inputs and outputs prior to collecting data for analysis
bull For any new or modified process in order to ensure the quality of the data
Measurement System Analysis is an analysis of the measurement process not an analysis of the people
IMPORTANT
Who Should be Involved
Everyone that measures and makes decisions about these measurements should be involved in the MSA
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The observed variation in process output measurements is not simply the variation in the process itself it is the variation in the process plus the variation in measurement that results from an inadequate measurement system
Conducting an MSA reduces the likelihood of passing a bad part or rejecting a good part
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The output of the process measured by bull Cycle time bull Dimensional data bull Number of defects and others
Observed Variation
Process Variation
Measurement System
Variation
Reproducibility
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Accuracy (Central Location)
OBSERVED VARIATION
Calibration addresses accuracy
Measurement System Analysis (MSA)
MEASUREMENT SYSTEM ERRORS
Accuracy difference between the observed measurement and the actual measurement
Precision variation that occurs when measuring the same part with the same instrument
MEASUREMENT SYSTEM ERROR
Precise but not
accurate
Accurate but not
precise
Not accurate or
precise
Accurate and
precise
ACCURACY OF MEASUREMENT
Broken down into three components
aStability
The consistency of measurements over time
bBias
A measure of the amount of partiality in the system
cLinearity
A measure of the bias values through the expected
range of measurements
OBSERVED VARIATION
Observed Variation
Process Variation
Measurement System
Variation
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Reproducibility
Accuracy (Central Location)
Calibration Addresses Accuracy
Letrsquos take a closer look at Precision
Measurement System Analysis (MSA)
Measurement System Analysis (MSA)
Error in Resolution The inability to detect small changes
Possible Cause
Wrong measurement device selected - divisions on scale not fine enough to detect changes
Resolution
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Repeatability The inability to get the same answer from repeated measurements made of the same item under absolutely identical conditions
Possible Cause
Lack of standard operating procedures (SOP) lack of training measuring system variablilty
Repeatability
Equipment Variation
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Reproducibility The inability to get the same answer from repeated measurements made under various conditions from different inspectors
Possible Cause
Lack of SOP lack of training
Reproducibility
Appraiser Variation
VARIABLE MSA ndash GAGE RampR STUDY
bull Gage RampR is the combined estimate of
measurement system Repeatability and
Reproducibility
bull Typically a 3-person study is performed Each person randomly measures 10 marked parts per trial
Each person can perform up to 3 trials
bull There are 3 key indicators EV or Equipment Variation
AV or Appraiser Variation
Overall GRR
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
WHAT IS SPC
Statistical - The collection of data and the arrangement of those data in clear pattern to allow predictions to be made on performance
Process ndash A process is considered as an any activity involving combination of people equipment and materials working together to produce an output
Control ndash Comparing actual performance against a target and identifiying when and what corrective action is necessary to achieve the target
4
STATISTICAL PROCESS CONTROL
In statistics when we look at groups of numbers they are centered in three different ways Mode Median Mean
Mode Mode is the number that occurs the most frequently in a group of numbers
7 9 11 6 13 6 6 311 Put them in order 3 6 6 6 7 9 11 11 13
The mode is 6
5
Median Median is like the geographical center it would be the middle number
7 9 11 6 13 6 6 311 Put them in order 3 6 6 6 7 9 11 11 13 7 is the median
Mean Mean is the average of all the numbers The mean is derived by adding all the numbers and then dividing by the quantity of numbers
X1 + X2 + X3 + X4 + X5 + X6 + X7 +hellip+Xn
n
STATISTICAL PROCESS CONTROL
6
1 2 3 6 8
VARIATION
No two products or characteristics are exactly alike because any process contains many sources of variability
The differences among products may be large or may be immeasurably small but they are present
For instance the diameter of a machined shaft would be susceptible to potential variation from
Machine - Clerancesbearing wear
Tool - Strength rate of wear
Material - Hardness strength
Operator - Part feed accuracy of centering
Maintenance - Lubrication replacement of worn out parts
Environment - Temperature consistency of power supply
The numbers that were not exactly on the mean are considered ldquovariationrdquo
7
TYPES OF VARIATION
There are two types of variation
Common cause variation
Special cause variation
8
COMMON CAUSES
Common cause variation is that normal variation that exists in a process when it is running exactly as it should
Eg In the production of that Shaft variation even
When the operator is running the machine properly
When the machine is running properly
When the material is correct
When the method is correct
When the environment is correct
When the original measurements are correct
9
As we have just reviewed common cause variation cannot be defined by one particular characteristic
It is the inherent variation of all the parts of the operation together
Eg
Voltage fluctuation
Looseness or tightness of machine bearings
Common cause variation must be optimized and run at a reasonable cost
If only common causes of variation are present the output of a process is predictable
COMMON CAUSES
10
SPECIAL CAUSES
Special cause is when one or more of the process specificationsconditions change
Temperatures
Tools dull
Voltage drops drastically
Material change
Bearings are failing
Special cause variations are the variations that need to be corrected immediately since it affect the process output in unpredictable ways
11
WHY DO WE NEED DATA
Assessment
Assessing the effectiveness of specific process or corrective actions
Evaluation
Determine the quality of a process or product
Improvement
Help us understand where improvement is needed
Control
To help control a process and to ensure it does not move out of control
Prediction
Provide information and trends that enables us to predict when an activity will fail in the future
12
TYPES OF DATA
Data can be grouped into two major categories
Attributes data
Variable data
13
TYPES OF DATA ndash ATTRIBUTE DATA
Attributes data Non-measurable characteristics Can be very subjective
Blush Scratched Color etc
Observations are counted YesNo PresentAbsent MeetsDoesnrsquot meet
Visually inspected Gono-go gauges
If color happens to be an attribute that is being inspected for Typically meet the expected color sample is given Maybe a light and dark compared to sample given The acceptable range is in between A reject is not measured just counted as one
14
Collected through measurement
Is very objective
Can be temperature length width weight force volts amps etc
Uses a measuring tool
Scale
Meters
Inspection should not be done to sort but for data collection and correction of the process
This will allow for quick response and rapid correction minimizing defect quantities
TYPES OF DATA ndash VARIABLE DATA
15
PARETO CHARTS
Vilfredo Pareto
Italyrsquos wealth
80 held by 20 of people
Used when analyzing attributes
Based on results of tally numbers in specific categories
What is a Pareto Chart used for
To display the relative importance of data
To direct efforts to the biggest improvement opportunity by highlighting the vital few in contrast to the useful many
16
CONSTRUCTING A PARETO CHART
Determine the categories and the units for comparison of the data such as frequency cost or time
Total the raw data in each category then determine the grand total by adding the totals of each category
Re-order the categories from largest to smallest
Determine the cumulative percent of each category (ie the sum of each category plus all categories that precede it in the rank order divided by the grand total and multiplied by 100)
17
CONSTRUCTING A PARETO CHART
Draw and label the left-hand vertical axis with the unit of comparison such as frequency cost or time
Draw and label the horizontal axis with the categories List from left to right in rank order
Draw and label the right-hand vertical axis from 0 to 100 percent The 100 percent should line up with the grand total on the left-hand vertical axis
Beginning with the largest category draw in bars for each category representing the total for that category
18
CONSTRUCTING A PARETO CHART
Draw a line graph beginning at the right-hand
corner of the first bar to represent the
cumulative percent for each category as
measured on the right-hand axis
Analyze the chart Usually the top 20 of the
categories will comprise roughly 80 of the
cumulative total
19
PARETO CHART - EXAMPLE
Lets assume we are listing all the rejected products that are removed from a candy manufacturing line in one week
First we put the rejects in specific categories
No wrapper - 10
No center - 37
Wrong shape - 53
Short shot - 6
Wrapper open - 132
Underweight - 4
Overweight ndash 17
Get the total rejects - 259
20
Develop a percentage for each category
No wrapper ndash 10259 = 39
No center ndash 37259 = 143
Wrong shape ndash 53259 = 205
Short shot ndash 6259 = 23
Wrapper open ndash 132259 = 51
Underweight ndash 4259 = 15
Overweight ndash 17259 = 66
PARETO CHART - EXAMPLE
21
Now place the counts in a histogram largest to smallest
0
10
20
30
40
50
60
Wrapper
Open
No Center No Wrapper Underweight
70
80
90
100
51
205
143
66 39
23 15
22
Finally add up each and plot as a line diagram
0
10
20
30
40
50
60
Wrapper
Open
No Center No Wrapper Underweight
70
80
90
100
715
51
205
143
858
66
924
39
963
23
986
15
1001
23
0
10
20
30
40
50
60
Wrapper
Open
No Center No Wrapper Underweight
70
80
90
100
715
51
205
143
858
66
924
39
963
23
986
15
1001
24
CONTROL CHARTS
Control charts are one of the most commonly used methods of Statistical Process Control (SPC) which
monitors the stability of a process
The main features of a control chart include the data points a centreline (mean value) and upper and
lower limits (bounds to indicate where a process output is considered out of control)They visually
display the fluctuations of a particular process variable that easily determine whether these variations
fall within the specified process limits
Control charts
a graphical method for detecting if the underlying distribution of variation of some measurable
characteristic of the product seems to have undergone a shift
monitor a process in real time
Map the output of a production process over time
A control chart always has a central line for the average an upper line for the upper control limit and a
lower line for the lower control limit These lines are determined from historical data
By comparing current data to these lines you can draw conclusions about whether the process
variation is consistent (in control) or is unpredictable
25
CONTROL CHART - PURPOSE
The main purpose of using a control chart is to monitor control and improve
process performance over time by studying variation and its source There are
several functions of a control chart
It centres attention on detecting and monitoring process variation over time
It provides a tool for on-going control of a process
It differentiates special from common causes of variation in order to be a guide for
local or management action
It helps improve a process to perform consistently and predictably to achieve higher
quality lower cost and higher effective capacity
It serves as a common language for discussing process performance
26
TYPES OF CONTROL CHARTS
The basic tool used in SPC is the control chart
There are various types of control charts
Variable Control Chart
Averages and range chart (X-Bar and R Bar Chart)
X bar and s chart
Moving Range Chart
Moving AveragendashMoving Range chart (also called MAndashMR chart)
p chart (also called proportion chart)
c chart (also called count chart)
np chart
u chart
27
POPULARITY OF CONTROL CHARTS
Control charts are a proven technique for improving productivity
Control charts are effective in defect prevention
Control charts prevent unnecessary process
adjustment
Control charts provide diagnostic information
Control charts provide information about process
capability
28
PROCEDURE FOR X ndashBAR AND R BAR CHART
1 Randomly sample ldquonrdquo units throughout the day (can be every 5
minutes every 30 minutes etc - whatever is appropriate for your
case)
2 For each sample calculate ldquoX-BARrdquo to estimate the mean and ldquoR
(range)rdquo to estimate variability NOTE THE RANGE CAN BE USED TO
ESTIMATE THE STANDARD DEVIATION
3 After collecting the 20-25 samples calculate X-BAR-BAR (the
average of all the X-BARs) and R-BAR (the average of all the ranges)
4 Using X-BAR-BAR and R-BAR calculate the control limits for your X-
BAR and R Control Charts
29
X-BAR CONTROL LIMITS
Upper Control Limit (UCL) = (X-BAR-BAR) + A2 (R-BAR)
Lower Control Limit(LCL) = (X-BAR-BAR) - A2 (R-BAR)
R CONTROL LIMITS
Upper Control Limit - D3 (R-BAR)
Lower Control Limit - D4 (R-BAR)
PROCEDURE FOR X ndashBAR AND R BAR CHART
30
CONTROL CHART CONSTANTS
sample size constant constant constant constant constant constant constant
n d2 A2 A3 B3 B4 D3 D4
2 1128 188 2659 0 3267 0 3267
3 1693 1023 1954 0 2568 0 2574
4 2059 0729 1628 0 2266 0 2282
5 2326 0577 1427 0 2089 0 2114
6 2534 0483 1287 003 197 0 2004
7 2704 0419 1182 0118 1882 0076 1924
8 2847 0373 1099 0185 1815 0136 1864
9 297 0337 1032 0239 1761 0184 1816
10 3078 0308 0975 0284 1716 0223 1777
31
5 For the R Control Chart plot all R values on the R Control Chart
to see if all the Ranges are ldquobetween the control limitsrdquo If they are
then your process is considered to be in a state of statistical control
(as far as the variability of the process is concerned)
6 For the X-BAR Control Chart plot all the X-BARs on the X-BAR
control chart to see if all the X-BARs are ldquobetween the control
limitsrdquo If they are then your process is considered in a state of
statistical control (as far as the average of the process is
concerned)
PROCEDURE FOR X ndashBAR AND R BAR CHART
32
SAMPLE DATA FOR X BAR ndashR CHART
Sub Group 1 2 3 4 5 X -Bar Range reg
1 1195 1191 1211 1203 1198 1200 02
2 1201 1198 1198 1197 12 1199 004
3 1193 1206 1198 1196 1202 1199 013
4 1205 1198 1205 1206 1198 1202 008
5 1198 1203 1206 1201 1199 1201 008
6 1202 1205 1196 1201 1195 1200 01
7 1199 1206 1201 1204 1201 1202 007
8 1201 1197 1198 1204 1198 1200 007
9 1198 1204 1198 1204 1204 1202 006
10 1205 1195 1198 1204 1196 1200 01
` X Bar-Bar 1200 009
X Bar Chart
UCL = X BAR-BAR + A2 R Bar
1200 +(0577009) 1205
LCL= X BAR-BAR - A2 R Bar
1200 - (0577009) 1195
R Chart
UCL = D4R Bar 211 009 021
LCL = D3 R Bar 0009 0
33
PLOT DATA ON CONTROL CHARTS
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1 2 3 4 5 6 7 8 9 10
Ave
rage
(X
ba
r)
X Bar Chart
UCL
LCL
X Bar
34
PLOT DATA ON CONTROL CHARTS
001
003
005
007
009
011
013
015
017
019
021
023
025
1 2 3 4 5 6 7 8 9 10
R Chart
UCL
LCL
35
PROCEDURE TO DETERMINE IF PROCESS IS IN A STATE OF
STATISTICAL CONTROL
7 If process is determined to be ldquoNOT STABLErdquo then stop and find out what
an assignable cause might be fix and then repeat the complete process of
collecting new data
8 If the process is determined to be ldquoSTABLErdquo then you may use the
control charts you developed to monitor future production to ensure that the
process REMAINS stable
More Samples for Control charts
36
READING OF CONTROL CHART
Control charts can determine whether a process is behaving in an unusual way The quality of the individual points of a subset is determined unstable if any of the
following occurs
Rule 1 Any point falls beyond 3σ from the centreline(this is represented by the upper and
lower control limits)
Rule 2 Two out of three consecutive points fall beyond 2σ on the same side of the
centreline
Rule 3 Four out of five consecutive points fall beyond 1σ on the same side of the
centreline
Rule 4 Nine or more consecutive points fall on the same side of the centreline
(Ref Next page for sample)
37
READING THE CONTROL CHART
38
CONTROL CHARTS FOR ATTRIBUTES ndashP-CHARTS amp C-CHARTS
Attributes are discrete events yesno or passfail
Use P-Charts for quality characteristics that are discrete and involve yesno or goodbad decisions
Eg
Number of leaking caulking tubes in a box of 48
Number of broken eggs in a carton
Use C-Charts for discrete defects when there can be more than one defect per unit
Eg
Number of stains in a carpet sample cut from a production run
Number of complaints per customer at a hotel
39
P-CHART EXAMPLE A PRODUCTION MANAGER FOR A TIRE COMPANY HAS INSPECTED THE NUMBER OF
DEFECTIVE TIRES IN FIVE RANDOM SAMPLES WITH 20 TIRES IN EACH SAMPLE THE TABLE BELOW SHOWS THE
NUMBER OF DEFECTIVE TIRES IN EACH SAMPLE OF 20 TIRES CALCULATE THE CONTROL LIMITS
Sample Number of
Defective Tires
Number of Tires in each
Sample
Proportion Defective
1 3 20 15
2 2 20 10
3 1 20 05
4 2 20 10
5 2 20 05
Total 9 100 09
01023(064)09σzpLCL
2823(064)09σzpUCL
06420
(09)(91)
n
)p(1pσ
09100
9
Inspected Total
DefectivespCL
p
p
p
Solution
40
P- CONTROL CHART
41
C-CHART EXAMPLE THE NUMBER OF WEEKLY CUSTOMER COMPLAINTS ARE MONITORED IN A LARGE HOTEL USING A C-CHART DEVELOP THREE SIGMA CONTROL LIMITS USING THE DATA TABLE BELOW
Week Number of Complaints
1 3
2 2
3 3
4 1
5 3
6 3
7 2
8 1
9 3
10 1
Total 22
022522322ccLCL
66522322ccUCL
2210
22
samples of
complaintsc
c
c
z
z
Solution
42
C- CONTROL CHART
43
The ability of a process to meet product designtechnical specifications
Assessing capability involves evaluating process variability relative to preset product or service specifications
Process Capability ndash Cp and Cpk
Cp assumes that the process is centered in the specification range
Cpk helps to address a possible lack of centering of the process
PROCESS CAPABILITY
6σ
LSLUSL
width process
width ionspecificatCp
3σ
LSLμ
3σ
μUSLminCpk
44
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
45
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
46
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
47
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
--and an individual part is measured at 520rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
48
GRAPHING THE TOLERANCE AND MEASUREMENTS
Suppose we made and measured several more
units and they were all EXACTLY the same
We wouldnrsquot have very many part problems
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
X
X
X
49
GRAPHING THE TOLERANCE AND MEASUREMENTS
In the real world units are NOT EXACTLY the same
Everything VARIES
The question isnrsquot IF units vary
Itrsquos how much when and why
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
XX
XXX
XXXXX
XXXXXXX
50
The ldquonormal bell curverdquo
Widths heights depths thicknesses weights speeds strengths
and many other types of measurements when charted as a
histogram often form the shape of a bell
A ldquoperfect bellrdquo like a ldquoperfect circlerdquo doesnrsquot occur in nature but
many processes are close enough to make the bell curve useful
(A number of common industrial measurements such as flatness and straightness do NOT tend to distribute in a bell shape their proper statistical analysis is performed using models other than the bell curve)
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
51
What is a ldquostandard deviationrdquo
If we measure the DISTANCE from the CENTER of the bell
to each individual measurement that makes up the bell curve
we can find a TYPICAL DISTANCE
The most commonly used statistic to estimate this distance is the
Standard Deviation (also called ldquoSigmardquo)
Because of the natural shape of the bell curve the area of +1 to ndash1
standard deviations includes about 68 of the curve
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
Typical distance
from the center +1
standard deviation
Typical distance
from the center -1
standard deviation
52
How much of the curve is included in how many standard
deviations
From ndash1 to +1 is about 68 of the bell curve
From ndash2 to +2 is about 95
From ndash3 to +3 is about 9973
From ndash4 to +4 is about 9999
(NOTE We usually show the bell from ndash3 to +3 to make it easier to draw but in concept the ldquotailsrdquo of the bell get very thin and go on forever)
-6 -5 -4 -3 -2 -1 +1 +2 +3 +4 +5 +6 0
53
A
B
What is Cpk It is a measure of how well a process is within a specification
Cpk = A divided by B
A = Distance from process mean to closest spec limit
B = 3 Standard Deviations (also called ldquo3 Sigmardquo)
A bigger Cpk is better because fewer units will be beyond spec
(A bigger ldquoArdquo and a smaller ldquoBrdquo are better)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
54
A
B
ldquoProcess Capabilityrdquo is the ability of a process
to fit its output within the tolerances
hellipa LARGER ldquoArdquo
hellipand a SMALLER ldquoBrdquo
hellipmeans BETTER ldquoProcess Capabilityrdquo
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
55
A
B
An Analogy
Analogy
The bell curve is your automobile
The spec limits are the edges of your garage door
If A = B you are hitting the frame of your garage door with your car
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
56
A
B
How can we make Cpk (A divided by B) better
1 Design the product so a wider tolerance is functional (ldquorobust designrdquo)
2 Choose equipment and methods for a good safety margin (ldquoprocess capabilityrdquo)
3 Correctly adjust but only when needed (ldquocontrolrdquo)
4 Discover ways to narrow the natural variation (ldquoimprovementrdquo)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
57
A
B
What does a very good Cpk do for us
This process is producing good units with a good safety margin
Note that when Cpk = 2 our process mean is 6 standard deviations from
the nearest spec so we say it has ldquo6 Sigma Capabilityrdquo
Specification
Limit
Specification
Limit
This Cpk is
about 2
Very good
Mean
58
A
B
What does a problem Cpk look like
This process is in danger of producing some defects
It is too close to the specification limits
(Remember the bell curve tail goes further than Bhellip hellipwe only show the bell to 3-sigma to make it easier to draw)
Specification
Limit
Specification
Limit
This Cpk is just
slightly greater
than 1 Not good
59
A
B
What does a very bad Cpk look like
A significant part of the ldquotailrdquo is hanging out beyond the spec limits
This process is producing scrap rework and customer rejects
Notice that if distance ldquoArdquo approaches zerohellip
hellipthe Cpk would approach zero andhellip
hellipthe process would become 50 defective
Specification
Limit
Specification
Limit
This Cpk is less
than 1 We desire
a minimum of 133
and ultimately we
want 2 or more
60
-
Q amp A
61
MEASUREMENT SYSTEM ANALYSIS (MSA)
An MSA is a statistical tool used to determine if a measurement system is capable of precise measurement
What is It
Objective or Purpose
bull To determine how much error is in the measurement due to the measurement process itself
bull Quantifies the variability added by the measurement system
bull Applicable to attribute data and variable data
When to Use It
bull On the critical inputs and outputs prior to collecting data for analysis
bull For any new or modified process in order to ensure the quality of the data
Measurement System Analysis is an analysis of the measurement process not an analysis of the people
IMPORTANT
Who Should be Involved
Everyone that measures and makes decisions about these measurements should be involved in the MSA
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The observed variation in process output measurements is not simply the variation in the process itself it is the variation in the process plus the variation in measurement that results from an inadequate measurement system
Conducting an MSA reduces the likelihood of passing a bad part or rejecting a good part
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The output of the process measured by bull Cycle time bull Dimensional data bull Number of defects and others
Observed Variation
Process Variation
Measurement System
Variation
Reproducibility
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Accuracy (Central Location)
OBSERVED VARIATION
Calibration addresses accuracy
Measurement System Analysis (MSA)
MEASUREMENT SYSTEM ERRORS
Accuracy difference between the observed measurement and the actual measurement
Precision variation that occurs when measuring the same part with the same instrument
MEASUREMENT SYSTEM ERROR
Precise but not
accurate
Accurate but not
precise
Not accurate or
precise
Accurate and
precise
ACCURACY OF MEASUREMENT
Broken down into three components
aStability
The consistency of measurements over time
bBias
A measure of the amount of partiality in the system
cLinearity
A measure of the bias values through the expected
range of measurements
OBSERVED VARIATION
Observed Variation
Process Variation
Measurement System
Variation
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Reproducibility
Accuracy (Central Location)
Calibration Addresses Accuracy
Letrsquos take a closer look at Precision
Measurement System Analysis (MSA)
Measurement System Analysis (MSA)
Error in Resolution The inability to detect small changes
Possible Cause
Wrong measurement device selected - divisions on scale not fine enough to detect changes
Resolution
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Repeatability The inability to get the same answer from repeated measurements made of the same item under absolutely identical conditions
Possible Cause
Lack of standard operating procedures (SOP) lack of training measuring system variablilty
Repeatability
Equipment Variation
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Reproducibility The inability to get the same answer from repeated measurements made under various conditions from different inspectors
Possible Cause
Lack of SOP lack of training
Reproducibility
Appraiser Variation
VARIABLE MSA ndash GAGE RampR STUDY
bull Gage RampR is the combined estimate of
measurement system Repeatability and
Reproducibility
bull Typically a 3-person study is performed Each person randomly measures 10 marked parts per trial
Each person can perform up to 3 trials
bull There are 3 key indicators EV or Equipment Variation
AV or Appraiser Variation
Overall GRR
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
STATISTICAL PROCESS CONTROL
In statistics when we look at groups of numbers they are centered in three different ways Mode Median Mean
Mode Mode is the number that occurs the most frequently in a group of numbers
7 9 11 6 13 6 6 311 Put them in order 3 6 6 6 7 9 11 11 13
The mode is 6
5
Median Median is like the geographical center it would be the middle number
7 9 11 6 13 6 6 311 Put them in order 3 6 6 6 7 9 11 11 13 7 is the median
Mean Mean is the average of all the numbers The mean is derived by adding all the numbers and then dividing by the quantity of numbers
X1 + X2 + X3 + X4 + X5 + X6 + X7 +hellip+Xn
n
STATISTICAL PROCESS CONTROL
6
1 2 3 6 8
VARIATION
No two products or characteristics are exactly alike because any process contains many sources of variability
The differences among products may be large or may be immeasurably small but they are present
For instance the diameter of a machined shaft would be susceptible to potential variation from
Machine - Clerancesbearing wear
Tool - Strength rate of wear
Material - Hardness strength
Operator - Part feed accuracy of centering
Maintenance - Lubrication replacement of worn out parts
Environment - Temperature consistency of power supply
The numbers that were not exactly on the mean are considered ldquovariationrdquo
7
TYPES OF VARIATION
There are two types of variation
Common cause variation
Special cause variation
8
COMMON CAUSES
Common cause variation is that normal variation that exists in a process when it is running exactly as it should
Eg In the production of that Shaft variation even
When the operator is running the machine properly
When the machine is running properly
When the material is correct
When the method is correct
When the environment is correct
When the original measurements are correct
9
As we have just reviewed common cause variation cannot be defined by one particular characteristic
It is the inherent variation of all the parts of the operation together
Eg
Voltage fluctuation
Looseness or tightness of machine bearings
Common cause variation must be optimized and run at a reasonable cost
If only common causes of variation are present the output of a process is predictable
COMMON CAUSES
10
SPECIAL CAUSES
Special cause is when one or more of the process specificationsconditions change
Temperatures
Tools dull
Voltage drops drastically
Material change
Bearings are failing
Special cause variations are the variations that need to be corrected immediately since it affect the process output in unpredictable ways
11
WHY DO WE NEED DATA
Assessment
Assessing the effectiveness of specific process or corrective actions
Evaluation
Determine the quality of a process or product
Improvement
Help us understand where improvement is needed
Control
To help control a process and to ensure it does not move out of control
Prediction
Provide information and trends that enables us to predict when an activity will fail in the future
12
TYPES OF DATA
Data can be grouped into two major categories
Attributes data
Variable data
13
TYPES OF DATA ndash ATTRIBUTE DATA
Attributes data Non-measurable characteristics Can be very subjective
Blush Scratched Color etc
Observations are counted YesNo PresentAbsent MeetsDoesnrsquot meet
Visually inspected Gono-go gauges
If color happens to be an attribute that is being inspected for Typically meet the expected color sample is given Maybe a light and dark compared to sample given The acceptable range is in between A reject is not measured just counted as one
14
Collected through measurement
Is very objective
Can be temperature length width weight force volts amps etc
Uses a measuring tool
Scale
Meters
Inspection should not be done to sort but for data collection and correction of the process
This will allow for quick response and rapid correction minimizing defect quantities
TYPES OF DATA ndash VARIABLE DATA
15
PARETO CHARTS
Vilfredo Pareto
Italyrsquos wealth
80 held by 20 of people
Used when analyzing attributes
Based on results of tally numbers in specific categories
What is a Pareto Chart used for
To display the relative importance of data
To direct efforts to the biggest improvement opportunity by highlighting the vital few in contrast to the useful many
16
CONSTRUCTING A PARETO CHART
Determine the categories and the units for comparison of the data such as frequency cost or time
Total the raw data in each category then determine the grand total by adding the totals of each category
Re-order the categories from largest to smallest
Determine the cumulative percent of each category (ie the sum of each category plus all categories that precede it in the rank order divided by the grand total and multiplied by 100)
17
CONSTRUCTING A PARETO CHART
Draw and label the left-hand vertical axis with the unit of comparison such as frequency cost or time
Draw and label the horizontal axis with the categories List from left to right in rank order
Draw and label the right-hand vertical axis from 0 to 100 percent The 100 percent should line up with the grand total on the left-hand vertical axis
Beginning with the largest category draw in bars for each category representing the total for that category
18
CONSTRUCTING A PARETO CHART
Draw a line graph beginning at the right-hand
corner of the first bar to represent the
cumulative percent for each category as
measured on the right-hand axis
Analyze the chart Usually the top 20 of the
categories will comprise roughly 80 of the
cumulative total
19
PARETO CHART - EXAMPLE
Lets assume we are listing all the rejected products that are removed from a candy manufacturing line in one week
First we put the rejects in specific categories
No wrapper - 10
No center - 37
Wrong shape - 53
Short shot - 6
Wrapper open - 132
Underweight - 4
Overweight ndash 17
Get the total rejects - 259
20
Develop a percentage for each category
No wrapper ndash 10259 = 39
No center ndash 37259 = 143
Wrong shape ndash 53259 = 205
Short shot ndash 6259 = 23
Wrapper open ndash 132259 = 51
Underweight ndash 4259 = 15
Overweight ndash 17259 = 66
PARETO CHART - EXAMPLE
21
Now place the counts in a histogram largest to smallest
0
10
20
30
40
50
60
Wrapper
Open
No Center No Wrapper Underweight
70
80
90
100
51
205
143
66 39
23 15
22
Finally add up each and plot as a line diagram
0
10
20
30
40
50
60
Wrapper
Open
No Center No Wrapper Underweight
70
80
90
100
715
51
205
143
858
66
924
39
963
23
986
15
1001
23
0
10
20
30
40
50
60
Wrapper
Open
No Center No Wrapper Underweight
70
80
90
100
715
51
205
143
858
66
924
39
963
23
986
15
1001
24
CONTROL CHARTS
Control charts are one of the most commonly used methods of Statistical Process Control (SPC) which
monitors the stability of a process
The main features of a control chart include the data points a centreline (mean value) and upper and
lower limits (bounds to indicate where a process output is considered out of control)They visually
display the fluctuations of a particular process variable that easily determine whether these variations
fall within the specified process limits
Control charts
a graphical method for detecting if the underlying distribution of variation of some measurable
characteristic of the product seems to have undergone a shift
monitor a process in real time
Map the output of a production process over time
A control chart always has a central line for the average an upper line for the upper control limit and a
lower line for the lower control limit These lines are determined from historical data
By comparing current data to these lines you can draw conclusions about whether the process
variation is consistent (in control) or is unpredictable
25
CONTROL CHART - PURPOSE
The main purpose of using a control chart is to monitor control and improve
process performance over time by studying variation and its source There are
several functions of a control chart
It centres attention on detecting and monitoring process variation over time
It provides a tool for on-going control of a process
It differentiates special from common causes of variation in order to be a guide for
local or management action
It helps improve a process to perform consistently and predictably to achieve higher
quality lower cost and higher effective capacity
It serves as a common language for discussing process performance
26
TYPES OF CONTROL CHARTS
The basic tool used in SPC is the control chart
There are various types of control charts
Variable Control Chart
Averages and range chart (X-Bar and R Bar Chart)
X bar and s chart
Moving Range Chart
Moving AveragendashMoving Range chart (also called MAndashMR chart)
p chart (also called proportion chart)
c chart (also called count chart)
np chart
u chart
27
POPULARITY OF CONTROL CHARTS
Control charts are a proven technique for improving productivity
Control charts are effective in defect prevention
Control charts prevent unnecessary process
adjustment
Control charts provide diagnostic information
Control charts provide information about process
capability
28
PROCEDURE FOR X ndashBAR AND R BAR CHART
1 Randomly sample ldquonrdquo units throughout the day (can be every 5
minutes every 30 minutes etc - whatever is appropriate for your
case)
2 For each sample calculate ldquoX-BARrdquo to estimate the mean and ldquoR
(range)rdquo to estimate variability NOTE THE RANGE CAN BE USED TO
ESTIMATE THE STANDARD DEVIATION
3 After collecting the 20-25 samples calculate X-BAR-BAR (the
average of all the X-BARs) and R-BAR (the average of all the ranges)
4 Using X-BAR-BAR and R-BAR calculate the control limits for your X-
BAR and R Control Charts
29
X-BAR CONTROL LIMITS
Upper Control Limit (UCL) = (X-BAR-BAR) + A2 (R-BAR)
Lower Control Limit(LCL) = (X-BAR-BAR) - A2 (R-BAR)
R CONTROL LIMITS
Upper Control Limit - D3 (R-BAR)
Lower Control Limit - D4 (R-BAR)
PROCEDURE FOR X ndashBAR AND R BAR CHART
30
CONTROL CHART CONSTANTS
sample size constant constant constant constant constant constant constant
n d2 A2 A3 B3 B4 D3 D4
2 1128 188 2659 0 3267 0 3267
3 1693 1023 1954 0 2568 0 2574
4 2059 0729 1628 0 2266 0 2282
5 2326 0577 1427 0 2089 0 2114
6 2534 0483 1287 003 197 0 2004
7 2704 0419 1182 0118 1882 0076 1924
8 2847 0373 1099 0185 1815 0136 1864
9 297 0337 1032 0239 1761 0184 1816
10 3078 0308 0975 0284 1716 0223 1777
31
5 For the R Control Chart plot all R values on the R Control Chart
to see if all the Ranges are ldquobetween the control limitsrdquo If they are
then your process is considered to be in a state of statistical control
(as far as the variability of the process is concerned)
6 For the X-BAR Control Chart plot all the X-BARs on the X-BAR
control chart to see if all the X-BARs are ldquobetween the control
limitsrdquo If they are then your process is considered in a state of
statistical control (as far as the average of the process is
concerned)
PROCEDURE FOR X ndashBAR AND R BAR CHART
32
SAMPLE DATA FOR X BAR ndashR CHART
Sub Group 1 2 3 4 5 X -Bar Range reg
1 1195 1191 1211 1203 1198 1200 02
2 1201 1198 1198 1197 12 1199 004
3 1193 1206 1198 1196 1202 1199 013
4 1205 1198 1205 1206 1198 1202 008
5 1198 1203 1206 1201 1199 1201 008
6 1202 1205 1196 1201 1195 1200 01
7 1199 1206 1201 1204 1201 1202 007
8 1201 1197 1198 1204 1198 1200 007
9 1198 1204 1198 1204 1204 1202 006
10 1205 1195 1198 1204 1196 1200 01
` X Bar-Bar 1200 009
X Bar Chart
UCL = X BAR-BAR + A2 R Bar
1200 +(0577009) 1205
LCL= X BAR-BAR - A2 R Bar
1200 - (0577009) 1195
R Chart
UCL = D4R Bar 211 009 021
LCL = D3 R Bar 0009 0
33
PLOT DATA ON CONTROL CHARTS
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1 2 3 4 5 6 7 8 9 10
Ave
rage
(X
ba
r)
X Bar Chart
UCL
LCL
X Bar
34
PLOT DATA ON CONTROL CHARTS
001
003
005
007
009
011
013
015
017
019
021
023
025
1 2 3 4 5 6 7 8 9 10
R Chart
UCL
LCL
35
PROCEDURE TO DETERMINE IF PROCESS IS IN A STATE OF
STATISTICAL CONTROL
7 If process is determined to be ldquoNOT STABLErdquo then stop and find out what
an assignable cause might be fix and then repeat the complete process of
collecting new data
8 If the process is determined to be ldquoSTABLErdquo then you may use the
control charts you developed to monitor future production to ensure that the
process REMAINS stable
More Samples for Control charts
36
READING OF CONTROL CHART
Control charts can determine whether a process is behaving in an unusual way The quality of the individual points of a subset is determined unstable if any of the
following occurs
Rule 1 Any point falls beyond 3σ from the centreline(this is represented by the upper and
lower control limits)
Rule 2 Two out of three consecutive points fall beyond 2σ on the same side of the
centreline
Rule 3 Four out of five consecutive points fall beyond 1σ on the same side of the
centreline
Rule 4 Nine or more consecutive points fall on the same side of the centreline
(Ref Next page for sample)
37
READING THE CONTROL CHART
38
CONTROL CHARTS FOR ATTRIBUTES ndashP-CHARTS amp C-CHARTS
Attributes are discrete events yesno or passfail
Use P-Charts for quality characteristics that are discrete and involve yesno or goodbad decisions
Eg
Number of leaking caulking tubes in a box of 48
Number of broken eggs in a carton
Use C-Charts for discrete defects when there can be more than one defect per unit
Eg
Number of stains in a carpet sample cut from a production run
Number of complaints per customer at a hotel
39
P-CHART EXAMPLE A PRODUCTION MANAGER FOR A TIRE COMPANY HAS INSPECTED THE NUMBER OF
DEFECTIVE TIRES IN FIVE RANDOM SAMPLES WITH 20 TIRES IN EACH SAMPLE THE TABLE BELOW SHOWS THE
NUMBER OF DEFECTIVE TIRES IN EACH SAMPLE OF 20 TIRES CALCULATE THE CONTROL LIMITS
Sample Number of
Defective Tires
Number of Tires in each
Sample
Proportion Defective
1 3 20 15
2 2 20 10
3 1 20 05
4 2 20 10
5 2 20 05
Total 9 100 09
01023(064)09σzpLCL
2823(064)09σzpUCL
06420
(09)(91)
n
)p(1pσ
09100
9
Inspected Total
DefectivespCL
p
p
p
Solution
40
P- CONTROL CHART
41
C-CHART EXAMPLE THE NUMBER OF WEEKLY CUSTOMER COMPLAINTS ARE MONITORED IN A LARGE HOTEL USING A C-CHART DEVELOP THREE SIGMA CONTROL LIMITS USING THE DATA TABLE BELOW
Week Number of Complaints
1 3
2 2
3 3
4 1
5 3
6 3
7 2
8 1
9 3
10 1
Total 22
022522322ccLCL
66522322ccUCL
2210
22
samples of
complaintsc
c
c
z
z
Solution
42
C- CONTROL CHART
43
The ability of a process to meet product designtechnical specifications
Assessing capability involves evaluating process variability relative to preset product or service specifications
Process Capability ndash Cp and Cpk
Cp assumes that the process is centered in the specification range
Cpk helps to address a possible lack of centering of the process
PROCESS CAPABILITY
6σ
LSLUSL
width process
width ionspecificatCp
3σ
LSLμ
3σ
μUSLminCpk
44
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
45
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
46
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
47
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
--and an individual part is measured at 520rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
48
GRAPHING THE TOLERANCE AND MEASUREMENTS
Suppose we made and measured several more
units and they were all EXACTLY the same
We wouldnrsquot have very many part problems
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
X
X
X
49
GRAPHING THE TOLERANCE AND MEASUREMENTS
In the real world units are NOT EXACTLY the same
Everything VARIES
The question isnrsquot IF units vary
Itrsquos how much when and why
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
XX
XXX
XXXXX
XXXXXXX
50
The ldquonormal bell curverdquo
Widths heights depths thicknesses weights speeds strengths
and many other types of measurements when charted as a
histogram often form the shape of a bell
A ldquoperfect bellrdquo like a ldquoperfect circlerdquo doesnrsquot occur in nature but
many processes are close enough to make the bell curve useful
(A number of common industrial measurements such as flatness and straightness do NOT tend to distribute in a bell shape their proper statistical analysis is performed using models other than the bell curve)
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
51
What is a ldquostandard deviationrdquo
If we measure the DISTANCE from the CENTER of the bell
to each individual measurement that makes up the bell curve
we can find a TYPICAL DISTANCE
The most commonly used statistic to estimate this distance is the
Standard Deviation (also called ldquoSigmardquo)
Because of the natural shape of the bell curve the area of +1 to ndash1
standard deviations includes about 68 of the curve
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
Typical distance
from the center +1
standard deviation
Typical distance
from the center -1
standard deviation
52
How much of the curve is included in how many standard
deviations
From ndash1 to +1 is about 68 of the bell curve
From ndash2 to +2 is about 95
From ndash3 to +3 is about 9973
From ndash4 to +4 is about 9999
(NOTE We usually show the bell from ndash3 to +3 to make it easier to draw but in concept the ldquotailsrdquo of the bell get very thin and go on forever)
-6 -5 -4 -3 -2 -1 +1 +2 +3 +4 +5 +6 0
53
A
B
What is Cpk It is a measure of how well a process is within a specification
Cpk = A divided by B
A = Distance from process mean to closest spec limit
B = 3 Standard Deviations (also called ldquo3 Sigmardquo)
A bigger Cpk is better because fewer units will be beyond spec
(A bigger ldquoArdquo and a smaller ldquoBrdquo are better)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
54
A
B
ldquoProcess Capabilityrdquo is the ability of a process
to fit its output within the tolerances
hellipa LARGER ldquoArdquo
hellipand a SMALLER ldquoBrdquo
hellipmeans BETTER ldquoProcess Capabilityrdquo
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
55
A
B
An Analogy
Analogy
The bell curve is your automobile
The spec limits are the edges of your garage door
If A = B you are hitting the frame of your garage door with your car
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
56
A
B
How can we make Cpk (A divided by B) better
1 Design the product so a wider tolerance is functional (ldquorobust designrdquo)
2 Choose equipment and methods for a good safety margin (ldquoprocess capabilityrdquo)
3 Correctly adjust but only when needed (ldquocontrolrdquo)
4 Discover ways to narrow the natural variation (ldquoimprovementrdquo)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
57
A
B
What does a very good Cpk do for us
This process is producing good units with a good safety margin
Note that when Cpk = 2 our process mean is 6 standard deviations from
the nearest spec so we say it has ldquo6 Sigma Capabilityrdquo
Specification
Limit
Specification
Limit
This Cpk is
about 2
Very good
Mean
58
A
B
What does a problem Cpk look like
This process is in danger of producing some defects
It is too close to the specification limits
(Remember the bell curve tail goes further than Bhellip hellipwe only show the bell to 3-sigma to make it easier to draw)
Specification
Limit
Specification
Limit
This Cpk is just
slightly greater
than 1 Not good
59
A
B
What does a very bad Cpk look like
A significant part of the ldquotailrdquo is hanging out beyond the spec limits
This process is producing scrap rework and customer rejects
Notice that if distance ldquoArdquo approaches zerohellip
hellipthe Cpk would approach zero andhellip
hellipthe process would become 50 defective
Specification
Limit
Specification
Limit
This Cpk is less
than 1 We desire
a minimum of 133
and ultimately we
want 2 or more
60
-
Q amp A
61
MEASUREMENT SYSTEM ANALYSIS (MSA)
An MSA is a statistical tool used to determine if a measurement system is capable of precise measurement
What is It
Objective or Purpose
bull To determine how much error is in the measurement due to the measurement process itself
bull Quantifies the variability added by the measurement system
bull Applicable to attribute data and variable data
When to Use It
bull On the critical inputs and outputs prior to collecting data for analysis
bull For any new or modified process in order to ensure the quality of the data
Measurement System Analysis is an analysis of the measurement process not an analysis of the people
IMPORTANT
Who Should be Involved
Everyone that measures and makes decisions about these measurements should be involved in the MSA
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The observed variation in process output measurements is not simply the variation in the process itself it is the variation in the process plus the variation in measurement that results from an inadequate measurement system
Conducting an MSA reduces the likelihood of passing a bad part or rejecting a good part
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The output of the process measured by bull Cycle time bull Dimensional data bull Number of defects and others
Observed Variation
Process Variation
Measurement System
Variation
Reproducibility
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Accuracy (Central Location)
OBSERVED VARIATION
Calibration addresses accuracy
Measurement System Analysis (MSA)
MEASUREMENT SYSTEM ERRORS
Accuracy difference between the observed measurement and the actual measurement
Precision variation that occurs when measuring the same part with the same instrument
MEASUREMENT SYSTEM ERROR
Precise but not
accurate
Accurate but not
precise
Not accurate or
precise
Accurate and
precise
ACCURACY OF MEASUREMENT
Broken down into three components
aStability
The consistency of measurements over time
bBias
A measure of the amount of partiality in the system
cLinearity
A measure of the bias values through the expected
range of measurements
OBSERVED VARIATION
Observed Variation
Process Variation
Measurement System
Variation
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Reproducibility
Accuracy (Central Location)
Calibration Addresses Accuracy
Letrsquos take a closer look at Precision
Measurement System Analysis (MSA)
Measurement System Analysis (MSA)
Error in Resolution The inability to detect small changes
Possible Cause
Wrong measurement device selected - divisions on scale not fine enough to detect changes
Resolution
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Repeatability The inability to get the same answer from repeated measurements made of the same item under absolutely identical conditions
Possible Cause
Lack of standard operating procedures (SOP) lack of training measuring system variablilty
Repeatability
Equipment Variation
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Reproducibility The inability to get the same answer from repeated measurements made under various conditions from different inspectors
Possible Cause
Lack of SOP lack of training
Reproducibility
Appraiser Variation
VARIABLE MSA ndash GAGE RampR STUDY
bull Gage RampR is the combined estimate of
measurement system Repeatability and
Reproducibility
bull Typically a 3-person study is performed Each person randomly measures 10 marked parts per trial
Each person can perform up to 3 trials
bull There are 3 key indicators EV or Equipment Variation
AV or Appraiser Variation
Overall GRR
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
Median Median is like the geographical center it would be the middle number
7 9 11 6 13 6 6 311 Put them in order 3 6 6 6 7 9 11 11 13 7 is the median
Mean Mean is the average of all the numbers The mean is derived by adding all the numbers and then dividing by the quantity of numbers
X1 + X2 + X3 + X4 + X5 + X6 + X7 +hellip+Xn
n
STATISTICAL PROCESS CONTROL
6
1 2 3 6 8
VARIATION
No two products or characteristics are exactly alike because any process contains many sources of variability
The differences among products may be large or may be immeasurably small but they are present
For instance the diameter of a machined shaft would be susceptible to potential variation from
Machine - Clerancesbearing wear
Tool - Strength rate of wear
Material - Hardness strength
Operator - Part feed accuracy of centering
Maintenance - Lubrication replacement of worn out parts
Environment - Temperature consistency of power supply
The numbers that were not exactly on the mean are considered ldquovariationrdquo
7
TYPES OF VARIATION
There are two types of variation
Common cause variation
Special cause variation
8
COMMON CAUSES
Common cause variation is that normal variation that exists in a process when it is running exactly as it should
Eg In the production of that Shaft variation even
When the operator is running the machine properly
When the machine is running properly
When the material is correct
When the method is correct
When the environment is correct
When the original measurements are correct
9
As we have just reviewed common cause variation cannot be defined by one particular characteristic
It is the inherent variation of all the parts of the operation together
Eg
Voltage fluctuation
Looseness or tightness of machine bearings
Common cause variation must be optimized and run at a reasonable cost
If only common causes of variation are present the output of a process is predictable
COMMON CAUSES
10
SPECIAL CAUSES
Special cause is when one or more of the process specificationsconditions change
Temperatures
Tools dull
Voltage drops drastically
Material change
Bearings are failing
Special cause variations are the variations that need to be corrected immediately since it affect the process output in unpredictable ways
11
WHY DO WE NEED DATA
Assessment
Assessing the effectiveness of specific process or corrective actions
Evaluation
Determine the quality of a process or product
Improvement
Help us understand where improvement is needed
Control
To help control a process and to ensure it does not move out of control
Prediction
Provide information and trends that enables us to predict when an activity will fail in the future
12
TYPES OF DATA
Data can be grouped into two major categories
Attributes data
Variable data
13
TYPES OF DATA ndash ATTRIBUTE DATA
Attributes data Non-measurable characteristics Can be very subjective
Blush Scratched Color etc
Observations are counted YesNo PresentAbsent MeetsDoesnrsquot meet
Visually inspected Gono-go gauges
If color happens to be an attribute that is being inspected for Typically meet the expected color sample is given Maybe a light and dark compared to sample given The acceptable range is in between A reject is not measured just counted as one
14
Collected through measurement
Is very objective
Can be temperature length width weight force volts amps etc
Uses a measuring tool
Scale
Meters
Inspection should not be done to sort but for data collection and correction of the process
This will allow for quick response and rapid correction minimizing defect quantities
TYPES OF DATA ndash VARIABLE DATA
15
PARETO CHARTS
Vilfredo Pareto
Italyrsquos wealth
80 held by 20 of people
Used when analyzing attributes
Based on results of tally numbers in specific categories
What is a Pareto Chart used for
To display the relative importance of data
To direct efforts to the biggest improvement opportunity by highlighting the vital few in contrast to the useful many
16
CONSTRUCTING A PARETO CHART
Determine the categories and the units for comparison of the data such as frequency cost or time
Total the raw data in each category then determine the grand total by adding the totals of each category
Re-order the categories from largest to smallest
Determine the cumulative percent of each category (ie the sum of each category plus all categories that precede it in the rank order divided by the grand total and multiplied by 100)
17
CONSTRUCTING A PARETO CHART
Draw and label the left-hand vertical axis with the unit of comparison such as frequency cost or time
Draw and label the horizontal axis with the categories List from left to right in rank order
Draw and label the right-hand vertical axis from 0 to 100 percent The 100 percent should line up with the grand total on the left-hand vertical axis
Beginning with the largest category draw in bars for each category representing the total for that category
18
CONSTRUCTING A PARETO CHART
Draw a line graph beginning at the right-hand
corner of the first bar to represent the
cumulative percent for each category as
measured on the right-hand axis
Analyze the chart Usually the top 20 of the
categories will comprise roughly 80 of the
cumulative total
19
PARETO CHART - EXAMPLE
Lets assume we are listing all the rejected products that are removed from a candy manufacturing line in one week
First we put the rejects in specific categories
No wrapper - 10
No center - 37
Wrong shape - 53
Short shot - 6
Wrapper open - 132
Underweight - 4
Overweight ndash 17
Get the total rejects - 259
20
Develop a percentage for each category
No wrapper ndash 10259 = 39
No center ndash 37259 = 143
Wrong shape ndash 53259 = 205
Short shot ndash 6259 = 23
Wrapper open ndash 132259 = 51
Underweight ndash 4259 = 15
Overweight ndash 17259 = 66
PARETO CHART - EXAMPLE
21
Now place the counts in a histogram largest to smallest
0
10
20
30
40
50
60
Wrapper
Open
No Center No Wrapper Underweight
70
80
90
100
51
205
143
66 39
23 15
22
Finally add up each and plot as a line diagram
0
10
20
30
40
50
60
Wrapper
Open
No Center No Wrapper Underweight
70
80
90
100
715
51
205
143
858
66
924
39
963
23
986
15
1001
23
0
10
20
30
40
50
60
Wrapper
Open
No Center No Wrapper Underweight
70
80
90
100
715
51
205
143
858
66
924
39
963
23
986
15
1001
24
CONTROL CHARTS
Control charts are one of the most commonly used methods of Statistical Process Control (SPC) which
monitors the stability of a process
The main features of a control chart include the data points a centreline (mean value) and upper and
lower limits (bounds to indicate where a process output is considered out of control)They visually
display the fluctuations of a particular process variable that easily determine whether these variations
fall within the specified process limits
Control charts
a graphical method for detecting if the underlying distribution of variation of some measurable
characteristic of the product seems to have undergone a shift
monitor a process in real time
Map the output of a production process over time
A control chart always has a central line for the average an upper line for the upper control limit and a
lower line for the lower control limit These lines are determined from historical data
By comparing current data to these lines you can draw conclusions about whether the process
variation is consistent (in control) or is unpredictable
25
CONTROL CHART - PURPOSE
The main purpose of using a control chart is to monitor control and improve
process performance over time by studying variation and its source There are
several functions of a control chart
It centres attention on detecting and monitoring process variation over time
It provides a tool for on-going control of a process
It differentiates special from common causes of variation in order to be a guide for
local or management action
It helps improve a process to perform consistently and predictably to achieve higher
quality lower cost and higher effective capacity
It serves as a common language for discussing process performance
26
TYPES OF CONTROL CHARTS
The basic tool used in SPC is the control chart
There are various types of control charts
Variable Control Chart
Averages and range chart (X-Bar and R Bar Chart)
X bar and s chart
Moving Range Chart
Moving AveragendashMoving Range chart (also called MAndashMR chart)
p chart (also called proportion chart)
c chart (also called count chart)
np chart
u chart
27
POPULARITY OF CONTROL CHARTS
Control charts are a proven technique for improving productivity
Control charts are effective in defect prevention
Control charts prevent unnecessary process
adjustment
Control charts provide diagnostic information
Control charts provide information about process
capability
28
PROCEDURE FOR X ndashBAR AND R BAR CHART
1 Randomly sample ldquonrdquo units throughout the day (can be every 5
minutes every 30 minutes etc - whatever is appropriate for your
case)
2 For each sample calculate ldquoX-BARrdquo to estimate the mean and ldquoR
(range)rdquo to estimate variability NOTE THE RANGE CAN BE USED TO
ESTIMATE THE STANDARD DEVIATION
3 After collecting the 20-25 samples calculate X-BAR-BAR (the
average of all the X-BARs) and R-BAR (the average of all the ranges)
4 Using X-BAR-BAR and R-BAR calculate the control limits for your X-
BAR and R Control Charts
29
X-BAR CONTROL LIMITS
Upper Control Limit (UCL) = (X-BAR-BAR) + A2 (R-BAR)
Lower Control Limit(LCL) = (X-BAR-BAR) - A2 (R-BAR)
R CONTROL LIMITS
Upper Control Limit - D3 (R-BAR)
Lower Control Limit - D4 (R-BAR)
PROCEDURE FOR X ndashBAR AND R BAR CHART
30
CONTROL CHART CONSTANTS
sample size constant constant constant constant constant constant constant
n d2 A2 A3 B3 B4 D3 D4
2 1128 188 2659 0 3267 0 3267
3 1693 1023 1954 0 2568 0 2574
4 2059 0729 1628 0 2266 0 2282
5 2326 0577 1427 0 2089 0 2114
6 2534 0483 1287 003 197 0 2004
7 2704 0419 1182 0118 1882 0076 1924
8 2847 0373 1099 0185 1815 0136 1864
9 297 0337 1032 0239 1761 0184 1816
10 3078 0308 0975 0284 1716 0223 1777
31
5 For the R Control Chart plot all R values on the R Control Chart
to see if all the Ranges are ldquobetween the control limitsrdquo If they are
then your process is considered to be in a state of statistical control
(as far as the variability of the process is concerned)
6 For the X-BAR Control Chart plot all the X-BARs on the X-BAR
control chart to see if all the X-BARs are ldquobetween the control
limitsrdquo If they are then your process is considered in a state of
statistical control (as far as the average of the process is
concerned)
PROCEDURE FOR X ndashBAR AND R BAR CHART
32
SAMPLE DATA FOR X BAR ndashR CHART
Sub Group 1 2 3 4 5 X -Bar Range reg
1 1195 1191 1211 1203 1198 1200 02
2 1201 1198 1198 1197 12 1199 004
3 1193 1206 1198 1196 1202 1199 013
4 1205 1198 1205 1206 1198 1202 008
5 1198 1203 1206 1201 1199 1201 008
6 1202 1205 1196 1201 1195 1200 01
7 1199 1206 1201 1204 1201 1202 007
8 1201 1197 1198 1204 1198 1200 007
9 1198 1204 1198 1204 1204 1202 006
10 1205 1195 1198 1204 1196 1200 01
` X Bar-Bar 1200 009
X Bar Chart
UCL = X BAR-BAR + A2 R Bar
1200 +(0577009) 1205
LCL= X BAR-BAR - A2 R Bar
1200 - (0577009) 1195
R Chart
UCL = D4R Bar 211 009 021
LCL = D3 R Bar 0009 0
33
PLOT DATA ON CONTROL CHARTS
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1 2 3 4 5 6 7 8 9 10
Ave
rage
(X
ba
r)
X Bar Chart
UCL
LCL
X Bar
34
PLOT DATA ON CONTROL CHARTS
001
003
005
007
009
011
013
015
017
019
021
023
025
1 2 3 4 5 6 7 8 9 10
R Chart
UCL
LCL
35
PROCEDURE TO DETERMINE IF PROCESS IS IN A STATE OF
STATISTICAL CONTROL
7 If process is determined to be ldquoNOT STABLErdquo then stop and find out what
an assignable cause might be fix and then repeat the complete process of
collecting new data
8 If the process is determined to be ldquoSTABLErdquo then you may use the
control charts you developed to monitor future production to ensure that the
process REMAINS stable
More Samples for Control charts
36
READING OF CONTROL CHART
Control charts can determine whether a process is behaving in an unusual way The quality of the individual points of a subset is determined unstable if any of the
following occurs
Rule 1 Any point falls beyond 3σ from the centreline(this is represented by the upper and
lower control limits)
Rule 2 Two out of three consecutive points fall beyond 2σ on the same side of the
centreline
Rule 3 Four out of five consecutive points fall beyond 1σ on the same side of the
centreline
Rule 4 Nine or more consecutive points fall on the same side of the centreline
(Ref Next page for sample)
37
READING THE CONTROL CHART
38
CONTROL CHARTS FOR ATTRIBUTES ndashP-CHARTS amp C-CHARTS
Attributes are discrete events yesno or passfail
Use P-Charts for quality characteristics that are discrete and involve yesno or goodbad decisions
Eg
Number of leaking caulking tubes in a box of 48
Number of broken eggs in a carton
Use C-Charts for discrete defects when there can be more than one defect per unit
Eg
Number of stains in a carpet sample cut from a production run
Number of complaints per customer at a hotel
39
P-CHART EXAMPLE A PRODUCTION MANAGER FOR A TIRE COMPANY HAS INSPECTED THE NUMBER OF
DEFECTIVE TIRES IN FIVE RANDOM SAMPLES WITH 20 TIRES IN EACH SAMPLE THE TABLE BELOW SHOWS THE
NUMBER OF DEFECTIVE TIRES IN EACH SAMPLE OF 20 TIRES CALCULATE THE CONTROL LIMITS
Sample Number of
Defective Tires
Number of Tires in each
Sample
Proportion Defective
1 3 20 15
2 2 20 10
3 1 20 05
4 2 20 10
5 2 20 05
Total 9 100 09
01023(064)09σzpLCL
2823(064)09σzpUCL
06420
(09)(91)
n
)p(1pσ
09100
9
Inspected Total
DefectivespCL
p
p
p
Solution
40
P- CONTROL CHART
41
C-CHART EXAMPLE THE NUMBER OF WEEKLY CUSTOMER COMPLAINTS ARE MONITORED IN A LARGE HOTEL USING A C-CHART DEVELOP THREE SIGMA CONTROL LIMITS USING THE DATA TABLE BELOW
Week Number of Complaints
1 3
2 2
3 3
4 1
5 3
6 3
7 2
8 1
9 3
10 1
Total 22
022522322ccLCL
66522322ccUCL
2210
22
samples of
complaintsc
c
c
z
z
Solution
42
C- CONTROL CHART
43
The ability of a process to meet product designtechnical specifications
Assessing capability involves evaluating process variability relative to preset product or service specifications
Process Capability ndash Cp and Cpk
Cp assumes that the process is centered in the specification range
Cpk helps to address a possible lack of centering of the process
PROCESS CAPABILITY
6σ
LSLUSL
width process
width ionspecificatCp
3σ
LSLμ
3σ
μUSLminCpk
44
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
45
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
46
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
47
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
--and an individual part is measured at 520rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
48
GRAPHING THE TOLERANCE AND MEASUREMENTS
Suppose we made and measured several more
units and they were all EXACTLY the same
We wouldnrsquot have very many part problems
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
X
X
X
49
GRAPHING THE TOLERANCE AND MEASUREMENTS
In the real world units are NOT EXACTLY the same
Everything VARIES
The question isnrsquot IF units vary
Itrsquos how much when and why
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
XX
XXX
XXXXX
XXXXXXX
50
The ldquonormal bell curverdquo
Widths heights depths thicknesses weights speeds strengths
and many other types of measurements when charted as a
histogram often form the shape of a bell
A ldquoperfect bellrdquo like a ldquoperfect circlerdquo doesnrsquot occur in nature but
many processes are close enough to make the bell curve useful
(A number of common industrial measurements such as flatness and straightness do NOT tend to distribute in a bell shape their proper statistical analysis is performed using models other than the bell curve)
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
51
What is a ldquostandard deviationrdquo
If we measure the DISTANCE from the CENTER of the bell
to each individual measurement that makes up the bell curve
we can find a TYPICAL DISTANCE
The most commonly used statistic to estimate this distance is the
Standard Deviation (also called ldquoSigmardquo)
Because of the natural shape of the bell curve the area of +1 to ndash1
standard deviations includes about 68 of the curve
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
Typical distance
from the center +1
standard deviation
Typical distance
from the center -1
standard deviation
52
How much of the curve is included in how many standard
deviations
From ndash1 to +1 is about 68 of the bell curve
From ndash2 to +2 is about 95
From ndash3 to +3 is about 9973
From ndash4 to +4 is about 9999
(NOTE We usually show the bell from ndash3 to +3 to make it easier to draw but in concept the ldquotailsrdquo of the bell get very thin and go on forever)
-6 -5 -4 -3 -2 -1 +1 +2 +3 +4 +5 +6 0
53
A
B
What is Cpk It is a measure of how well a process is within a specification
Cpk = A divided by B
A = Distance from process mean to closest spec limit
B = 3 Standard Deviations (also called ldquo3 Sigmardquo)
A bigger Cpk is better because fewer units will be beyond spec
(A bigger ldquoArdquo and a smaller ldquoBrdquo are better)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
54
A
B
ldquoProcess Capabilityrdquo is the ability of a process
to fit its output within the tolerances
hellipa LARGER ldquoArdquo
hellipand a SMALLER ldquoBrdquo
hellipmeans BETTER ldquoProcess Capabilityrdquo
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
55
A
B
An Analogy
Analogy
The bell curve is your automobile
The spec limits are the edges of your garage door
If A = B you are hitting the frame of your garage door with your car
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
56
A
B
How can we make Cpk (A divided by B) better
1 Design the product so a wider tolerance is functional (ldquorobust designrdquo)
2 Choose equipment and methods for a good safety margin (ldquoprocess capabilityrdquo)
3 Correctly adjust but only when needed (ldquocontrolrdquo)
4 Discover ways to narrow the natural variation (ldquoimprovementrdquo)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
57
A
B
What does a very good Cpk do for us
This process is producing good units with a good safety margin
Note that when Cpk = 2 our process mean is 6 standard deviations from
the nearest spec so we say it has ldquo6 Sigma Capabilityrdquo
Specification
Limit
Specification
Limit
This Cpk is
about 2
Very good
Mean
58
A
B
What does a problem Cpk look like
This process is in danger of producing some defects
It is too close to the specification limits
(Remember the bell curve tail goes further than Bhellip hellipwe only show the bell to 3-sigma to make it easier to draw)
Specification
Limit
Specification
Limit
This Cpk is just
slightly greater
than 1 Not good
59
A
B
What does a very bad Cpk look like
A significant part of the ldquotailrdquo is hanging out beyond the spec limits
This process is producing scrap rework and customer rejects
Notice that if distance ldquoArdquo approaches zerohellip
hellipthe Cpk would approach zero andhellip
hellipthe process would become 50 defective
Specification
Limit
Specification
Limit
This Cpk is less
than 1 We desire
a minimum of 133
and ultimately we
want 2 or more
60
-
Q amp A
61
MEASUREMENT SYSTEM ANALYSIS (MSA)
An MSA is a statistical tool used to determine if a measurement system is capable of precise measurement
What is It
Objective or Purpose
bull To determine how much error is in the measurement due to the measurement process itself
bull Quantifies the variability added by the measurement system
bull Applicable to attribute data and variable data
When to Use It
bull On the critical inputs and outputs prior to collecting data for analysis
bull For any new or modified process in order to ensure the quality of the data
Measurement System Analysis is an analysis of the measurement process not an analysis of the people
IMPORTANT
Who Should be Involved
Everyone that measures and makes decisions about these measurements should be involved in the MSA
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The observed variation in process output measurements is not simply the variation in the process itself it is the variation in the process plus the variation in measurement that results from an inadequate measurement system
Conducting an MSA reduces the likelihood of passing a bad part or rejecting a good part
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The output of the process measured by bull Cycle time bull Dimensional data bull Number of defects and others
Observed Variation
Process Variation
Measurement System
Variation
Reproducibility
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Accuracy (Central Location)
OBSERVED VARIATION
Calibration addresses accuracy
Measurement System Analysis (MSA)
MEASUREMENT SYSTEM ERRORS
Accuracy difference between the observed measurement and the actual measurement
Precision variation that occurs when measuring the same part with the same instrument
MEASUREMENT SYSTEM ERROR
Precise but not
accurate
Accurate but not
precise
Not accurate or
precise
Accurate and
precise
ACCURACY OF MEASUREMENT
Broken down into three components
aStability
The consistency of measurements over time
bBias
A measure of the amount of partiality in the system
cLinearity
A measure of the bias values through the expected
range of measurements
OBSERVED VARIATION
Observed Variation
Process Variation
Measurement System
Variation
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Reproducibility
Accuracy (Central Location)
Calibration Addresses Accuracy
Letrsquos take a closer look at Precision
Measurement System Analysis (MSA)
Measurement System Analysis (MSA)
Error in Resolution The inability to detect small changes
Possible Cause
Wrong measurement device selected - divisions on scale not fine enough to detect changes
Resolution
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Repeatability The inability to get the same answer from repeated measurements made of the same item under absolutely identical conditions
Possible Cause
Lack of standard operating procedures (SOP) lack of training measuring system variablilty
Repeatability
Equipment Variation
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Reproducibility The inability to get the same answer from repeated measurements made under various conditions from different inspectors
Possible Cause
Lack of SOP lack of training
Reproducibility
Appraiser Variation
VARIABLE MSA ndash GAGE RampR STUDY
bull Gage RampR is the combined estimate of
measurement system Repeatability and
Reproducibility
bull Typically a 3-person study is performed Each person randomly measures 10 marked parts per trial
Each person can perform up to 3 trials
bull There are 3 key indicators EV or Equipment Variation
AV or Appraiser Variation
Overall GRR
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
VARIATION
No two products or characteristics are exactly alike because any process contains many sources of variability
The differences among products may be large or may be immeasurably small but they are present
For instance the diameter of a machined shaft would be susceptible to potential variation from
Machine - Clerancesbearing wear
Tool - Strength rate of wear
Material - Hardness strength
Operator - Part feed accuracy of centering
Maintenance - Lubrication replacement of worn out parts
Environment - Temperature consistency of power supply
The numbers that were not exactly on the mean are considered ldquovariationrdquo
7
TYPES OF VARIATION
There are two types of variation
Common cause variation
Special cause variation
8
COMMON CAUSES
Common cause variation is that normal variation that exists in a process when it is running exactly as it should
Eg In the production of that Shaft variation even
When the operator is running the machine properly
When the machine is running properly
When the material is correct
When the method is correct
When the environment is correct
When the original measurements are correct
9
As we have just reviewed common cause variation cannot be defined by one particular characteristic
It is the inherent variation of all the parts of the operation together
Eg
Voltage fluctuation
Looseness or tightness of machine bearings
Common cause variation must be optimized and run at a reasonable cost
If only common causes of variation are present the output of a process is predictable
COMMON CAUSES
10
SPECIAL CAUSES
Special cause is when one or more of the process specificationsconditions change
Temperatures
Tools dull
Voltage drops drastically
Material change
Bearings are failing
Special cause variations are the variations that need to be corrected immediately since it affect the process output in unpredictable ways
11
WHY DO WE NEED DATA
Assessment
Assessing the effectiveness of specific process or corrective actions
Evaluation
Determine the quality of a process or product
Improvement
Help us understand where improvement is needed
Control
To help control a process and to ensure it does not move out of control
Prediction
Provide information and trends that enables us to predict when an activity will fail in the future
12
TYPES OF DATA
Data can be grouped into two major categories
Attributes data
Variable data
13
TYPES OF DATA ndash ATTRIBUTE DATA
Attributes data Non-measurable characteristics Can be very subjective
Blush Scratched Color etc
Observations are counted YesNo PresentAbsent MeetsDoesnrsquot meet
Visually inspected Gono-go gauges
If color happens to be an attribute that is being inspected for Typically meet the expected color sample is given Maybe a light and dark compared to sample given The acceptable range is in between A reject is not measured just counted as one
14
Collected through measurement
Is very objective
Can be temperature length width weight force volts amps etc
Uses a measuring tool
Scale
Meters
Inspection should not be done to sort but for data collection and correction of the process
This will allow for quick response and rapid correction minimizing defect quantities
TYPES OF DATA ndash VARIABLE DATA
15
PARETO CHARTS
Vilfredo Pareto
Italyrsquos wealth
80 held by 20 of people
Used when analyzing attributes
Based on results of tally numbers in specific categories
What is a Pareto Chart used for
To display the relative importance of data
To direct efforts to the biggest improvement opportunity by highlighting the vital few in contrast to the useful many
16
CONSTRUCTING A PARETO CHART
Determine the categories and the units for comparison of the data such as frequency cost or time
Total the raw data in each category then determine the grand total by adding the totals of each category
Re-order the categories from largest to smallest
Determine the cumulative percent of each category (ie the sum of each category plus all categories that precede it in the rank order divided by the grand total and multiplied by 100)
17
CONSTRUCTING A PARETO CHART
Draw and label the left-hand vertical axis with the unit of comparison such as frequency cost or time
Draw and label the horizontal axis with the categories List from left to right in rank order
Draw and label the right-hand vertical axis from 0 to 100 percent The 100 percent should line up with the grand total on the left-hand vertical axis
Beginning with the largest category draw in bars for each category representing the total for that category
18
CONSTRUCTING A PARETO CHART
Draw a line graph beginning at the right-hand
corner of the first bar to represent the
cumulative percent for each category as
measured on the right-hand axis
Analyze the chart Usually the top 20 of the
categories will comprise roughly 80 of the
cumulative total
19
PARETO CHART - EXAMPLE
Lets assume we are listing all the rejected products that are removed from a candy manufacturing line in one week
First we put the rejects in specific categories
No wrapper - 10
No center - 37
Wrong shape - 53
Short shot - 6
Wrapper open - 132
Underweight - 4
Overweight ndash 17
Get the total rejects - 259
20
Develop a percentage for each category
No wrapper ndash 10259 = 39
No center ndash 37259 = 143
Wrong shape ndash 53259 = 205
Short shot ndash 6259 = 23
Wrapper open ndash 132259 = 51
Underweight ndash 4259 = 15
Overweight ndash 17259 = 66
PARETO CHART - EXAMPLE
21
Now place the counts in a histogram largest to smallest
0
10
20
30
40
50
60
Wrapper
Open
No Center No Wrapper Underweight
70
80
90
100
51
205
143
66 39
23 15
22
Finally add up each and plot as a line diagram
0
10
20
30
40
50
60
Wrapper
Open
No Center No Wrapper Underweight
70
80
90
100
715
51
205
143
858
66
924
39
963
23
986
15
1001
23
0
10
20
30
40
50
60
Wrapper
Open
No Center No Wrapper Underweight
70
80
90
100
715
51
205
143
858
66
924
39
963
23
986
15
1001
24
CONTROL CHARTS
Control charts are one of the most commonly used methods of Statistical Process Control (SPC) which
monitors the stability of a process
The main features of a control chart include the data points a centreline (mean value) and upper and
lower limits (bounds to indicate where a process output is considered out of control)They visually
display the fluctuations of a particular process variable that easily determine whether these variations
fall within the specified process limits
Control charts
a graphical method for detecting if the underlying distribution of variation of some measurable
characteristic of the product seems to have undergone a shift
monitor a process in real time
Map the output of a production process over time
A control chart always has a central line for the average an upper line for the upper control limit and a
lower line for the lower control limit These lines are determined from historical data
By comparing current data to these lines you can draw conclusions about whether the process
variation is consistent (in control) or is unpredictable
25
CONTROL CHART - PURPOSE
The main purpose of using a control chart is to monitor control and improve
process performance over time by studying variation and its source There are
several functions of a control chart
It centres attention on detecting and monitoring process variation over time
It provides a tool for on-going control of a process
It differentiates special from common causes of variation in order to be a guide for
local or management action
It helps improve a process to perform consistently and predictably to achieve higher
quality lower cost and higher effective capacity
It serves as a common language for discussing process performance
26
TYPES OF CONTROL CHARTS
The basic tool used in SPC is the control chart
There are various types of control charts
Variable Control Chart
Averages and range chart (X-Bar and R Bar Chart)
X bar and s chart
Moving Range Chart
Moving AveragendashMoving Range chart (also called MAndashMR chart)
p chart (also called proportion chart)
c chart (also called count chart)
np chart
u chart
27
POPULARITY OF CONTROL CHARTS
Control charts are a proven technique for improving productivity
Control charts are effective in defect prevention
Control charts prevent unnecessary process
adjustment
Control charts provide diagnostic information
Control charts provide information about process
capability
28
PROCEDURE FOR X ndashBAR AND R BAR CHART
1 Randomly sample ldquonrdquo units throughout the day (can be every 5
minutes every 30 minutes etc - whatever is appropriate for your
case)
2 For each sample calculate ldquoX-BARrdquo to estimate the mean and ldquoR
(range)rdquo to estimate variability NOTE THE RANGE CAN BE USED TO
ESTIMATE THE STANDARD DEVIATION
3 After collecting the 20-25 samples calculate X-BAR-BAR (the
average of all the X-BARs) and R-BAR (the average of all the ranges)
4 Using X-BAR-BAR and R-BAR calculate the control limits for your X-
BAR and R Control Charts
29
X-BAR CONTROL LIMITS
Upper Control Limit (UCL) = (X-BAR-BAR) + A2 (R-BAR)
Lower Control Limit(LCL) = (X-BAR-BAR) - A2 (R-BAR)
R CONTROL LIMITS
Upper Control Limit - D3 (R-BAR)
Lower Control Limit - D4 (R-BAR)
PROCEDURE FOR X ndashBAR AND R BAR CHART
30
CONTROL CHART CONSTANTS
sample size constant constant constant constant constant constant constant
n d2 A2 A3 B3 B4 D3 D4
2 1128 188 2659 0 3267 0 3267
3 1693 1023 1954 0 2568 0 2574
4 2059 0729 1628 0 2266 0 2282
5 2326 0577 1427 0 2089 0 2114
6 2534 0483 1287 003 197 0 2004
7 2704 0419 1182 0118 1882 0076 1924
8 2847 0373 1099 0185 1815 0136 1864
9 297 0337 1032 0239 1761 0184 1816
10 3078 0308 0975 0284 1716 0223 1777
31
5 For the R Control Chart plot all R values on the R Control Chart
to see if all the Ranges are ldquobetween the control limitsrdquo If they are
then your process is considered to be in a state of statistical control
(as far as the variability of the process is concerned)
6 For the X-BAR Control Chart plot all the X-BARs on the X-BAR
control chart to see if all the X-BARs are ldquobetween the control
limitsrdquo If they are then your process is considered in a state of
statistical control (as far as the average of the process is
concerned)
PROCEDURE FOR X ndashBAR AND R BAR CHART
32
SAMPLE DATA FOR X BAR ndashR CHART
Sub Group 1 2 3 4 5 X -Bar Range reg
1 1195 1191 1211 1203 1198 1200 02
2 1201 1198 1198 1197 12 1199 004
3 1193 1206 1198 1196 1202 1199 013
4 1205 1198 1205 1206 1198 1202 008
5 1198 1203 1206 1201 1199 1201 008
6 1202 1205 1196 1201 1195 1200 01
7 1199 1206 1201 1204 1201 1202 007
8 1201 1197 1198 1204 1198 1200 007
9 1198 1204 1198 1204 1204 1202 006
10 1205 1195 1198 1204 1196 1200 01
` X Bar-Bar 1200 009
X Bar Chart
UCL = X BAR-BAR + A2 R Bar
1200 +(0577009) 1205
LCL= X BAR-BAR - A2 R Bar
1200 - (0577009) 1195
R Chart
UCL = D4R Bar 211 009 021
LCL = D3 R Bar 0009 0
33
PLOT DATA ON CONTROL CHARTS
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1 2 3 4 5 6 7 8 9 10
Ave
rage
(X
ba
r)
X Bar Chart
UCL
LCL
X Bar
34
PLOT DATA ON CONTROL CHARTS
001
003
005
007
009
011
013
015
017
019
021
023
025
1 2 3 4 5 6 7 8 9 10
R Chart
UCL
LCL
35
PROCEDURE TO DETERMINE IF PROCESS IS IN A STATE OF
STATISTICAL CONTROL
7 If process is determined to be ldquoNOT STABLErdquo then stop and find out what
an assignable cause might be fix and then repeat the complete process of
collecting new data
8 If the process is determined to be ldquoSTABLErdquo then you may use the
control charts you developed to monitor future production to ensure that the
process REMAINS stable
More Samples for Control charts
36
READING OF CONTROL CHART
Control charts can determine whether a process is behaving in an unusual way The quality of the individual points of a subset is determined unstable if any of the
following occurs
Rule 1 Any point falls beyond 3σ from the centreline(this is represented by the upper and
lower control limits)
Rule 2 Two out of three consecutive points fall beyond 2σ on the same side of the
centreline
Rule 3 Four out of five consecutive points fall beyond 1σ on the same side of the
centreline
Rule 4 Nine or more consecutive points fall on the same side of the centreline
(Ref Next page for sample)
37
READING THE CONTROL CHART
38
CONTROL CHARTS FOR ATTRIBUTES ndashP-CHARTS amp C-CHARTS
Attributes are discrete events yesno or passfail
Use P-Charts for quality characteristics that are discrete and involve yesno or goodbad decisions
Eg
Number of leaking caulking tubes in a box of 48
Number of broken eggs in a carton
Use C-Charts for discrete defects when there can be more than one defect per unit
Eg
Number of stains in a carpet sample cut from a production run
Number of complaints per customer at a hotel
39
P-CHART EXAMPLE A PRODUCTION MANAGER FOR A TIRE COMPANY HAS INSPECTED THE NUMBER OF
DEFECTIVE TIRES IN FIVE RANDOM SAMPLES WITH 20 TIRES IN EACH SAMPLE THE TABLE BELOW SHOWS THE
NUMBER OF DEFECTIVE TIRES IN EACH SAMPLE OF 20 TIRES CALCULATE THE CONTROL LIMITS
Sample Number of
Defective Tires
Number of Tires in each
Sample
Proportion Defective
1 3 20 15
2 2 20 10
3 1 20 05
4 2 20 10
5 2 20 05
Total 9 100 09
01023(064)09σzpLCL
2823(064)09σzpUCL
06420
(09)(91)
n
)p(1pσ
09100
9
Inspected Total
DefectivespCL
p
p
p
Solution
40
P- CONTROL CHART
41
C-CHART EXAMPLE THE NUMBER OF WEEKLY CUSTOMER COMPLAINTS ARE MONITORED IN A LARGE HOTEL USING A C-CHART DEVELOP THREE SIGMA CONTROL LIMITS USING THE DATA TABLE BELOW
Week Number of Complaints
1 3
2 2
3 3
4 1
5 3
6 3
7 2
8 1
9 3
10 1
Total 22
022522322ccLCL
66522322ccUCL
2210
22
samples of
complaintsc
c
c
z
z
Solution
42
C- CONTROL CHART
43
The ability of a process to meet product designtechnical specifications
Assessing capability involves evaluating process variability relative to preset product or service specifications
Process Capability ndash Cp and Cpk
Cp assumes that the process is centered in the specification range
Cpk helps to address a possible lack of centering of the process
PROCESS CAPABILITY
6σ
LSLUSL
width process
width ionspecificatCp
3σ
LSLμ
3σ
μUSLminCpk
44
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
45
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
46
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
47
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
--and an individual part is measured at 520rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
48
GRAPHING THE TOLERANCE AND MEASUREMENTS
Suppose we made and measured several more
units and they were all EXACTLY the same
We wouldnrsquot have very many part problems
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
X
X
X
49
GRAPHING THE TOLERANCE AND MEASUREMENTS
In the real world units are NOT EXACTLY the same
Everything VARIES
The question isnrsquot IF units vary
Itrsquos how much when and why
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
XX
XXX
XXXXX
XXXXXXX
50
The ldquonormal bell curverdquo
Widths heights depths thicknesses weights speeds strengths
and many other types of measurements when charted as a
histogram often form the shape of a bell
A ldquoperfect bellrdquo like a ldquoperfect circlerdquo doesnrsquot occur in nature but
many processes are close enough to make the bell curve useful
(A number of common industrial measurements such as flatness and straightness do NOT tend to distribute in a bell shape their proper statistical analysis is performed using models other than the bell curve)
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
51
What is a ldquostandard deviationrdquo
If we measure the DISTANCE from the CENTER of the bell
to each individual measurement that makes up the bell curve
we can find a TYPICAL DISTANCE
The most commonly used statistic to estimate this distance is the
Standard Deviation (also called ldquoSigmardquo)
Because of the natural shape of the bell curve the area of +1 to ndash1
standard deviations includes about 68 of the curve
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
Typical distance
from the center +1
standard deviation
Typical distance
from the center -1
standard deviation
52
How much of the curve is included in how many standard
deviations
From ndash1 to +1 is about 68 of the bell curve
From ndash2 to +2 is about 95
From ndash3 to +3 is about 9973
From ndash4 to +4 is about 9999
(NOTE We usually show the bell from ndash3 to +3 to make it easier to draw but in concept the ldquotailsrdquo of the bell get very thin and go on forever)
-6 -5 -4 -3 -2 -1 +1 +2 +3 +4 +5 +6 0
53
A
B
What is Cpk It is a measure of how well a process is within a specification
Cpk = A divided by B
A = Distance from process mean to closest spec limit
B = 3 Standard Deviations (also called ldquo3 Sigmardquo)
A bigger Cpk is better because fewer units will be beyond spec
(A bigger ldquoArdquo and a smaller ldquoBrdquo are better)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
54
A
B
ldquoProcess Capabilityrdquo is the ability of a process
to fit its output within the tolerances
hellipa LARGER ldquoArdquo
hellipand a SMALLER ldquoBrdquo
hellipmeans BETTER ldquoProcess Capabilityrdquo
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
55
A
B
An Analogy
Analogy
The bell curve is your automobile
The spec limits are the edges of your garage door
If A = B you are hitting the frame of your garage door with your car
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
56
A
B
How can we make Cpk (A divided by B) better
1 Design the product so a wider tolerance is functional (ldquorobust designrdquo)
2 Choose equipment and methods for a good safety margin (ldquoprocess capabilityrdquo)
3 Correctly adjust but only when needed (ldquocontrolrdquo)
4 Discover ways to narrow the natural variation (ldquoimprovementrdquo)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
57
A
B
What does a very good Cpk do for us
This process is producing good units with a good safety margin
Note that when Cpk = 2 our process mean is 6 standard deviations from
the nearest spec so we say it has ldquo6 Sigma Capabilityrdquo
Specification
Limit
Specification
Limit
This Cpk is
about 2
Very good
Mean
58
A
B
What does a problem Cpk look like
This process is in danger of producing some defects
It is too close to the specification limits
(Remember the bell curve tail goes further than Bhellip hellipwe only show the bell to 3-sigma to make it easier to draw)
Specification
Limit
Specification
Limit
This Cpk is just
slightly greater
than 1 Not good
59
A
B
What does a very bad Cpk look like
A significant part of the ldquotailrdquo is hanging out beyond the spec limits
This process is producing scrap rework and customer rejects
Notice that if distance ldquoArdquo approaches zerohellip
hellipthe Cpk would approach zero andhellip
hellipthe process would become 50 defective
Specification
Limit
Specification
Limit
This Cpk is less
than 1 We desire
a minimum of 133
and ultimately we
want 2 or more
60
-
Q amp A
61
MEASUREMENT SYSTEM ANALYSIS (MSA)
An MSA is a statistical tool used to determine if a measurement system is capable of precise measurement
What is It
Objective or Purpose
bull To determine how much error is in the measurement due to the measurement process itself
bull Quantifies the variability added by the measurement system
bull Applicable to attribute data and variable data
When to Use It
bull On the critical inputs and outputs prior to collecting data for analysis
bull For any new or modified process in order to ensure the quality of the data
Measurement System Analysis is an analysis of the measurement process not an analysis of the people
IMPORTANT
Who Should be Involved
Everyone that measures and makes decisions about these measurements should be involved in the MSA
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The observed variation in process output measurements is not simply the variation in the process itself it is the variation in the process plus the variation in measurement that results from an inadequate measurement system
Conducting an MSA reduces the likelihood of passing a bad part or rejecting a good part
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The output of the process measured by bull Cycle time bull Dimensional data bull Number of defects and others
Observed Variation
Process Variation
Measurement System
Variation
Reproducibility
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Accuracy (Central Location)
OBSERVED VARIATION
Calibration addresses accuracy
Measurement System Analysis (MSA)
MEASUREMENT SYSTEM ERRORS
Accuracy difference between the observed measurement and the actual measurement
Precision variation that occurs when measuring the same part with the same instrument
MEASUREMENT SYSTEM ERROR
Precise but not
accurate
Accurate but not
precise
Not accurate or
precise
Accurate and
precise
ACCURACY OF MEASUREMENT
Broken down into three components
aStability
The consistency of measurements over time
bBias
A measure of the amount of partiality in the system
cLinearity
A measure of the bias values through the expected
range of measurements
OBSERVED VARIATION
Observed Variation
Process Variation
Measurement System
Variation
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Reproducibility
Accuracy (Central Location)
Calibration Addresses Accuracy
Letrsquos take a closer look at Precision
Measurement System Analysis (MSA)
Measurement System Analysis (MSA)
Error in Resolution The inability to detect small changes
Possible Cause
Wrong measurement device selected - divisions on scale not fine enough to detect changes
Resolution
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Repeatability The inability to get the same answer from repeated measurements made of the same item under absolutely identical conditions
Possible Cause
Lack of standard operating procedures (SOP) lack of training measuring system variablilty
Repeatability
Equipment Variation
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Reproducibility The inability to get the same answer from repeated measurements made under various conditions from different inspectors
Possible Cause
Lack of SOP lack of training
Reproducibility
Appraiser Variation
VARIABLE MSA ndash GAGE RampR STUDY
bull Gage RampR is the combined estimate of
measurement system Repeatability and
Reproducibility
bull Typically a 3-person study is performed Each person randomly measures 10 marked parts per trial
Each person can perform up to 3 trials
bull There are 3 key indicators EV or Equipment Variation
AV or Appraiser Variation
Overall GRR
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
TYPES OF VARIATION
There are two types of variation
Common cause variation
Special cause variation
8
COMMON CAUSES
Common cause variation is that normal variation that exists in a process when it is running exactly as it should
Eg In the production of that Shaft variation even
When the operator is running the machine properly
When the machine is running properly
When the material is correct
When the method is correct
When the environment is correct
When the original measurements are correct
9
As we have just reviewed common cause variation cannot be defined by one particular characteristic
It is the inherent variation of all the parts of the operation together
Eg
Voltage fluctuation
Looseness or tightness of machine bearings
Common cause variation must be optimized and run at a reasonable cost
If only common causes of variation are present the output of a process is predictable
COMMON CAUSES
10
SPECIAL CAUSES
Special cause is when one or more of the process specificationsconditions change
Temperatures
Tools dull
Voltage drops drastically
Material change
Bearings are failing
Special cause variations are the variations that need to be corrected immediately since it affect the process output in unpredictable ways
11
WHY DO WE NEED DATA
Assessment
Assessing the effectiveness of specific process or corrective actions
Evaluation
Determine the quality of a process or product
Improvement
Help us understand where improvement is needed
Control
To help control a process and to ensure it does not move out of control
Prediction
Provide information and trends that enables us to predict when an activity will fail in the future
12
TYPES OF DATA
Data can be grouped into two major categories
Attributes data
Variable data
13
TYPES OF DATA ndash ATTRIBUTE DATA
Attributes data Non-measurable characteristics Can be very subjective
Blush Scratched Color etc
Observations are counted YesNo PresentAbsent MeetsDoesnrsquot meet
Visually inspected Gono-go gauges
If color happens to be an attribute that is being inspected for Typically meet the expected color sample is given Maybe a light and dark compared to sample given The acceptable range is in between A reject is not measured just counted as one
14
Collected through measurement
Is very objective
Can be temperature length width weight force volts amps etc
Uses a measuring tool
Scale
Meters
Inspection should not be done to sort but for data collection and correction of the process
This will allow for quick response and rapid correction minimizing defect quantities
TYPES OF DATA ndash VARIABLE DATA
15
PARETO CHARTS
Vilfredo Pareto
Italyrsquos wealth
80 held by 20 of people
Used when analyzing attributes
Based on results of tally numbers in specific categories
What is a Pareto Chart used for
To display the relative importance of data
To direct efforts to the biggest improvement opportunity by highlighting the vital few in contrast to the useful many
16
CONSTRUCTING A PARETO CHART
Determine the categories and the units for comparison of the data such as frequency cost or time
Total the raw data in each category then determine the grand total by adding the totals of each category
Re-order the categories from largest to smallest
Determine the cumulative percent of each category (ie the sum of each category plus all categories that precede it in the rank order divided by the grand total and multiplied by 100)
17
CONSTRUCTING A PARETO CHART
Draw and label the left-hand vertical axis with the unit of comparison such as frequency cost or time
Draw and label the horizontal axis with the categories List from left to right in rank order
Draw and label the right-hand vertical axis from 0 to 100 percent The 100 percent should line up with the grand total on the left-hand vertical axis
Beginning with the largest category draw in bars for each category representing the total for that category
18
CONSTRUCTING A PARETO CHART
Draw a line graph beginning at the right-hand
corner of the first bar to represent the
cumulative percent for each category as
measured on the right-hand axis
Analyze the chart Usually the top 20 of the
categories will comprise roughly 80 of the
cumulative total
19
PARETO CHART - EXAMPLE
Lets assume we are listing all the rejected products that are removed from a candy manufacturing line in one week
First we put the rejects in specific categories
No wrapper - 10
No center - 37
Wrong shape - 53
Short shot - 6
Wrapper open - 132
Underweight - 4
Overweight ndash 17
Get the total rejects - 259
20
Develop a percentage for each category
No wrapper ndash 10259 = 39
No center ndash 37259 = 143
Wrong shape ndash 53259 = 205
Short shot ndash 6259 = 23
Wrapper open ndash 132259 = 51
Underweight ndash 4259 = 15
Overweight ndash 17259 = 66
PARETO CHART - EXAMPLE
21
Now place the counts in a histogram largest to smallest
0
10
20
30
40
50
60
Wrapper
Open
No Center No Wrapper Underweight
70
80
90
100
51
205
143
66 39
23 15
22
Finally add up each and plot as a line diagram
0
10
20
30
40
50
60
Wrapper
Open
No Center No Wrapper Underweight
70
80
90
100
715
51
205
143
858
66
924
39
963
23
986
15
1001
23
0
10
20
30
40
50
60
Wrapper
Open
No Center No Wrapper Underweight
70
80
90
100
715
51
205
143
858
66
924
39
963
23
986
15
1001
24
CONTROL CHARTS
Control charts are one of the most commonly used methods of Statistical Process Control (SPC) which
monitors the stability of a process
The main features of a control chart include the data points a centreline (mean value) and upper and
lower limits (bounds to indicate where a process output is considered out of control)They visually
display the fluctuations of a particular process variable that easily determine whether these variations
fall within the specified process limits
Control charts
a graphical method for detecting if the underlying distribution of variation of some measurable
characteristic of the product seems to have undergone a shift
monitor a process in real time
Map the output of a production process over time
A control chart always has a central line for the average an upper line for the upper control limit and a
lower line for the lower control limit These lines are determined from historical data
By comparing current data to these lines you can draw conclusions about whether the process
variation is consistent (in control) or is unpredictable
25
CONTROL CHART - PURPOSE
The main purpose of using a control chart is to monitor control and improve
process performance over time by studying variation and its source There are
several functions of a control chart
It centres attention on detecting and monitoring process variation over time
It provides a tool for on-going control of a process
It differentiates special from common causes of variation in order to be a guide for
local or management action
It helps improve a process to perform consistently and predictably to achieve higher
quality lower cost and higher effective capacity
It serves as a common language for discussing process performance
26
TYPES OF CONTROL CHARTS
The basic tool used in SPC is the control chart
There are various types of control charts
Variable Control Chart
Averages and range chart (X-Bar and R Bar Chart)
X bar and s chart
Moving Range Chart
Moving AveragendashMoving Range chart (also called MAndashMR chart)
p chart (also called proportion chart)
c chart (also called count chart)
np chart
u chart
27
POPULARITY OF CONTROL CHARTS
Control charts are a proven technique for improving productivity
Control charts are effective in defect prevention
Control charts prevent unnecessary process
adjustment
Control charts provide diagnostic information
Control charts provide information about process
capability
28
PROCEDURE FOR X ndashBAR AND R BAR CHART
1 Randomly sample ldquonrdquo units throughout the day (can be every 5
minutes every 30 minutes etc - whatever is appropriate for your
case)
2 For each sample calculate ldquoX-BARrdquo to estimate the mean and ldquoR
(range)rdquo to estimate variability NOTE THE RANGE CAN BE USED TO
ESTIMATE THE STANDARD DEVIATION
3 After collecting the 20-25 samples calculate X-BAR-BAR (the
average of all the X-BARs) and R-BAR (the average of all the ranges)
4 Using X-BAR-BAR and R-BAR calculate the control limits for your X-
BAR and R Control Charts
29
X-BAR CONTROL LIMITS
Upper Control Limit (UCL) = (X-BAR-BAR) + A2 (R-BAR)
Lower Control Limit(LCL) = (X-BAR-BAR) - A2 (R-BAR)
R CONTROL LIMITS
Upper Control Limit - D3 (R-BAR)
Lower Control Limit - D4 (R-BAR)
PROCEDURE FOR X ndashBAR AND R BAR CHART
30
CONTROL CHART CONSTANTS
sample size constant constant constant constant constant constant constant
n d2 A2 A3 B3 B4 D3 D4
2 1128 188 2659 0 3267 0 3267
3 1693 1023 1954 0 2568 0 2574
4 2059 0729 1628 0 2266 0 2282
5 2326 0577 1427 0 2089 0 2114
6 2534 0483 1287 003 197 0 2004
7 2704 0419 1182 0118 1882 0076 1924
8 2847 0373 1099 0185 1815 0136 1864
9 297 0337 1032 0239 1761 0184 1816
10 3078 0308 0975 0284 1716 0223 1777
31
5 For the R Control Chart plot all R values on the R Control Chart
to see if all the Ranges are ldquobetween the control limitsrdquo If they are
then your process is considered to be in a state of statistical control
(as far as the variability of the process is concerned)
6 For the X-BAR Control Chart plot all the X-BARs on the X-BAR
control chart to see if all the X-BARs are ldquobetween the control
limitsrdquo If they are then your process is considered in a state of
statistical control (as far as the average of the process is
concerned)
PROCEDURE FOR X ndashBAR AND R BAR CHART
32
SAMPLE DATA FOR X BAR ndashR CHART
Sub Group 1 2 3 4 5 X -Bar Range reg
1 1195 1191 1211 1203 1198 1200 02
2 1201 1198 1198 1197 12 1199 004
3 1193 1206 1198 1196 1202 1199 013
4 1205 1198 1205 1206 1198 1202 008
5 1198 1203 1206 1201 1199 1201 008
6 1202 1205 1196 1201 1195 1200 01
7 1199 1206 1201 1204 1201 1202 007
8 1201 1197 1198 1204 1198 1200 007
9 1198 1204 1198 1204 1204 1202 006
10 1205 1195 1198 1204 1196 1200 01
` X Bar-Bar 1200 009
X Bar Chart
UCL = X BAR-BAR + A2 R Bar
1200 +(0577009) 1205
LCL= X BAR-BAR - A2 R Bar
1200 - (0577009) 1195
R Chart
UCL = D4R Bar 211 009 021
LCL = D3 R Bar 0009 0
33
PLOT DATA ON CONTROL CHARTS
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1 2 3 4 5 6 7 8 9 10
Ave
rage
(X
ba
r)
X Bar Chart
UCL
LCL
X Bar
34
PLOT DATA ON CONTROL CHARTS
001
003
005
007
009
011
013
015
017
019
021
023
025
1 2 3 4 5 6 7 8 9 10
R Chart
UCL
LCL
35
PROCEDURE TO DETERMINE IF PROCESS IS IN A STATE OF
STATISTICAL CONTROL
7 If process is determined to be ldquoNOT STABLErdquo then stop and find out what
an assignable cause might be fix and then repeat the complete process of
collecting new data
8 If the process is determined to be ldquoSTABLErdquo then you may use the
control charts you developed to monitor future production to ensure that the
process REMAINS stable
More Samples for Control charts
36
READING OF CONTROL CHART
Control charts can determine whether a process is behaving in an unusual way The quality of the individual points of a subset is determined unstable if any of the
following occurs
Rule 1 Any point falls beyond 3σ from the centreline(this is represented by the upper and
lower control limits)
Rule 2 Two out of three consecutive points fall beyond 2σ on the same side of the
centreline
Rule 3 Four out of five consecutive points fall beyond 1σ on the same side of the
centreline
Rule 4 Nine or more consecutive points fall on the same side of the centreline
(Ref Next page for sample)
37
READING THE CONTROL CHART
38
CONTROL CHARTS FOR ATTRIBUTES ndashP-CHARTS amp C-CHARTS
Attributes are discrete events yesno or passfail
Use P-Charts for quality characteristics that are discrete and involve yesno or goodbad decisions
Eg
Number of leaking caulking tubes in a box of 48
Number of broken eggs in a carton
Use C-Charts for discrete defects when there can be more than one defect per unit
Eg
Number of stains in a carpet sample cut from a production run
Number of complaints per customer at a hotel
39
P-CHART EXAMPLE A PRODUCTION MANAGER FOR A TIRE COMPANY HAS INSPECTED THE NUMBER OF
DEFECTIVE TIRES IN FIVE RANDOM SAMPLES WITH 20 TIRES IN EACH SAMPLE THE TABLE BELOW SHOWS THE
NUMBER OF DEFECTIVE TIRES IN EACH SAMPLE OF 20 TIRES CALCULATE THE CONTROL LIMITS
Sample Number of
Defective Tires
Number of Tires in each
Sample
Proportion Defective
1 3 20 15
2 2 20 10
3 1 20 05
4 2 20 10
5 2 20 05
Total 9 100 09
01023(064)09σzpLCL
2823(064)09σzpUCL
06420
(09)(91)
n
)p(1pσ
09100
9
Inspected Total
DefectivespCL
p
p
p
Solution
40
P- CONTROL CHART
41
C-CHART EXAMPLE THE NUMBER OF WEEKLY CUSTOMER COMPLAINTS ARE MONITORED IN A LARGE HOTEL USING A C-CHART DEVELOP THREE SIGMA CONTROL LIMITS USING THE DATA TABLE BELOW
Week Number of Complaints
1 3
2 2
3 3
4 1
5 3
6 3
7 2
8 1
9 3
10 1
Total 22
022522322ccLCL
66522322ccUCL
2210
22
samples of
complaintsc
c
c
z
z
Solution
42
C- CONTROL CHART
43
The ability of a process to meet product designtechnical specifications
Assessing capability involves evaluating process variability relative to preset product or service specifications
Process Capability ndash Cp and Cpk
Cp assumes that the process is centered in the specification range
Cpk helps to address a possible lack of centering of the process
PROCESS CAPABILITY
6σ
LSLUSL
width process
width ionspecificatCp
3σ
LSLμ
3σ
μUSLminCpk
44
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
45
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
46
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
47
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
--and an individual part is measured at 520rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
48
GRAPHING THE TOLERANCE AND MEASUREMENTS
Suppose we made and measured several more
units and they were all EXACTLY the same
We wouldnrsquot have very many part problems
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
X
X
X
49
GRAPHING THE TOLERANCE AND MEASUREMENTS
In the real world units are NOT EXACTLY the same
Everything VARIES
The question isnrsquot IF units vary
Itrsquos how much when and why
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
XX
XXX
XXXXX
XXXXXXX
50
The ldquonormal bell curverdquo
Widths heights depths thicknesses weights speeds strengths
and many other types of measurements when charted as a
histogram often form the shape of a bell
A ldquoperfect bellrdquo like a ldquoperfect circlerdquo doesnrsquot occur in nature but
many processes are close enough to make the bell curve useful
(A number of common industrial measurements such as flatness and straightness do NOT tend to distribute in a bell shape their proper statistical analysis is performed using models other than the bell curve)
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
51
What is a ldquostandard deviationrdquo
If we measure the DISTANCE from the CENTER of the bell
to each individual measurement that makes up the bell curve
we can find a TYPICAL DISTANCE
The most commonly used statistic to estimate this distance is the
Standard Deviation (also called ldquoSigmardquo)
Because of the natural shape of the bell curve the area of +1 to ndash1
standard deviations includes about 68 of the curve
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
Typical distance
from the center +1
standard deviation
Typical distance
from the center -1
standard deviation
52
How much of the curve is included in how many standard
deviations
From ndash1 to +1 is about 68 of the bell curve
From ndash2 to +2 is about 95
From ndash3 to +3 is about 9973
From ndash4 to +4 is about 9999
(NOTE We usually show the bell from ndash3 to +3 to make it easier to draw but in concept the ldquotailsrdquo of the bell get very thin and go on forever)
-6 -5 -4 -3 -2 -1 +1 +2 +3 +4 +5 +6 0
53
A
B
What is Cpk It is a measure of how well a process is within a specification
Cpk = A divided by B
A = Distance from process mean to closest spec limit
B = 3 Standard Deviations (also called ldquo3 Sigmardquo)
A bigger Cpk is better because fewer units will be beyond spec
(A bigger ldquoArdquo and a smaller ldquoBrdquo are better)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
54
A
B
ldquoProcess Capabilityrdquo is the ability of a process
to fit its output within the tolerances
hellipa LARGER ldquoArdquo
hellipand a SMALLER ldquoBrdquo
hellipmeans BETTER ldquoProcess Capabilityrdquo
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
55
A
B
An Analogy
Analogy
The bell curve is your automobile
The spec limits are the edges of your garage door
If A = B you are hitting the frame of your garage door with your car
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
56
A
B
How can we make Cpk (A divided by B) better
1 Design the product so a wider tolerance is functional (ldquorobust designrdquo)
2 Choose equipment and methods for a good safety margin (ldquoprocess capabilityrdquo)
3 Correctly adjust but only when needed (ldquocontrolrdquo)
4 Discover ways to narrow the natural variation (ldquoimprovementrdquo)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
57
A
B
What does a very good Cpk do for us
This process is producing good units with a good safety margin
Note that when Cpk = 2 our process mean is 6 standard deviations from
the nearest spec so we say it has ldquo6 Sigma Capabilityrdquo
Specification
Limit
Specification
Limit
This Cpk is
about 2
Very good
Mean
58
A
B
What does a problem Cpk look like
This process is in danger of producing some defects
It is too close to the specification limits
(Remember the bell curve tail goes further than Bhellip hellipwe only show the bell to 3-sigma to make it easier to draw)
Specification
Limit
Specification
Limit
This Cpk is just
slightly greater
than 1 Not good
59
A
B
What does a very bad Cpk look like
A significant part of the ldquotailrdquo is hanging out beyond the spec limits
This process is producing scrap rework and customer rejects
Notice that if distance ldquoArdquo approaches zerohellip
hellipthe Cpk would approach zero andhellip
hellipthe process would become 50 defective
Specification
Limit
Specification
Limit
This Cpk is less
than 1 We desire
a minimum of 133
and ultimately we
want 2 or more
60
-
Q amp A
61
MEASUREMENT SYSTEM ANALYSIS (MSA)
An MSA is a statistical tool used to determine if a measurement system is capable of precise measurement
What is It
Objective or Purpose
bull To determine how much error is in the measurement due to the measurement process itself
bull Quantifies the variability added by the measurement system
bull Applicable to attribute data and variable data
When to Use It
bull On the critical inputs and outputs prior to collecting data for analysis
bull For any new or modified process in order to ensure the quality of the data
Measurement System Analysis is an analysis of the measurement process not an analysis of the people
IMPORTANT
Who Should be Involved
Everyone that measures and makes decisions about these measurements should be involved in the MSA
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The observed variation in process output measurements is not simply the variation in the process itself it is the variation in the process plus the variation in measurement that results from an inadequate measurement system
Conducting an MSA reduces the likelihood of passing a bad part or rejecting a good part
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The output of the process measured by bull Cycle time bull Dimensional data bull Number of defects and others
Observed Variation
Process Variation
Measurement System
Variation
Reproducibility
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Accuracy (Central Location)
OBSERVED VARIATION
Calibration addresses accuracy
Measurement System Analysis (MSA)
MEASUREMENT SYSTEM ERRORS
Accuracy difference between the observed measurement and the actual measurement
Precision variation that occurs when measuring the same part with the same instrument
MEASUREMENT SYSTEM ERROR
Precise but not
accurate
Accurate but not
precise
Not accurate or
precise
Accurate and
precise
ACCURACY OF MEASUREMENT
Broken down into three components
aStability
The consistency of measurements over time
bBias
A measure of the amount of partiality in the system
cLinearity
A measure of the bias values through the expected
range of measurements
OBSERVED VARIATION
Observed Variation
Process Variation
Measurement System
Variation
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Reproducibility
Accuracy (Central Location)
Calibration Addresses Accuracy
Letrsquos take a closer look at Precision
Measurement System Analysis (MSA)
Measurement System Analysis (MSA)
Error in Resolution The inability to detect small changes
Possible Cause
Wrong measurement device selected - divisions on scale not fine enough to detect changes
Resolution
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Repeatability The inability to get the same answer from repeated measurements made of the same item under absolutely identical conditions
Possible Cause
Lack of standard operating procedures (SOP) lack of training measuring system variablilty
Repeatability
Equipment Variation
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Reproducibility The inability to get the same answer from repeated measurements made under various conditions from different inspectors
Possible Cause
Lack of SOP lack of training
Reproducibility
Appraiser Variation
VARIABLE MSA ndash GAGE RampR STUDY
bull Gage RampR is the combined estimate of
measurement system Repeatability and
Reproducibility
bull Typically a 3-person study is performed Each person randomly measures 10 marked parts per trial
Each person can perform up to 3 trials
bull There are 3 key indicators EV or Equipment Variation
AV or Appraiser Variation
Overall GRR
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
COMMON CAUSES
Common cause variation is that normal variation that exists in a process when it is running exactly as it should
Eg In the production of that Shaft variation even
When the operator is running the machine properly
When the machine is running properly
When the material is correct
When the method is correct
When the environment is correct
When the original measurements are correct
9
As we have just reviewed common cause variation cannot be defined by one particular characteristic
It is the inherent variation of all the parts of the operation together
Eg
Voltage fluctuation
Looseness or tightness of machine bearings
Common cause variation must be optimized and run at a reasonable cost
If only common causes of variation are present the output of a process is predictable
COMMON CAUSES
10
SPECIAL CAUSES
Special cause is when one or more of the process specificationsconditions change
Temperatures
Tools dull
Voltage drops drastically
Material change
Bearings are failing
Special cause variations are the variations that need to be corrected immediately since it affect the process output in unpredictable ways
11
WHY DO WE NEED DATA
Assessment
Assessing the effectiveness of specific process or corrective actions
Evaluation
Determine the quality of a process or product
Improvement
Help us understand where improvement is needed
Control
To help control a process and to ensure it does not move out of control
Prediction
Provide information and trends that enables us to predict when an activity will fail in the future
12
TYPES OF DATA
Data can be grouped into two major categories
Attributes data
Variable data
13
TYPES OF DATA ndash ATTRIBUTE DATA
Attributes data Non-measurable characteristics Can be very subjective
Blush Scratched Color etc
Observations are counted YesNo PresentAbsent MeetsDoesnrsquot meet
Visually inspected Gono-go gauges
If color happens to be an attribute that is being inspected for Typically meet the expected color sample is given Maybe a light and dark compared to sample given The acceptable range is in between A reject is not measured just counted as one
14
Collected through measurement
Is very objective
Can be temperature length width weight force volts amps etc
Uses a measuring tool
Scale
Meters
Inspection should not be done to sort but for data collection and correction of the process
This will allow for quick response and rapid correction minimizing defect quantities
TYPES OF DATA ndash VARIABLE DATA
15
PARETO CHARTS
Vilfredo Pareto
Italyrsquos wealth
80 held by 20 of people
Used when analyzing attributes
Based on results of tally numbers in specific categories
What is a Pareto Chart used for
To display the relative importance of data
To direct efforts to the biggest improvement opportunity by highlighting the vital few in contrast to the useful many
16
CONSTRUCTING A PARETO CHART
Determine the categories and the units for comparison of the data such as frequency cost or time
Total the raw data in each category then determine the grand total by adding the totals of each category
Re-order the categories from largest to smallest
Determine the cumulative percent of each category (ie the sum of each category plus all categories that precede it in the rank order divided by the grand total and multiplied by 100)
17
CONSTRUCTING A PARETO CHART
Draw and label the left-hand vertical axis with the unit of comparison such as frequency cost or time
Draw and label the horizontal axis with the categories List from left to right in rank order
Draw and label the right-hand vertical axis from 0 to 100 percent The 100 percent should line up with the grand total on the left-hand vertical axis
Beginning with the largest category draw in bars for each category representing the total for that category
18
CONSTRUCTING A PARETO CHART
Draw a line graph beginning at the right-hand
corner of the first bar to represent the
cumulative percent for each category as
measured on the right-hand axis
Analyze the chart Usually the top 20 of the
categories will comprise roughly 80 of the
cumulative total
19
PARETO CHART - EXAMPLE
Lets assume we are listing all the rejected products that are removed from a candy manufacturing line in one week
First we put the rejects in specific categories
No wrapper - 10
No center - 37
Wrong shape - 53
Short shot - 6
Wrapper open - 132
Underweight - 4
Overweight ndash 17
Get the total rejects - 259
20
Develop a percentage for each category
No wrapper ndash 10259 = 39
No center ndash 37259 = 143
Wrong shape ndash 53259 = 205
Short shot ndash 6259 = 23
Wrapper open ndash 132259 = 51
Underweight ndash 4259 = 15
Overweight ndash 17259 = 66
PARETO CHART - EXAMPLE
21
Now place the counts in a histogram largest to smallest
0
10
20
30
40
50
60
Wrapper
Open
No Center No Wrapper Underweight
70
80
90
100
51
205
143
66 39
23 15
22
Finally add up each and plot as a line diagram
0
10
20
30
40
50
60
Wrapper
Open
No Center No Wrapper Underweight
70
80
90
100
715
51
205
143
858
66
924
39
963
23
986
15
1001
23
0
10
20
30
40
50
60
Wrapper
Open
No Center No Wrapper Underweight
70
80
90
100
715
51
205
143
858
66
924
39
963
23
986
15
1001
24
CONTROL CHARTS
Control charts are one of the most commonly used methods of Statistical Process Control (SPC) which
monitors the stability of a process
The main features of a control chart include the data points a centreline (mean value) and upper and
lower limits (bounds to indicate where a process output is considered out of control)They visually
display the fluctuations of a particular process variable that easily determine whether these variations
fall within the specified process limits
Control charts
a graphical method for detecting if the underlying distribution of variation of some measurable
characteristic of the product seems to have undergone a shift
monitor a process in real time
Map the output of a production process over time
A control chart always has a central line for the average an upper line for the upper control limit and a
lower line for the lower control limit These lines are determined from historical data
By comparing current data to these lines you can draw conclusions about whether the process
variation is consistent (in control) or is unpredictable
25
CONTROL CHART - PURPOSE
The main purpose of using a control chart is to monitor control and improve
process performance over time by studying variation and its source There are
several functions of a control chart
It centres attention on detecting and monitoring process variation over time
It provides a tool for on-going control of a process
It differentiates special from common causes of variation in order to be a guide for
local or management action
It helps improve a process to perform consistently and predictably to achieve higher
quality lower cost and higher effective capacity
It serves as a common language for discussing process performance
26
TYPES OF CONTROL CHARTS
The basic tool used in SPC is the control chart
There are various types of control charts
Variable Control Chart
Averages and range chart (X-Bar and R Bar Chart)
X bar and s chart
Moving Range Chart
Moving AveragendashMoving Range chart (also called MAndashMR chart)
p chart (also called proportion chart)
c chart (also called count chart)
np chart
u chart
27
POPULARITY OF CONTROL CHARTS
Control charts are a proven technique for improving productivity
Control charts are effective in defect prevention
Control charts prevent unnecessary process
adjustment
Control charts provide diagnostic information
Control charts provide information about process
capability
28
PROCEDURE FOR X ndashBAR AND R BAR CHART
1 Randomly sample ldquonrdquo units throughout the day (can be every 5
minutes every 30 minutes etc - whatever is appropriate for your
case)
2 For each sample calculate ldquoX-BARrdquo to estimate the mean and ldquoR
(range)rdquo to estimate variability NOTE THE RANGE CAN BE USED TO
ESTIMATE THE STANDARD DEVIATION
3 After collecting the 20-25 samples calculate X-BAR-BAR (the
average of all the X-BARs) and R-BAR (the average of all the ranges)
4 Using X-BAR-BAR and R-BAR calculate the control limits for your X-
BAR and R Control Charts
29
X-BAR CONTROL LIMITS
Upper Control Limit (UCL) = (X-BAR-BAR) + A2 (R-BAR)
Lower Control Limit(LCL) = (X-BAR-BAR) - A2 (R-BAR)
R CONTROL LIMITS
Upper Control Limit - D3 (R-BAR)
Lower Control Limit - D4 (R-BAR)
PROCEDURE FOR X ndashBAR AND R BAR CHART
30
CONTROL CHART CONSTANTS
sample size constant constant constant constant constant constant constant
n d2 A2 A3 B3 B4 D3 D4
2 1128 188 2659 0 3267 0 3267
3 1693 1023 1954 0 2568 0 2574
4 2059 0729 1628 0 2266 0 2282
5 2326 0577 1427 0 2089 0 2114
6 2534 0483 1287 003 197 0 2004
7 2704 0419 1182 0118 1882 0076 1924
8 2847 0373 1099 0185 1815 0136 1864
9 297 0337 1032 0239 1761 0184 1816
10 3078 0308 0975 0284 1716 0223 1777
31
5 For the R Control Chart plot all R values on the R Control Chart
to see if all the Ranges are ldquobetween the control limitsrdquo If they are
then your process is considered to be in a state of statistical control
(as far as the variability of the process is concerned)
6 For the X-BAR Control Chart plot all the X-BARs on the X-BAR
control chart to see if all the X-BARs are ldquobetween the control
limitsrdquo If they are then your process is considered in a state of
statistical control (as far as the average of the process is
concerned)
PROCEDURE FOR X ndashBAR AND R BAR CHART
32
SAMPLE DATA FOR X BAR ndashR CHART
Sub Group 1 2 3 4 5 X -Bar Range reg
1 1195 1191 1211 1203 1198 1200 02
2 1201 1198 1198 1197 12 1199 004
3 1193 1206 1198 1196 1202 1199 013
4 1205 1198 1205 1206 1198 1202 008
5 1198 1203 1206 1201 1199 1201 008
6 1202 1205 1196 1201 1195 1200 01
7 1199 1206 1201 1204 1201 1202 007
8 1201 1197 1198 1204 1198 1200 007
9 1198 1204 1198 1204 1204 1202 006
10 1205 1195 1198 1204 1196 1200 01
` X Bar-Bar 1200 009
X Bar Chart
UCL = X BAR-BAR + A2 R Bar
1200 +(0577009) 1205
LCL= X BAR-BAR - A2 R Bar
1200 - (0577009) 1195
R Chart
UCL = D4R Bar 211 009 021
LCL = D3 R Bar 0009 0
33
PLOT DATA ON CONTROL CHARTS
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1 2 3 4 5 6 7 8 9 10
Ave
rage
(X
ba
r)
X Bar Chart
UCL
LCL
X Bar
34
PLOT DATA ON CONTROL CHARTS
001
003
005
007
009
011
013
015
017
019
021
023
025
1 2 3 4 5 6 7 8 9 10
R Chart
UCL
LCL
35
PROCEDURE TO DETERMINE IF PROCESS IS IN A STATE OF
STATISTICAL CONTROL
7 If process is determined to be ldquoNOT STABLErdquo then stop and find out what
an assignable cause might be fix and then repeat the complete process of
collecting new data
8 If the process is determined to be ldquoSTABLErdquo then you may use the
control charts you developed to monitor future production to ensure that the
process REMAINS stable
More Samples for Control charts
36
READING OF CONTROL CHART
Control charts can determine whether a process is behaving in an unusual way The quality of the individual points of a subset is determined unstable if any of the
following occurs
Rule 1 Any point falls beyond 3σ from the centreline(this is represented by the upper and
lower control limits)
Rule 2 Two out of three consecutive points fall beyond 2σ on the same side of the
centreline
Rule 3 Four out of five consecutive points fall beyond 1σ on the same side of the
centreline
Rule 4 Nine or more consecutive points fall on the same side of the centreline
(Ref Next page for sample)
37
READING THE CONTROL CHART
38
CONTROL CHARTS FOR ATTRIBUTES ndashP-CHARTS amp C-CHARTS
Attributes are discrete events yesno or passfail
Use P-Charts for quality characteristics that are discrete and involve yesno or goodbad decisions
Eg
Number of leaking caulking tubes in a box of 48
Number of broken eggs in a carton
Use C-Charts for discrete defects when there can be more than one defect per unit
Eg
Number of stains in a carpet sample cut from a production run
Number of complaints per customer at a hotel
39
P-CHART EXAMPLE A PRODUCTION MANAGER FOR A TIRE COMPANY HAS INSPECTED THE NUMBER OF
DEFECTIVE TIRES IN FIVE RANDOM SAMPLES WITH 20 TIRES IN EACH SAMPLE THE TABLE BELOW SHOWS THE
NUMBER OF DEFECTIVE TIRES IN EACH SAMPLE OF 20 TIRES CALCULATE THE CONTROL LIMITS
Sample Number of
Defective Tires
Number of Tires in each
Sample
Proportion Defective
1 3 20 15
2 2 20 10
3 1 20 05
4 2 20 10
5 2 20 05
Total 9 100 09
01023(064)09σzpLCL
2823(064)09σzpUCL
06420
(09)(91)
n
)p(1pσ
09100
9
Inspected Total
DefectivespCL
p
p
p
Solution
40
P- CONTROL CHART
41
C-CHART EXAMPLE THE NUMBER OF WEEKLY CUSTOMER COMPLAINTS ARE MONITORED IN A LARGE HOTEL USING A C-CHART DEVELOP THREE SIGMA CONTROL LIMITS USING THE DATA TABLE BELOW
Week Number of Complaints
1 3
2 2
3 3
4 1
5 3
6 3
7 2
8 1
9 3
10 1
Total 22
022522322ccLCL
66522322ccUCL
2210
22
samples of
complaintsc
c
c
z
z
Solution
42
C- CONTROL CHART
43
The ability of a process to meet product designtechnical specifications
Assessing capability involves evaluating process variability relative to preset product or service specifications
Process Capability ndash Cp and Cpk
Cp assumes that the process is centered in the specification range
Cpk helps to address a possible lack of centering of the process
PROCESS CAPABILITY
6σ
LSLUSL
width process
width ionspecificatCp
3σ
LSLμ
3σ
μUSLminCpk
44
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
45
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
46
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
47
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
--and an individual part is measured at 520rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
48
GRAPHING THE TOLERANCE AND MEASUREMENTS
Suppose we made and measured several more
units and they were all EXACTLY the same
We wouldnrsquot have very many part problems
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
X
X
X
49
GRAPHING THE TOLERANCE AND MEASUREMENTS
In the real world units are NOT EXACTLY the same
Everything VARIES
The question isnrsquot IF units vary
Itrsquos how much when and why
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
XX
XXX
XXXXX
XXXXXXX
50
The ldquonormal bell curverdquo
Widths heights depths thicknesses weights speeds strengths
and many other types of measurements when charted as a
histogram often form the shape of a bell
A ldquoperfect bellrdquo like a ldquoperfect circlerdquo doesnrsquot occur in nature but
many processes are close enough to make the bell curve useful
(A number of common industrial measurements such as flatness and straightness do NOT tend to distribute in a bell shape their proper statistical analysis is performed using models other than the bell curve)
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
51
What is a ldquostandard deviationrdquo
If we measure the DISTANCE from the CENTER of the bell
to each individual measurement that makes up the bell curve
we can find a TYPICAL DISTANCE
The most commonly used statistic to estimate this distance is the
Standard Deviation (also called ldquoSigmardquo)
Because of the natural shape of the bell curve the area of +1 to ndash1
standard deviations includes about 68 of the curve
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
Typical distance
from the center +1
standard deviation
Typical distance
from the center -1
standard deviation
52
How much of the curve is included in how many standard
deviations
From ndash1 to +1 is about 68 of the bell curve
From ndash2 to +2 is about 95
From ndash3 to +3 is about 9973
From ndash4 to +4 is about 9999
(NOTE We usually show the bell from ndash3 to +3 to make it easier to draw but in concept the ldquotailsrdquo of the bell get very thin and go on forever)
-6 -5 -4 -3 -2 -1 +1 +2 +3 +4 +5 +6 0
53
A
B
What is Cpk It is a measure of how well a process is within a specification
Cpk = A divided by B
A = Distance from process mean to closest spec limit
B = 3 Standard Deviations (also called ldquo3 Sigmardquo)
A bigger Cpk is better because fewer units will be beyond spec
(A bigger ldquoArdquo and a smaller ldquoBrdquo are better)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
54
A
B
ldquoProcess Capabilityrdquo is the ability of a process
to fit its output within the tolerances
hellipa LARGER ldquoArdquo
hellipand a SMALLER ldquoBrdquo
hellipmeans BETTER ldquoProcess Capabilityrdquo
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
55
A
B
An Analogy
Analogy
The bell curve is your automobile
The spec limits are the edges of your garage door
If A = B you are hitting the frame of your garage door with your car
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
56
A
B
How can we make Cpk (A divided by B) better
1 Design the product so a wider tolerance is functional (ldquorobust designrdquo)
2 Choose equipment and methods for a good safety margin (ldquoprocess capabilityrdquo)
3 Correctly adjust but only when needed (ldquocontrolrdquo)
4 Discover ways to narrow the natural variation (ldquoimprovementrdquo)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
57
A
B
What does a very good Cpk do for us
This process is producing good units with a good safety margin
Note that when Cpk = 2 our process mean is 6 standard deviations from
the nearest spec so we say it has ldquo6 Sigma Capabilityrdquo
Specification
Limit
Specification
Limit
This Cpk is
about 2
Very good
Mean
58
A
B
What does a problem Cpk look like
This process is in danger of producing some defects
It is too close to the specification limits
(Remember the bell curve tail goes further than Bhellip hellipwe only show the bell to 3-sigma to make it easier to draw)
Specification
Limit
Specification
Limit
This Cpk is just
slightly greater
than 1 Not good
59
A
B
What does a very bad Cpk look like
A significant part of the ldquotailrdquo is hanging out beyond the spec limits
This process is producing scrap rework and customer rejects
Notice that if distance ldquoArdquo approaches zerohellip
hellipthe Cpk would approach zero andhellip
hellipthe process would become 50 defective
Specification
Limit
Specification
Limit
This Cpk is less
than 1 We desire
a minimum of 133
and ultimately we
want 2 or more
60
-
Q amp A
61
MEASUREMENT SYSTEM ANALYSIS (MSA)
An MSA is a statistical tool used to determine if a measurement system is capable of precise measurement
What is It
Objective or Purpose
bull To determine how much error is in the measurement due to the measurement process itself
bull Quantifies the variability added by the measurement system
bull Applicable to attribute data and variable data
When to Use It
bull On the critical inputs and outputs prior to collecting data for analysis
bull For any new or modified process in order to ensure the quality of the data
Measurement System Analysis is an analysis of the measurement process not an analysis of the people
IMPORTANT
Who Should be Involved
Everyone that measures and makes decisions about these measurements should be involved in the MSA
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The observed variation in process output measurements is not simply the variation in the process itself it is the variation in the process plus the variation in measurement that results from an inadequate measurement system
Conducting an MSA reduces the likelihood of passing a bad part or rejecting a good part
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The output of the process measured by bull Cycle time bull Dimensional data bull Number of defects and others
Observed Variation
Process Variation
Measurement System
Variation
Reproducibility
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Accuracy (Central Location)
OBSERVED VARIATION
Calibration addresses accuracy
Measurement System Analysis (MSA)
MEASUREMENT SYSTEM ERRORS
Accuracy difference between the observed measurement and the actual measurement
Precision variation that occurs when measuring the same part with the same instrument
MEASUREMENT SYSTEM ERROR
Precise but not
accurate
Accurate but not
precise
Not accurate or
precise
Accurate and
precise
ACCURACY OF MEASUREMENT
Broken down into three components
aStability
The consistency of measurements over time
bBias
A measure of the amount of partiality in the system
cLinearity
A measure of the bias values through the expected
range of measurements
OBSERVED VARIATION
Observed Variation
Process Variation
Measurement System
Variation
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Reproducibility
Accuracy (Central Location)
Calibration Addresses Accuracy
Letrsquos take a closer look at Precision
Measurement System Analysis (MSA)
Measurement System Analysis (MSA)
Error in Resolution The inability to detect small changes
Possible Cause
Wrong measurement device selected - divisions on scale not fine enough to detect changes
Resolution
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Repeatability The inability to get the same answer from repeated measurements made of the same item under absolutely identical conditions
Possible Cause
Lack of standard operating procedures (SOP) lack of training measuring system variablilty
Repeatability
Equipment Variation
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Reproducibility The inability to get the same answer from repeated measurements made under various conditions from different inspectors
Possible Cause
Lack of SOP lack of training
Reproducibility
Appraiser Variation
VARIABLE MSA ndash GAGE RampR STUDY
bull Gage RampR is the combined estimate of
measurement system Repeatability and
Reproducibility
bull Typically a 3-person study is performed Each person randomly measures 10 marked parts per trial
Each person can perform up to 3 trials
bull There are 3 key indicators EV or Equipment Variation
AV or Appraiser Variation
Overall GRR
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
As we have just reviewed common cause variation cannot be defined by one particular characteristic
It is the inherent variation of all the parts of the operation together
Eg
Voltage fluctuation
Looseness or tightness of machine bearings
Common cause variation must be optimized and run at a reasonable cost
If only common causes of variation are present the output of a process is predictable
COMMON CAUSES
10
SPECIAL CAUSES
Special cause is when one or more of the process specificationsconditions change
Temperatures
Tools dull
Voltage drops drastically
Material change
Bearings are failing
Special cause variations are the variations that need to be corrected immediately since it affect the process output in unpredictable ways
11
WHY DO WE NEED DATA
Assessment
Assessing the effectiveness of specific process or corrective actions
Evaluation
Determine the quality of a process or product
Improvement
Help us understand where improvement is needed
Control
To help control a process and to ensure it does not move out of control
Prediction
Provide information and trends that enables us to predict when an activity will fail in the future
12
TYPES OF DATA
Data can be grouped into two major categories
Attributes data
Variable data
13
TYPES OF DATA ndash ATTRIBUTE DATA
Attributes data Non-measurable characteristics Can be very subjective
Blush Scratched Color etc
Observations are counted YesNo PresentAbsent MeetsDoesnrsquot meet
Visually inspected Gono-go gauges
If color happens to be an attribute that is being inspected for Typically meet the expected color sample is given Maybe a light and dark compared to sample given The acceptable range is in between A reject is not measured just counted as one
14
Collected through measurement
Is very objective
Can be temperature length width weight force volts amps etc
Uses a measuring tool
Scale
Meters
Inspection should not be done to sort but for data collection and correction of the process
This will allow for quick response and rapid correction minimizing defect quantities
TYPES OF DATA ndash VARIABLE DATA
15
PARETO CHARTS
Vilfredo Pareto
Italyrsquos wealth
80 held by 20 of people
Used when analyzing attributes
Based on results of tally numbers in specific categories
What is a Pareto Chart used for
To display the relative importance of data
To direct efforts to the biggest improvement opportunity by highlighting the vital few in contrast to the useful many
16
CONSTRUCTING A PARETO CHART
Determine the categories and the units for comparison of the data such as frequency cost or time
Total the raw data in each category then determine the grand total by adding the totals of each category
Re-order the categories from largest to smallest
Determine the cumulative percent of each category (ie the sum of each category plus all categories that precede it in the rank order divided by the grand total and multiplied by 100)
17
CONSTRUCTING A PARETO CHART
Draw and label the left-hand vertical axis with the unit of comparison such as frequency cost or time
Draw and label the horizontal axis with the categories List from left to right in rank order
Draw and label the right-hand vertical axis from 0 to 100 percent The 100 percent should line up with the grand total on the left-hand vertical axis
Beginning with the largest category draw in bars for each category representing the total for that category
18
CONSTRUCTING A PARETO CHART
Draw a line graph beginning at the right-hand
corner of the first bar to represent the
cumulative percent for each category as
measured on the right-hand axis
Analyze the chart Usually the top 20 of the
categories will comprise roughly 80 of the
cumulative total
19
PARETO CHART - EXAMPLE
Lets assume we are listing all the rejected products that are removed from a candy manufacturing line in one week
First we put the rejects in specific categories
No wrapper - 10
No center - 37
Wrong shape - 53
Short shot - 6
Wrapper open - 132
Underweight - 4
Overweight ndash 17
Get the total rejects - 259
20
Develop a percentage for each category
No wrapper ndash 10259 = 39
No center ndash 37259 = 143
Wrong shape ndash 53259 = 205
Short shot ndash 6259 = 23
Wrapper open ndash 132259 = 51
Underweight ndash 4259 = 15
Overweight ndash 17259 = 66
PARETO CHART - EXAMPLE
21
Now place the counts in a histogram largest to smallest
0
10
20
30
40
50
60
Wrapper
Open
No Center No Wrapper Underweight
70
80
90
100
51
205
143
66 39
23 15
22
Finally add up each and plot as a line diagram
0
10
20
30
40
50
60
Wrapper
Open
No Center No Wrapper Underweight
70
80
90
100
715
51
205
143
858
66
924
39
963
23
986
15
1001
23
0
10
20
30
40
50
60
Wrapper
Open
No Center No Wrapper Underweight
70
80
90
100
715
51
205
143
858
66
924
39
963
23
986
15
1001
24
CONTROL CHARTS
Control charts are one of the most commonly used methods of Statistical Process Control (SPC) which
monitors the stability of a process
The main features of a control chart include the data points a centreline (mean value) and upper and
lower limits (bounds to indicate where a process output is considered out of control)They visually
display the fluctuations of a particular process variable that easily determine whether these variations
fall within the specified process limits
Control charts
a graphical method for detecting if the underlying distribution of variation of some measurable
characteristic of the product seems to have undergone a shift
monitor a process in real time
Map the output of a production process over time
A control chart always has a central line for the average an upper line for the upper control limit and a
lower line for the lower control limit These lines are determined from historical data
By comparing current data to these lines you can draw conclusions about whether the process
variation is consistent (in control) or is unpredictable
25
CONTROL CHART - PURPOSE
The main purpose of using a control chart is to monitor control and improve
process performance over time by studying variation and its source There are
several functions of a control chart
It centres attention on detecting and monitoring process variation over time
It provides a tool for on-going control of a process
It differentiates special from common causes of variation in order to be a guide for
local or management action
It helps improve a process to perform consistently and predictably to achieve higher
quality lower cost and higher effective capacity
It serves as a common language for discussing process performance
26
TYPES OF CONTROL CHARTS
The basic tool used in SPC is the control chart
There are various types of control charts
Variable Control Chart
Averages and range chart (X-Bar and R Bar Chart)
X bar and s chart
Moving Range Chart
Moving AveragendashMoving Range chart (also called MAndashMR chart)
p chart (also called proportion chart)
c chart (also called count chart)
np chart
u chart
27
POPULARITY OF CONTROL CHARTS
Control charts are a proven technique for improving productivity
Control charts are effective in defect prevention
Control charts prevent unnecessary process
adjustment
Control charts provide diagnostic information
Control charts provide information about process
capability
28
PROCEDURE FOR X ndashBAR AND R BAR CHART
1 Randomly sample ldquonrdquo units throughout the day (can be every 5
minutes every 30 minutes etc - whatever is appropriate for your
case)
2 For each sample calculate ldquoX-BARrdquo to estimate the mean and ldquoR
(range)rdquo to estimate variability NOTE THE RANGE CAN BE USED TO
ESTIMATE THE STANDARD DEVIATION
3 After collecting the 20-25 samples calculate X-BAR-BAR (the
average of all the X-BARs) and R-BAR (the average of all the ranges)
4 Using X-BAR-BAR and R-BAR calculate the control limits for your X-
BAR and R Control Charts
29
X-BAR CONTROL LIMITS
Upper Control Limit (UCL) = (X-BAR-BAR) + A2 (R-BAR)
Lower Control Limit(LCL) = (X-BAR-BAR) - A2 (R-BAR)
R CONTROL LIMITS
Upper Control Limit - D3 (R-BAR)
Lower Control Limit - D4 (R-BAR)
PROCEDURE FOR X ndashBAR AND R BAR CHART
30
CONTROL CHART CONSTANTS
sample size constant constant constant constant constant constant constant
n d2 A2 A3 B3 B4 D3 D4
2 1128 188 2659 0 3267 0 3267
3 1693 1023 1954 0 2568 0 2574
4 2059 0729 1628 0 2266 0 2282
5 2326 0577 1427 0 2089 0 2114
6 2534 0483 1287 003 197 0 2004
7 2704 0419 1182 0118 1882 0076 1924
8 2847 0373 1099 0185 1815 0136 1864
9 297 0337 1032 0239 1761 0184 1816
10 3078 0308 0975 0284 1716 0223 1777
31
5 For the R Control Chart plot all R values on the R Control Chart
to see if all the Ranges are ldquobetween the control limitsrdquo If they are
then your process is considered to be in a state of statistical control
(as far as the variability of the process is concerned)
6 For the X-BAR Control Chart plot all the X-BARs on the X-BAR
control chart to see if all the X-BARs are ldquobetween the control
limitsrdquo If they are then your process is considered in a state of
statistical control (as far as the average of the process is
concerned)
PROCEDURE FOR X ndashBAR AND R BAR CHART
32
SAMPLE DATA FOR X BAR ndashR CHART
Sub Group 1 2 3 4 5 X -Bar Range reg
1 1195 1191 1211 1203 1198 1200 02
2 1201 1198 1198 1197 12 1199 004
3 1193 1206 1198 1196 1202 1199 013
4 1205 1198 1205 1206 1198 1202 008
5 1198 1203 1206 1201 1199 1201 008
6 1202 1205 1196 1201 1195 1200 01
7 1199 1206 1201 1204 1201 1202 007
8 1201 1197 1198 1204 1198 1200 007
9 1198 1204 1198 1204 1204 1202 006
10 1205 1195 1198 1204 1196 1200 01
` X Bar-Bar 1200 009
X Bar Chart
UCL = X BAR-BAR + A2 R Bar
1200 +(0577009) 1205
LCL= X BAR-BAR - A2 R Bar
1200 - (0577009) 1195
R Chart
UCL = D4R Bar 211 009 021
LCL = D3 R Bar 0009 0
33
PLOT DATA ON CONTROL CHARTS
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1 2 3 4 5 6 7 8 9 10
Ave
rage
(X
ba
r)
X Bar Chart
UCL
LCL
X Bar
34
PLOT DATA ON CONTROL CHARTS
001
003
005
007
009
011
013
015
017
019
021
023
025
1 2 3 4 5 6 7 8 9 10
R Chart
UCL
LCL
35
PROCEDURE TO DETERMINE IF PROCESS IS IN A STATE OF
STATISTICAL CONTROL
7 If process is determined to be ldquoNOT STABLErdquo then stop and find out what
an assignable cause might be fix and then repeat the complete process of
collecting new data
8 If the process is determined to be ldquoSTABLErdquo then you may use the
control charts you developed to monitor future production to ensure that the
process REMAINS stable
More Samples for Control charts
36
READING OF CONTROL CHART
Control charts can determine whether a process is behaving in an unusual way The quality of the individual points of a subset is determined unstable if any of the
following occurs
Rule 1 Any point falls beyond 3σ from the centreline(this is represented by the upper and
lower control limits)
Rule 2 Two out of three consecutive points fall beyond 2σ on the same side of the
centreline
Rule 3 Four out of five consecutive points fall beyond 1σ on the same side of the
centreline
Rule 4 Nine or more consecutive points fall on the same side of the centreline
(Ref Next page for sample)
37
READING THE CONTROL CHART
38
CONTROL CHARTS FOR ATTRIBUTES ndashP-CHARTS amp C-CHARTS
Attributes are discrete events yesno or passfail
Use P-Charts for quality characteristics that are discrete and involve yesno or goodbad decisions
Eg
Number of leaking caulking tubes in a box of 48
Number of broken eggs in a carton
Use C-Charts for discrete defects when there can be more than one defect per unit
Eg
Number of stains in a carpet sample cut from a production run
Number of complaints per customer at a hotel
39
P-CHART EXAMPLE A PRODUCTION MANAGER FOR A TIRE COMPANY HAS INSPECTED THE NUMBER OF
DEFECTIVE TIRES IN FIVE RANDOM SAMPLES WITH 20 TIRES IN EACH SAMPLE THE TABLE BELOW SHOWS THE
NUMBER OF DEFECTIVE TIRES IN EACH SAMPLE OF 20 TIRES CALCULATE THE CONTROL LIMITS
Sample Number of
Defective Tires
Number of Tires in each
Sample
Proportion Defective
1 3 20 15
2 2 20 10
3 1 20 05
4 2 20 10
5 2 20 05
Total 9 100 09
01023(064)09σzpLCL
2823(064)09σzpUCL
06420
(09)(91)
n
)p(1pσ
09100
9
Inspected Total
DefectivespCL
p
p
p
Solution
40
P- CONTROL CHART
41
C-CHART EXAMPLE THE NUMBER OF WEEKLY CUSTOMER COMPLAINTS ARE MONITORED IN A LARGE HOTEL USING A C-CHART DEVELOP THREE SIGMA CONTROL LIMITS USING THE DATA TABLE BELOW
Week Number of Complaints
1 3
2 2
3 3
4 1
5 3
6 3
7 2
8 1
9 3
10 1
Total 22
022522322ccLCL
66522322ccUCL
2210
22
samples of
complaintsc
c
c
z
z
Solution
42
C- CONTROL CHART
43
The ability of a process to meet product designtechnical specifications
Assessing capability involves evaluating process variability relative to preset product or service specifications
Process Capability ndash Cp and Cpk
Cp assumes that the process is centered in the specification range
Cpk helps to address a possible lack of centering of the process
PROCESS CAPABILITY
6σ
LSLUSL
width process
width ionspecificatCp
3σ
LSLμ
3σ
μUSLminCpk
44
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
45
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
46
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
47
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
--and an individual part is measured at 520rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
48
GRAPHING THE TOLERANCE AND MEASUREMENTS
Suppose we made and measured several more
units and they were all EXACTLY the same
We wouldnrsquot have very many part problems
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
X
X
X
49
GRAPHING THE TOLERANCE AND MEASUREMENTS
In the real world units are NOT EXACTLY the same
Everything VARIES
The question isnrsquot IF units vary
Itrsquos how much when and why
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
XX
XXX
XXXXX
XXXXXXX
50
The ldquonormal bell curverdquo
Widths heights depths thicknesses weights speeds strengths
and many other types of measurements when charted as a
histogram often form the shape of a bell
A ldquoperfect bellrdquo like a ldquoperfect circlerdquo doesnrsquot occur in nature but
many processes are close enough to make the bell curve useful
(A number of common industrial measurements such as flatness and straightness do NOT tend to distribute in a bell shape their proper statistical analysis is performed using models other than the bell curve)
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
51
What is a ldquostandard deviationrdquo
If we measure the DISTANCE from the CENTER of the bell
to each individual measurement that makes up the bell curve
we can find a TYPICAL DISTANCE
The most commonly used statistic to estimate this distance is the
Standard Deviation (also called ldquoSigmardquo)
Because of the natural shape of the bell curve the area of +1 to ndash1
standard deviations includes about 68 of the curve
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
Typical distance
from the center +1
standard deviation
Typical distance
from the center -1
standard deviation
52
How much of the curve is included in how many standard
deviations
From ndash1 to +1 is about 68 of the bell curve
From ndash2 to +2 is about 95
From ndash3 to +3 is about 9973
From ndash4 to +4 is about 9999
(NOTE We usually show the bell from ndash3 to +3 to make it easier to draw but in concept the ldquotailsrdquo of the bell get very thin and go on forever)
-6 -5 -4 -3 -2 -1 +1 +2 +3 +4 +5 +6 0
53
A
B
What is Cpk It is a measure of how well a process is within a specification
Cpk = A divided by B
A = Distance from process mean to closest spec limit
B = 3 Standard Deviations (also called ldquo3 Sigmardquo)
A bigger Cpk is better because fewer units will be beyond spec
(A bigger ldquoArdquo and a smaller ldquoBrdquo are better)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
54
A
B
ldquoProcess Capabilityrdquo is the ability of a process
to fit its output within the tolerances
hellipa LARGER ldquoArdquo
hellipand a SMALLER ldquoBrdquo
hellipmeans BETTER ldquoProcess Capabilityrdquo
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
55
A
B
An Analogy
Analogy
The bell curve is your automobile
The spec limits are the edges of your garage door
If A = B you are hitting the frame of your garage door with your car
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
56
A
B
How can we make Cpk (A divided by B) better
1 Design the product so a wider tolerance is functional (ldquorobust designrdquo)
2 Choose equipment and methods for a good safety margin (ldquoprocess capabilityrdquo)
3 Correctly adjust but only when needed (ldquocontrolrdquo)
4 Discover ways to narrow the natural variation (ldquoimprovementrdquo)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
57
A
B
What does a very good Cpk do for us
This process is producing good units with a good safety margin
Note that when Cpk = 2 our process mean is 6 standard deviations from
the nearest spec so we say it has ldquo6 Sigma Capabilityrdquo
Specification
Limit
Specification
Limit
This Cpk is
about 2
Very good
Mean
58
A
B
What does a problem Cpk look like
This process is in danger of producing some defects
It is too close to the specification limits
(Remember the bell curve tail goes further than Bhellip hellipwe only show the bell to 3-sigma to make it easier to draw)
Specification
Limit
Specification
Limit
This Cpk is just
slightly greater
than 1 Not good
59
A
B
What does a very bad Cpk look like
A significant part of the ldquotailrdquo is hanging out beyond the spec limits
This process is producing scrap rework and customer rejects
Notice that if distance ldquoArdquo approaches zerohellip
hellipthe Cpk would approach zero andhellip
hellipthe process would become 50 defective
Specification
Limit
Specification
Limit
This Cpk is less
than 1 We desire
a minimum of 133
and ultimately we
want 2 or more
60
-
Q amp A
61
MEASUREMENT SYSTEM ANALYSIS (MSA)
An MSA is a statistical tool used to determine if a measurement system is capable of precise measurement
What is It
Objective or Purpose
bull To determine how much error is in the measurement due to the measurement process itself
bull Quantifies the variability added by the measurement system
bull Applicable to attribute data and variable data
When to Use It
bull On the critical inputs and outputs prior to collecting data for analysis
bull For any new or modified process in order to ensure the quality of the data
Measurement System Analysis is an analysis of the measurement process not an analysis of the people
IMPORTANT
Who Should be Involved
Everyone that measures and makes decisions about these measurements should be involved in the MSA
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The observed variation in process output measurements is not simply the variation in the process itself it is the variation in the process plus the variation in measurement that results from an inadequate measurement system
Conducting an MSA reduces the likelihood of passing a bad part or rejecting a good part
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The output of the process measured by bull Cycle time bull Dimensional data bull Number of defects and others
Observed Variation
Process Variation
Measurement System
Variation
Reproducibility
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Accuracy (Central Location)
OBSERVED VARIATION
Calibration addresses accuracy
Measurement System Analysis (MSA)
MEASUREMENT SYSTEM ERRORS
Accuracy difference between the observed measurement and the actual measurement
Precision variation that occurs when measuring the same part with the same instrument
MEASUREMENT SYSTEM ERROR
Precise but not
accurate
Accurate but not
precise
Not accurate or
precise
Accurate and
precise
ACCURACY OF MEASUREMENT
Broken down into three components
aStability
The consistency of measurements over time
bBias
A measure of the amount of partiality in the system
cLinearity
A measure of the bias values through the expected
range of measurements
OBSERVED VARIATION
Observed Variation
Process Variation
Measurement System
Variation
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Reproducibility
Accuracy (Central Location)
Calibration Addresses Accuracy
Letrsquos take a closer look at Precision
Measurement System Analysis (MSA)
Measurement System Analysis (MSA)
Error in Resolution The inability to detect small changes
Possible Cause
Wrong measurement device selected - divisions on scale not fine enough to detect changes
Resolution
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Repeatability The inability to get the same answer from repeated measurements made of the same item under absolutely identical conditions
Possible Cause
Lack of standard operating procedures (SOP) lack of training measuring system variablilty
Repeatability
Equipment Variation
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Reproducibility The inability to get the same answer from repeated measurements made under various conditions from different inspectors
Possible Cause
Lack of SOP lack of training
Reproducibility
Appraiser Variation
VARIABLE MSA ndash GAGE RampR STUDY
bull Gage RampR is the combined estimate of
measurement system Repeatability and
Reproducibility
bull Typically a 3-person study is performed Each person randomly measures 10 marked parts per trial
Each person can perform up to 3 trials
bull There are 3 key indicators EV or Equipment Variation
AV or Appraiser Variation
Overall GRR
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
SPECIAL CAUSES
Special cause is when one or more of the process specificationsconditions change
Temperatures
Tools dull
Voltage drops drastically
Material change
Bearings are failing
Special cause variations are the variations that need to be corrected immediately since it affect the process output in unpredictable ways
11
WHY DO WE NEED DATA
Assessment
Assessing the effectiveness of specific process or corrective actions
Evaluation
Determine the quality of a process or product
Improvement
Help us understand where improvement is needed
Control
To help control a process and to ensure it does not move out of control
Prediction
Provide information and trends that enables us to predict when an activity will fail in the future
12
TYPES OF DATA
Data can be grouped into two major categories
Attributes data
Variable data
13
TYPES OF DATA ndash ATTRIBUTE DATA
Attributes data Non-measurable characteristics Can be very subjective
Blush Scratched Color etc
Observations are counted YesNo PresentAbsent MeetsDoesnrsquot meet
Visually inspected Gono-go gauges
If color happens to be an attribute that is being inspected for Typically meet the expected color sample is given Maybe a light and dark compared to sample given The acceptable range is in between A reject is not measured just counted as one
14
Collected through measurement
Is very objective
Can be temperature length width weight force volts amps etc
Uses a measuring tool
Scale
Meters
Inspection should not be done to sort but for data collection and correction of the process
This will allow for quick response and rapid correction minimizing defect quantities
TYPES OF DATA ndash VARIABLE DATA
15
PARETO CHARTS
Vilfredo Pareto
Italyrsquos wealth
80 held by 20 of people
Used when analyzing attributes
Based on results of tally numbers in specific categories
What is a Pareto Chart used for
To display the relative importance of data
To direct efforts to the biggest improvement opportunity by highlighting the vital few in contrast to the useful many
16
CONSTRUCTING A PARETO CHART
Determine the categories and the units for comparison of the data such as frequency cost or time
Total the raw data in each category then determine the grand total by adding the totals of each category
Re-order the categories from largest to smallest
Determine the cumulative percent of each category (ie the sum of each category plus all categories that precede it in the rank order divided by the grand total and multiplied by 100)
17
CONSTRUCTING A PARETO CHART
Draw and label the left-hand vertical axis with the unit of comparison such as frequency cost or time
Draw and label the horizontal axis with the categories List from left to right in rank order
Draw and label the right-hand vertical axis from 0 to 100 percent The 100 percent should line up with the grand total on the left-hand vertical axis
Beginning with the largest category draw in bars for each category representing the total for that category
18
CONSTRUCTING A PARETO CHART
Draw a line graph beginning at the right-hand
corner of the first bar to represent the
cumulative percent for each category as
measured on the right-hand axis
Analyze the chart Usually the top 20 of the
categories will comprise roughly 80 of the
cumulative total
19
PARETO CHART - EXAMPLE
Lets assume we are listing all the rejected products that are removed from a candy manufacturing line in one week
First we put the rejects in specific categories
No wrapper - 10
No center - 37
Wrong shape - 53
Short shot - 6
Wrapper open - 132
Underweight - 4
Overweight ndash 17
Get the total rejects - 259
20
Develop a percentage for each category
No wrapper ndash 10259 = 39
No center ndash 37259 = 143
Wrong shape ndash 53259 = 205
Short shot ndash 6259 = 23
Wrapper open ndash 132259 = 51
Underweight ndash 4259 = 15
Overweight ndash 17259 = 66
PARETO CHART - EXAMPLE
21
Now place the counts in a histogram largest to smallest
0
10
20
30
40
50
60
Wrapper
Open
No Center No Wrapper Underweight
70
80
90
100
51
205
143
66 39
23 15
22
Finally add up each and plot as a line diagram
0
10
20
30
40
50
60
Wrapper
Open
No Center No Wrapper Underweight
70
80
90
100
715
51
205
143
858
66
924
39
963
23
986
15
1001
23
0
10
20
30
40
50
60
Wrapper
Open
No Center No Wrapper Underweight
70
80
90
100
715
51
205
143
858
66
924
39
963
23
986
15
1001
24
CONTROL CHARTS
Control charts are one of the most commonly used methods of Statistical Process Control (SPC) which
monitors the stability of a process
The main features of a control chart include the data points a centreline (mean value) and upper and
lower limits (bounds to indicate where a process output is considered out of control)They visually
display the fluctuations of a particular process variable that easily determine whether these variations
fall within the specified process limits
Control charts
a graphical method for detecting if the underlying distribution of variation of some measurable
characteristic of the product seems to have undergone a shift
monitor a process in real time
Map the output of a production process over time
A control chart always has a central line for the average an upper line for the upper control limit and a
lower line for the lower control limit These lines are determined from historical data
By comparing current data to these lines you can draw conclusions about whether the process
variation is consistent (in control) or is unpredictable
25
CONTROL CHART - PURPOSE
The main purpose of using a control chart is to monitor control and improve
process performance over time by studying variation and its source There are
several functions of a control chart
It centres attention on detecting and monitoring process variation over time
It provides a tool for on-going control of a process
It differentiates special from common causes of variation in order to be a guide for
local or management action
It helps improve a process to perform consistently and predictably to achieve higher
quality lower cost and higher effective capacity
It serves as a common language for discussing process performance
26
TYPES OF CONTROL CHARTS
The basic tool used in SPC is the control chart
There are various types of control charts
Variable Control Chart
Averages and range chart (X-Bar and R Bar Chart)
X bar and s chart
Moving Range Chart
Moving AveragendashMoving Range chart (also called MAndashMR chart)
p chart (also called proportion chart)
c chart (also called count chart)
np chart
u chart
27
POPULARITY OF CONTROL CHARTS
Control charts are a proven technique for improving productivity
Control charts are effective in defect prevention
Control charts prevent unnecessary process
adjustment
Control charts provide diagnostic information
Control charts provide information about process
capability
28
PROCEDURE FOR X ndashBAR AND R BAR CHART
1 Randomly sample ldquonrdquo units throughout the day (can be every 5
minutes every 30 minutes etc - whatever is appropriate for your
case)
2 For each sample calculate ldquoX-BARrdquo to estimate the mean and ldquoR
(range)rdquo to estimate variability NOTE THE RANGE CAN BE USED TO
ESTIMATE THE STANDARD DEVIATION
3 After collecting the 20-25 samples calculate X-BAR-BAR (the
average of all the X-BARs) and R-BAR (the average of all the ranges)
4 Using X-BAR-BAR and R-BAR calculate the control limits for your X-
BAR and R Control Charts
29
X-BAR CONTROL LIMITS
Upper Control Limit (UCL) = (X-BAR-BAR) + A2 (R-BAR)
Lower Control Limit(LCL) = (X-BAR-BAR) - A2 (R-BAR)
R CONTROL LIMITS
Upper Control Limit - D3 (R-BAR)
Lower Control Limit - D4 (R-BAR)
PROCEDURE FOR X ndashBAR AND R BAR CHART
30
CONTROL CHART CONSTANTS
sample size constant constant constant constant constant constant constant
n d2 A2 A3 B3 B4 D3 D4
2 1128 188 2659 0 3267 0 3267
3 1693 1023 1954 0 2568 0 2574
4 2059 0729 1628 0 2266 0 2282
5 2326 0577 1427 0 2089 0 2114
6 2534 0483 1287 003 197 0 2004
7 2704 0419 1182 0118 1882 0076 1924
8 2847 0373 1099 0185 1815 0136 1864
9 297 0337 1032 0239 1761 0184 1816
10 3078 0308 0975 0284 1716 0223 1777
31
5 For the R Control Chart plot all R values on the R Control Chart
to see if all the Ranges are ldquobetween the control limitsrdquo If they are
then your process is considered to be in a state of statistical control
(as far as the variability of the process is concerned)
6 For the X-BAR Control Chart plot all the X-BARs on the X-BAR
control chart to see if all the X-BARs are ldquobetween the control
limitsrdquo If they are then your process is considered in a state of
statistical control (as far as the average of the process is
concerned)
PROCEDURE FOR X ndashBAR AND R BAR CHART
32
SAMPLE DATA FOR X BAR ndashR CHART
Sub Group 1 2 3 4 5 X -Bar Range reg
1 1195 1191 1211 1203 1198 1200 02
2 1201 1198 1198 1197 12 1199 004
3 1193 1206 1198 1196 1202 1199 013
4 1205 1198 1205 1206 1198 1202 008
5 1198 1203 1206 1201 1199 1201 008
6 1202 1205 1196 1201 1195 1200 01
7 1199 1206 1201 1204 1201 1202 007
8 1201 1197 1198 1204 1198 1200 007
9 1198 1204 1198 1204 1204 1202 006
10 1205 1195 1198 1204 1196 1200 01
` X Bar-Bar 1200 009
X Bar Chart
UCL = X BAR-BAR + A2 R Bar
1200 +(0577009) 1205
LCL= X BAR-BAR - A2 R Bar
1200 - (0577009) 1195
R Chart
UCL = D4R Bar 211 009 021
LCL = D3 R Bar 0009 0
33
PLOT DATA ON CONTROL CHARTS
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1 2 3 4 5 6 7 8 9 10
Ave
rage
(X
ba
r)
X Bar Chart
UCL
LCL
X Bar
34
PLOT DATA ON CONTROL CHARTS
001
003
005
007
009
011
013
015
017
019
021
023
025
1 2 3 4 5 6 7 8 9 10
R Chart
UCL
LCL
35
PROCEDURE TO DETERMINE IF PROCESS IS IN A STATE OF
STATISTICAL CONTROL
7 If process is determined to be ldquoNOT STABLErdquo then stop and find out what
an assignable cause might be fix and then repeat the complete process of
collecting new data
8 If the process is determined to be ldquoSTABLErdquo then you may use the
control charts you developed to monitor future production to ensure that the
process REMAINS stable
More Samples for Control charts
36
READING OF CONTROL CHART
Control charts can determine whether a process is behaving in an unusual way The quality of the individual points of a subset is determined unstable if any of the
following occurs
Rule 1 Any point falls beyond 3σ from the centreline(this is represented by the upper and
lower control limits)
Rule 2 Two out of three consecutive points fall beyond 2σ on the same side of the
centreline
Rule 3 Four out of five consecutive points fall beyond 1σ on the same side of the
centreline
Rule 4 Nine or more consecutive points fall on the same side of the centreline
(Ref Next page for sample)
37
READING THE CONTROL CHART
38
CONTROL CHARTS FOR ATTRIBUTES ndashP-CHARTS amp C-CHARTS
Attributes are discrete events yesno or passfail
Use P-Charts for quality characteristics that are discrete and involve yesno or goodbad decisions
Eg
Number of leaking caulking tubes in a box of 48
Number of broken eggs in a carton
Use C-Charts for discrete defects when there can be more than one defect per unit
Eg
Number of stains in a carpet sample cut from a production run
Number of complaints per customer at a hotel
39
P-CHART EXAMPLE A PRODUCTION MANAGER FOR A TIRE COMPANY HAS INSPECTED THE NUMBER OF
DEFECTIVE TIRES IN FIVE RANDOM SAMPLES WITH 20 TIRES IN EACH SAMPLE THE TABLE BELOW SHOWS THE
NUMBER OF DEFECTIVE TIRES IN EACH SAMPLE OF 20 TIRES CALCULATE THE CONTROL LIMITS
Sample Number of
Defective Tires
Number of Tires in each
Sample
Proportion Defective
1 3 20 15
2 2 20 10
3 1 20 05
4 2 20 10
5 2 20 05
Total 9 100 09
01023(064)09σzpLCL
2823(064)09σzpUCL
06420
(09)(91)
n
)p(1pσ
09100
9
Inspected Total
DefectivespCL
p
p
p
Solution
40
P- CONTROL CHART
41
C-CHART EXAMPLE THE NUMBER OF WEEKLY CUSTOMER COMPLAINTS ARE MONITORED IN A LARGE HOTEL USING A C-CHART DEVELOP THREE SIGMA CONTROL LIMITS USING THE DATA TABLE BELOW
Week Number of Complaints
1 3
2 2
3 3
4 1
5 3
6 3
7 2
8 1
9 3
10 1
Total 22
022522322ccLCL
66522322ccUCL
2210
22
samples of
complaintsc
c
c
z
z
Solution
42
C- CONTROL CHART
43
The ability of a process to meet product designtechnical specifications
Assessing capability involves evaluating process variability relative to preset product or service specifications
Process Capability ndash Cp and Cpk
Cp assumes that the process is centered in the specification range
Cpk helps to address a possible lack of centering of the process
PROCESS CAPABILITY
6σ
LSLUSL
width process
width ionspecificatCp
3σ
LSLμ
3σ
μUSLminCpk
44
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
45
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
46
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
47
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
--and an individual part is measured at 520rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
48
GRAPHING THE TOLERANCE AND MEASUREMENTS
Suppose we made and measured several more
units and they were all EXACTLY the same
We wouldnrsquot have very many part problems
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
X
X
X
49
GRAPHING THE TOLERANCE AND MEASUREMENTS
In the real world units are NOT EXACTLY the same
Everything VARIES
The question isnrsquot IF units vary
Itrsquos how much when and why
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
XX
XXX
XXXXX
XXXXXXX
50
The ldquonormal bell curverdquo
Widths heights depths thicknesses weights speeds strengths
and many other types of measurements when charted as a
histogram often form the shape of a bell
A ldquoperfect bellrdquo like a ldquoperfect circlerdquo doesnrsquot occur in nature but
many processes are close enough to make the bell curve useful
(A number of common industrial measurements such as flatness and straightness do NOT tend to distribute in a bell shape their proper statistical analysis is performed using models other than the bell curve)
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
51
What is a ldquostandard deviationrdquo
If we measure the DISTANCE from the CENTER of the bell
to each individual measurement that makes up the bell curve
we can find a TYPICAL DISTANCE
The most commonly used statistic to estimate this distance is the
Standard Deviation (also called ldquoSigmardquo)
Because of the natural shape of the bell curve the area of +1 to ndash1
standard deviations includes about 68 of the curve
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
Typical distance
from the center +1
standard deviation
Typical distance
from the center -1
standard deviation
52
How much of the curve is included in how many standard
deviations
From ndash1 to +1 is about 68 of the bell curve
From ndash2 to +2 is about 95
From ndash3 to +3 is about 9973
From ndash4 to +4 is about 9999
(NOTE We usually show the bell from ndash3 to +3 to make it easier to draw but in concept the ldquotailsrdquo of the bell get very thin and go on forever)
-6 -5 -4 -3 -2 -1 +1 +2 +3 +4 +5 +6 0
53
A
B
What is Cpk It is a measure of how well a process is within a specification
Cpk = A divided by B
A = Distance from process mean to closest spec limit
B = 3 Standard Deviations (also called ldquo3 Sigmardquo)
A bigger Cpk is better because fewer units will be beyond spec
(A bigger ldquoArdquo and a smaller ldquoBrdquo are better)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
54
A
B
ldquoProcess Capabilityrdquo is the ability of a process
to fit its output within the tolerances
hellipa LARGER ldquoArdquo
hellipand a SMALLER ldquoBrdquo
hellipmeans BETTER ldquoProcess Capabilityrdquo
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
55
A
B
An Analogy
Analogy
The bell curve is your automobile
The spec limits are the edges of your garage door
If A = B you are hitting the frame of your garage door with your car
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
56
A
B
How can we make Cpk (A divided by B) better
1 Design the product so a wider tolerance is functional (ldquorobust designrdquo)
2 Choose equipment and methods for a good safety margin (ldquoprocess capabilityrdquo)
3 Correctly adjust but only when needed (ldquocontrolrdquo)
4 Discover ways to narrow the natural variation (ldquoimprovementrdquo)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
57
A
B
What does a very good Cpk do for us
This process is producing good units with a good safety margin
Note that when Cpk = 2 our process mean is 6 standard deviations from
the nearest spec so we say it has ldquo6 Sigma Capabilityrdquo
Specification
Limit
Specification
Limit
This Cpk is
about 2
Very good
Mean
58
A
B
What does a problem Cpk look like
This process is in danger of producing some defects
It is too close to the specification limits
(Remember the bell curve tail goes further than Bhellip hellipwe only show the bell to 3-sigma to make it easier to draw)
Specification
Limit
Specification
Limit
This Cpk is just
slightly greater
than 1 Not good
59
A
B
What does a very bad Cpk look like
A significant part of the ldquotailrdquo is hanging out beyond the spec limits
This process is producing scrap rework and customer rejects
Notice that if distance ldquoArdquo approaches zerohellip
hellipthe Cpk would approach zero andhellip
hellipthe process would become 50 defective
Specification
Limit
Specification
Limit
This Cpk is less
than 1 We desire
a minimum of 133
and ultimately we
want 2 or more
60
-
Q amp A
61
MEASUREMENT SYSTEM ANALYSIS (MSA)
An MSA is a statistical tool used to determine if a measurement system is capable of precise measurement
What is It
Objective or Purpose
bull To determine how much error is in the measurement due to the measurement process itself
bull Quantifies the variability added by the measurement system
bull Applicable to attribute data and variable data
When to Use It
bull On the critical inputs and outputs prior to collecting data for analysis
bull For any new or modified process in order to ensure the quality of the data
Measurement System Analysis is an analysis of the measurement process not an analysis of the people
IMPORTANT
Who Should be Involved
Everyone that measures and makes decisions about these measurements should be involved in the MSA
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The observed variation in process output measurements is not simply the variation in the process itself it is the variation in the process plus the variation in measurement that results from an inadequate measurement system
Conducting an MSA reduces the likelihood of passing a bad part or rejecting a good part
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The output of the process measured by bull Cycle time bull Dimensional data bull Number of defects and others
Observed Variation
Process Variation
Measurement System
Variation
Reproducibility
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Accuracy (Central Location)
OBSERVED VARIATION
Calibration addresses accuracy
Measurement System Analysis (MSA)
MEASUREMENT SYSTEM ERRORS
Accuracy difference between the observed measurement and the actual measurement
Precision variation that occurs when measuring the same part with the same instrument
MEASUREMENT SYSTEM ERROR
Precise but not
accurate
Accurate but not
precise
Not accurate or
precise
Accurate and
precise
ACCURACY OF MEASUREMENT
Broken down into three components
aStability
The consistency of measurements over time
bBias
A measure of the amount of partiality in the system
cLinearity
A measure of the bias values through the expected
range of measurements
OBSERVED VARIATION
Observed Variation
Process Variation
Measurement System
Variation
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Reproducibility
Accuracy (Central Location)
Calibration Addresses Accuracy
Letrsquos take a closer look at Precision
Measurement System Analysis (MSA)
Measurement System Analysis (MSA)
Error in Resolution The inability to detect small changes
Possible Cause
Wrong measurement device selected - divisions on scale not fine enough to detect changes
Resolution
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Repeatability The inability to get the same answer from repeated measurements made of the same item under absolutely identical conditions
Possible Cause
Lack of standard operating procedures (SOP) lack of training measuring system variablilty
Repeatability
Equipment Variation
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Reproducibility The inability to get the same answer from repeated measurements made under various conditions from different inspectors
Possible Cause
Lack of SOP lack of training
Reproducibility
Appraiser Variation
VARIABLE MSA ndash GAGE RampR STUDY
bull Gage RampR is the combined estimate of
measurement system Repeatability and
Reproducibility
bull Typically a 3-person study is performed Each person randomly measures 10 marked parts per trial
Each person can perform up to 3 trials
bull There are 3 key indicators EV or Equipment Variation
AV or Appraiser Variation
Overall GRR
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
WHY DO WE NEED DATA
Assessment
Assessing the effectiveness of specific process or corrective actions
Evaluation
Determine the quality of a process or product
Improvement
Help us understand where improvement is needed
Control
To help control a process and to ensure it does not move out of control
Prediction
Provide information and trends that enables us to predict when an activity will fail in the future
12
TYPES OF DATA
Data can be grouped into two major categories
Attributes data
Variable data
13
TYPES OF DATA ndash ATTRIBUTE DATA
Attributes data Non-measurable characteristics Can be very subjective
Blush Scratched Color etc
Observations are counted YesNo PresentAbsent MeetsDoesnrsquot meet
Visually inspected Gono-go gauges
If color happens to be an attribute that is being inspected for Typically meet the expected color sample is given Maybe a light and dark compared to sample given The acceptable range is in between A reject is not measured just counted as one
14
Collected through measurement
Is very objective
Can be temperature length width weight force volts amps etc
Uses a measuring tool
Scale
Meters
Inspection should not be done to sort but for data collection and correction of the process
This will allow for quick response and rapid correction minimizing defect quantities
TYPES OF DATA ndash VARIABLE DATA
15
PARETO CHARTS
Vilfredo Pareto
Italyrsquos wealth
80 held by 20 of people
Used when analyzing attributes
Based on results of tally numbers in specific categories
What is a Pareto Chart used for
To display the relative importance of data
To direct efforts to the biggest improvement opportunity by highlighting the vital few in contrast to the useful many
16
CONSTRUCTING A PARETO CHART
Determine the categories and the units for comparison of the data such as frequency cost or time
Total the raw data in each category then determine the grand total by adding the totals of each category
Re-order the categories from largest to smallest
Determine the cumulative percent of each category (ie the sum of each category plus all categories that precede it in the rank order divided by the grand total and multiplied by 100)
17
CONSTRUCTING A PARETO CHART
Draw and label the left-hand vertical axis with the unit of comparison such as frequency cost or time
Draw and label the horizontal axis with the categories List from left to right in rank order
Draw and label the right-hand vertical axis from 0 to 100 percent The 100 percent should line up with the grand total on the left-hand vertical axis
Beginning with the largest category draw in bars for each category representing the total for that category
18
CONSTRUCTING A PARETO CHART
Draw a line graph beginning at the right-hand
corner of the first bar to represent the
cumulative percent for each category as
measured on the right-hand axis
Analyze the chart Usually the top 20 of the
categories will comprise roughly 80 of the
cumulative total
19
PARETO CHART - EXAMPLE
Lets assume we are listing all the rejected products that are removed from a candy manufacturing line in one week
First we put the rejects in specific categories
No wrapper - 10
No center - 37
Wrong shape - 53
Short shot - 6
Wrapper open - 132
Underweight - 4
Overweight ndash 17
Get the total rejects - 259
20
Develop a percentage for each category
No wrapper ndash 10259 = 39
No center ndash 37259 = 143
Wrong shape ndash 53259 = 205
Short shot ndash 6259 = 23
Wrapper open ndash 132259 = 51
Underweight ndash 4259 = 15
Overweight ndash 17259 = 66
PARETO CHART - EXAMPLE
21
Now place the counts in a histogram largest to smallest
0
10
20
30
40
50
60
Wrapper
Open
No Center No Wrapper Underweight
70
80
90
100
51
205
143
66 39
23 15
22
Finally add up each and plot as a line diagram
0
10
20
30
40
50
60
Wrapper
Open
No Center No Wrapper Underweight
70
80
90
100
715
51
205
143
858
66
924
39
963
23
986
15
1001
23
0
10
20
30
40
50
60
Wrapper
Open
No Center No Wrapper Underweight
70
80
90
100
715
51
205
143
858
66
924
39
963
23
986
15
1001
24
CONTROL CHARTS
Control charts are one of the most commonly used methods of Statistical Process Control (SPC) which
monitors the stability of a process
The main features of a control chart include the data points a centreline (mean value) and upper and
lower limits (bounds to indicate where a process output is considered out of control)They visually
display the fluctuations of a particular process variable that easily determine whether these variations
fall within the specified process limits
Control charts
a graphical method for detecting if the underlying distribution of variation of some measurable
characteristic of the product seems to have undergone a shift
monitor a process in real time
Map the output of a production process over time
A control chart always has a central line for the average an upper line for the upper control limit and a
lower line for the lower control limit These lines are determined from historical data
By comparing current data to these lines you can draw conclusions about whether the process
variation is consistent (in control) or is unpredictable
25
CONTROL CHART - PURPOSE
The main purpose of using a control chart is to monitor control and improve
process performance over time by studying variation and its source There are
several functions of a control chart
It centres attention on detecting and monitoring process variation over time
It provides a tool for on-going control of a process
It differentiates special from common causes of variation in order to be a guide for
local or management action
It helps improve a process to perform consistently and predictably to achieve higher
quality lower cost and higher effective capacity
It serves as a common language for discussing process performance
26
TYPES OF CONTROL CHARTS
The basic tool used in SPC is the control chart
There are various types of control charts
Variable Control Chart
Averages and range chart (X-Bar and R Bar Chart)
X bar and s chart
Moving Range Chart
Moving AveragendashMoving Range chart (also called MAndashMR chart)
p chart (also called proportion chart)
c chart (also called count chart)
np chart
u chart
27
POPULARITY OF CONTROL CHARTS
Control charts are a proven technique for improving productivity
Control charts are effective in defect prevention
Control charts prevent unnecessary process
adjustment
Control charts provide diagnostic information
Control charts provide information about process
capability
28
PROCEDURE FOR X ndashBAR AND R BAR CHART
1 Randomly sample ldquonrdquo units throughout the day (can be every 5
minutes every 30 minutes etc - whatever is appropriate for your
case)
2 For each sample calculate ldquoX-BARrdquo to estimate the mean and ldquoR
(range)rdquo to estimate variability NOTE THE RANGE CAN BE USED TO
ESTIMATE THE STANDARD DEVIATION
3 After collecting the 20-25 samples calculate X-BAR-BAR (the
average of all the X-BARs) and R-BAR (the average of all the ranges)
4 Using X-BAR-BAR and R-BAR calculate the control limits for your X-
BAR and R Control Charts
29
X-BAR CONTROL LIMITS
Upper Control Limit (UCL) = (X-BAR-BAR) + A2 (R-BAR)
Lower Control Limit(LCL) = (X-BAR-BAR) - A2 (R-BAR)
R CONTROL LIMITS
Upper Control Limit - D3 (R-BAR)
Lower Control Limit - D4 (R-BAR)
PROCEDURE FOR X ndashBAR AND R BAR CHART
30
CONTROL CHART CONSTANTS
sample size constant constant constant constant constant constant constant
n d2 A2 A3 B3 B4 D3 D4
2 1128 188 2659 0 3267 0 3267
3 1693 1023 1954 0 2568 0 2574
4 2059 0729 1628 0 2266 0 2282
5 2326 0577 1427 0 2089 0 2114
6 2534 0483 1287 003 197 0 2004
7 2704 0419 1182 0118 1882 0076 1924
8 2847 0373 1099 0185 1815 0136 1864
9 297 0337 1032 0239 1761 0184 1816
10 3078 0308 0975 0284 1716 0223 1777
31
5 For the R Control Chart plot all R values on the R Control Chart
to see if all the Ranges are ldquobetween the control limitsrdquo If they are
then your process is considered to be in a state of statistical control
(as far as the variability of the process is concerned)
6 For the X-BAR Control Chart plot all the X-BARs on the X-BAR
control chart to see if all the X-BARs are ldquobetween the control
limitsrdquo If they are then your process is considered in a state of
statistical control (as far as the average of the process is
concerned)
PROCEDURE FOR X ndashBAR AND R BAR CHART
32
SAMPLE DATA FOR X BAR ndashR CHART
Sub Group 1 2 3 4 5 X -Bar Range reg
1 1195 1191 1211 1203 1198 1200 02
2 1201 1198 1198 1197 12 1199 004
3 1193 1206 1198 1196 1202 1199 013
4 1205 1198 1205 1206 1198 1202 008
5 1198 1203 1206 1201 1199 1201 008
6 1202 1205 1196 1201 1195 1200 01
7 1199 1206 1201 1204 1201 1202 007
8 1201 1197 1198 1204 1198 1200 007
9 1198 1204 1198 1204 1204 1202 006
10 1205 1195 1198 1204 1196 1200 01
` X Bar-Bar 1200 009
X Bar Chart
UCL = X BAR-BAR + A2 R Bar
1200 +(0577009) 1205
LCL= X BAR-BAR - A2 R Bar
1200 - (0577009) 1195
R Chart
UCL = D4R Bar 211 009 021
LCL = D3 R Bar 0009 0
33
PLOT DATA ON CONTROL CHARTS
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1 2 3 4 5 6 7 8 9 10
Ave
rage
(X
ba
r)
X Bar Chart
UCL
LCL
X Bar
34
PLOT DATA ON CONTROL CHARTS
001
003
005
007
009
011
013
015
017
019
021
023
025
1 2 3 4 5 6 7 8 9 10
R Chart
UCL
LCL
35
PROCEDURE TO DETERMINE IF PROCESS IS IN A STATE OF
STATISTICAL CONTROL
7 If process is determined to be ldquoNOT STABLErdquo then stop and find out what
an assignable cause might be fix and then repeat the complete process of
collecting new data
8 If the process is determined to be ldquoSTABLErdquo then you may use the
control charts you developed to monitor future production to ensure that the
process REMAINS stable
More Samples for Control charts
36
READING OF CONTROL CHART
Control charts can determine whether a process is behaving in an unusual way The quality of the individual points of a subset is determined unstable if any of the
following occurs
Rule 1 Any point falls beyond 3σ from the centreline(this is represented by the upper and
lower control limits)
Rule 2 Two out of three consecutive points fall beyond 2σ on the same side of the
centreline
Rule 3 Four out of five consecutive points fall beyond 1σ on the same side of the
centreline
Rule 4 Nine or more consecutive points fall on the same side of the centreline
(Ref Next page for sample)
37
READING THE CONTROL CHART
38
CONTROL CHARTS FOR ATTRIBUTES ndashP-CHARTS amp C-CHARTS
Attributes are discrete events yesno or passfail
Use P-Charts for quality characteristics that are discrete and involve yesno or goodbad decisions
Eg
Number of leaking caulking tubes in a box of 48
Number of broken eggs in a carton
Use C-Charts for discrete defects when there can be more than one defect per unit
Eg
Number of stains in a carpet sample cut from a production run
Number of complaints per customer at a hotel
39
P-CHART EXAMPLE A PRODUCTION MANAGER FOR A TIRE COMPANY HAS INSPECTED THE NUMBER OF
DEFECTIVE TIRES IN FIVE RANDOM SAMPLES WITH 20 TIRES IN EACH SAMPLE THE TABLE BELOW SHOWS THE
NUMBER OF DEFECTIVE TIRES IN EACH SAMPLE OF 20 TIRES CALCULATE THE CONTROL LIMITS
Sample Number of
Defective Tires
Number of Tires in each
Sample
Proportion Defective
1 3 20 15
2 2 20 10
3 1 20 05
4 2 20 10
5 2 20 05
Total 9 100 09
01023(064)09σzpLCL
2823(064)09σzpUCL
06420
(09)(91)
n
)p(1pσ
09100
9
Inspected Total
DefectivespCL
p
p
p
Solution
40
P- CONTROL CHART
41
C-CHART EXAMPLE THE NUMBER OF WEEKLY CUSTOMER COMPLAINTS ARE MONITORED IN A LARGE HOTEL USING A C-CHART DEVELOP THREE SIGMA CONTROL LIMITS USING THE DATA TABLE BELOW
Week Number of Complaints
1 3
2 2
3 3
4 1
5 3
6 3
7 2
8 1
9 3
10 1
Total 22
022522322ccLCL
66522322ccUCL
2210
22
samples of
complaintsc
c
c
z
z
Solution
42
C- CONTROL CHART
43
The ability of a process to meet product designtechnical specifications
Assessing capability involves evaluating process variability relative to preset product or service specifications
Process Capability ndash Cp and Cpk
Cp assumes that the process is centered in the specification range
Cpk helps to address a possible lack of centering of the process
PROCESS CAPABILITY
6σ
LSLUSL
width process
width ionspecificatCp
3σ
LSLμ
3σ
μUSLminCpk
44
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
45
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
46
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
47
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
--and an individual part is measured at 520rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
48
GRAPHING THE TOLERANCE AND MEASUREMENTS
Suppose we made and measured several more
units and they were all EXACTLY the same
We wouldnrsquot have very many part problems
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
X
X
X
49
GRAPHING THE TOLERANCE AND MEASUREMENTS
In the real world units are NOT EXACTLY the same
Everything VARIES
The question isnrsquot IF units vary
Itrsquos how much when and why
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
XX
XXX
XXXXX
XXXXXXX
50
The ldquonormal bell curverdquo
Widths heights depths thicknesses weights speeds strengths
and many other types of measurements when charted as a
histogram often form the shape of a bell
A ldquoperfect bellrdquo like a ldquoperfect circlerdquo doesnrsquot occur in nature but
many processes are close enough to make the bell curve useful
(A number of common industrial measurements such as flatness and straightness do NOT tend to distribute in a bell shape their proper statistical analysis is performed using models other than the bell curve)
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
51
What is a ldquostandard deviationrdquo
If we measure the DISTANCE from the CENTER of the bell
to each individual measurement that makes up the bell curve
we can find a TYPICAL DISTANCE
The most commonly used statistic to estimate this distance is the
Standard Deviation (also called ldquoSigmardquo)
Because of the natural shape of the bell curve the area of +1 to ndash1
standard deviations includes about 68 of the curve
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
Typical distance
from the center +1
standard deviation
Typical distance
from the center -1
standard deviation
52
How much of the curve is included in how many standard
deviations
From ndash1 to +1 is about 68 of the bell curve
From ndash2 to +2 is about 95
From ndash3 to +3 is about 9973
From ndash4 to +4 is about 9999
(NOTE We usually show the bell from ndash3 to +3 to make it easier to draw but in concept the ldquotailsrdquo of the bell get very thin and go on forever)
-6 -5 -4 -3 -2 -1 +1 +2 +3 +4 +5 +6 0
53
A
B
What is Cpk It is a measure of how well a process is within a specification
Cpk = A divided by B
A = Distance from process mean to closest spec limit
B = 3 Standard Deviations (also called ldquo3 Sigmardquo)
A bigger Cpk is better because fewer units will be beyond spec
(A bigger ldquoArdquo and a smaller ldquoBrdquo are better)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
54
A
B
ldquoProcess Capabilityrdquo is the ability of a process
to fit its output within the tolerances
hellipa LARGER ldquoArdquo
hellipand a SMALLER ldquoBrdquo
hellipmeans BETTER ldquoProcess Capabilityrdquo
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
55
A
B
An Analogy
Analogy
The bell curve is your automobile
The spec limits are the edges of your garage door
If A = B you are hitting the frame of your garage door with your car
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
56
A
B
How can we make Cpk (A divided by B) better
1 Design the product so a wider tolerance is functional (ldquorobust designrdquo)
2 Choose equipment and methods for a good safety margin (ldquoprocess capabilityrdquo)
3 Correctly adjust but only when needed (ldquocontrolrdquo)
4 Discover ways to narrow the natural variation (ldquoimprovementrdquo)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
57
A
B
What does a very good Cpk do for us
This process is producing good units with a good safety margin
Note that when Cpk = 2 our process mean is 6 standard deviations from
the nearest spec so we say it has ldquo6 Sigma Capabilityrdquo
Specification
Limit
Specification
Limit
This Cpk is
about 2
Very good
Mean
58
A
B
What does a problem Cpk look like
This process is in danger of producing some defects
It is too close to the specification limits
(Remember the bell curve tail goes further than Bhellip hellipwe only show the bell to 3-sigma to make it easier to draw)
Specification
Limit
Specification
Limit
This Cpk is just
slightly greater
than 1 Not good
59
A
B
What does a very bad Cpk look like
A significant part of the ldquotailrdquo is hanging out beyond the spec limits
This process is producing scrap rework and customer rejects
Notice that if distance ldquoArdquo approaches zerohellip
hellipthe Cpk would approach zero andhellip
hellipthe process would become 50 defective
Specification
Limit
Specification
Limit
This Cpk is less
than 1 We desire
a minimum of 133
and ultimately we
want 2 or more
60
-
Q amp A
61
MEASUREMENT SYSTEM ANALYSIS (MSA)
An MSA is a statistical tool used to determine if a measurement system is capable of precise measurement
What is It
Objective or Purpose
bull To determine how much error is in the measurement due to the measurement process itself
bull Quantifies the variability added by the measurement system
bull Applicable to attribute data and variable data
When to Use It
bull On the critical inputs and outputs prior to collecting data for analysis
bull For any new or modified process in order to ensure the quality of the data
Measurement System Analysis is an analysis of the measurement process not an analysis of the people
IMPORTANT
Who Should be Involved
Everyone that measures and makes decisions about these measurements should be involved in the MSA
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The observed variation in process output measurements is not simply the variation in the process itself it is the variation in the process plus the variation in measurement that results from an inadequate measurement system
Conducting an MSA reduces the likelihood of passing a bad part or rejecting a good part
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The output of the process measured by bull Cycle time bull Dimensional data bull Number of defects and others
Observed Variation
Process Variation
Measurement System
Variation
Reproducibility
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Accuracy (Central Location)
OBSERVED VARIATION
Calibration addresses accuracy
Measurement System Analysis (MSA)
MEASUREMENT SYSTEM ERRORS
Accuracy difference between the observed measurement and the actual measurement
Precision variation that occurs when measuring the same part with the same instrument
MEASUREMENT SYSTEM ERROR
Precise but not
accurate
Accurate but not
precise
Not accurate or
precise
Accurate and
precise
ACCURACY OF MEASUREMENT
Broken down into three components
aStability
The consistency of measurements over time
bBias
A measure of the amount of partiality in the system
cLinearity
A measure of the bias values through the expected
range of measurements
OBSERVED VARIATION
Observed Variation
Process Variation
Measurement System
Variation
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Reproducibility
Accuracy (Central Location)
Calibration Addresses Accuracy
Letrsquos take a closer look at Precision
Measurement System Analysis (MSA)
Measurement System Analysis (MSA)
Error in Resolution The inability to detect small changes
Possible Cause
Wrong measurement device selected - divisions on scale not fine enough to detect changes
Resolution
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Repeatability The inability to get the same answer from repeated measurements made of the same item under absolutely identical conditions
Possible Cause
Lack of standard operating procedures (SOP) lack of training measuring system variablilty
Repeatability
Equipment Variation
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Reproducibility The inability to get the same answer from repeated measurements made under various conditions from different inspectors
Possible Cause
Lack of SOP lack of training
Reproducibility
Appraiser Variation
VARIABLE MSA ndash GAGE RampR STUDY
bull Gage RampR is the combined estimate of
measurement system Repeatability and
Reproducibility
bull Typically a 3-person study is performed Each person randomly measures 10 marked parts per trial
Each person can perform up to 3 trials
bull There are 3 key indicators EV or Equipment Variation
AV or Appraiser Variation
Overall GRR
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
TYPES OF DATA
Data can be grouped into two major categories
Attributes data
Variable data
13
TYPES OF DATA ndash ATTRIBUTE DATA
Attributes data Non-measurable characteristics Can be very subjective
Blush Scratched Color etc
Observations are counted YesNo PresentAbsent MeetsDoesnrsquot meet
Visually inspected Gono-go gauges
If color happens to be an attribute that is being inspected for Typically meet the expected color sample is given Maybe a light and dark compared to sample given The acceptable range is in between A reject is not measured just counted as one
14
Collected through measurement
Is very objective
Can be temperature length width weight force volts amps etc
Uses a measuring tool
Scale
Meters
Inspection should not be done to sort but for data collection and correction of the process
This will allow for quick response and rapid correction minimizing defect quantities
TYPES OF DATA ndash VARIABLE DATA
15
PARETO CHARTS
Vilfredo Pareto
Italyrsquos wealth
80 held by 20 of people
Used when analyzing attributes
Based on results of tally numbers in specific categories
What is a Pareto Chart used for
To display the relative importance of data
To direct efforts to the biggest improvement opportunity by highlighting the vital few in contrast to the useful many
16
CONSTRUCTING A PARETO CHART
Determine the categories and the units for comparison of the data such as frequency cost or time
Total the raw data in each category then determine the grand total by adding the totals of each category
Re-order the categories from largest to smallest
Determine the cumulative percent of each category (ie the sum of each category plus all categories that precede it in the rank order divided by the grand total and multiplied by 100)
17
CONSTRUCTING A PARETO CHART
Draw and label the left-hand vertical axis with the unit of comparison such as frequency cost or time
Draw and label the horizontal axis with the categories List from left to right in rank order
Draw and label the right-hand vertical axis from 0 to 100 percent The 100 percent should line up with the grand total on the left-hand vertical axis
Beginning with the largest category draw in bars for each category representing the total for that category
18
CONSTRUCTING A PARETO CHART
Draw a line graph beginning at the right-hand
corner of the first bar to represent the
cumulative percent for each category as
measured on the right-hand axis
Analyze the chart Usually the top 20 of the
categories will comprise roughly 80 of the
cumulative total
19
PARETO CHART - EXAMPLE
Lets assume we are listing all the rejected products that are removed from a candy manufacturing line in one week
First we put the rejects in specific categories
No wrapper - 10
No center - 37
Wrong shape - 53
Short shot - 6
Wrapper open - 132
Underweight - 4
Overweight ndash 17
Get the total rejects - 259
20
Develop a percentage for each category
No wrapper ndash 10259 = 39
No center ndash 37259 = 143
Wrong shape ndash 53259 = 205
Short shot ndash 6259 = 23
Wrapper open ndash 132259 = 51
Underweight ndash 4259 = 15
Overweight ndash 17259 = 66
PARETO CHART - EXAMPLE
21
Now place the counts in a histogram largest to smallest
0
10
20
30
40
50
60
Wrapper
Open
No Center No Wrapper Underweight
70
80
90
100
51
205
143
66 39
23 15
22
Finally add up each and plot as a line diagram
0
10
20
30
40
50
60
Wrapper
Open
No Center No Wrapper Underweight
70
80
90
100
715
51
205
143
858
66
924
39
963
23
986
15
1001
23
0
10
20
30
40
50
60
Wrapper
Open
No Center No Wrapper Underweight
70
80
90
100
715
51
205
143
858
66
924
39
963
23
986
15
1001
24
CONTROL CHARTS
Control charts are one of the most commonly used methods of Statistical Process Control (SPC) which
monitors the stability of a process
The main features of a control chart include the data points a centreline (mean value) and upper and
lower limits (bounds to indicate where a process output is considered out of control)They visually
display the fluctuations of a particular process variable that easily determine whether these variations
fall within the specified process limits
Control charts
a graphical method for detecting if the underlying distribution of variation of some measurable
characteristic of the product seems to have undergone a shift
monitor a process in real time
Map the output of a production process over time
A control chart always has a central line for the average an upper line for the upper control limit and a
lower line for the lower control limit These lines are determined from historical data
By comparing current data to these lines you can draw conclusions about whether the process
variation is consistent (in control) or is unpredictable
25
CONTROL CHART - PURPOSE
The main purpose of using a control chart is to monitor control and improve
process performance over time by studying variation and its source There are
several functions of a control chart
It centres attention on detecting and monitoring process variation over time
It provides a tool for on-going control of a process
It differentiates special from common causes of variation in order to be a guide for
local or management action
It helps improve a process to perform consistently and predictably to achieve higher
quality lower cost and higher effective capacity
It serves as a common language for discussing process performance
26
TYPES OF CONTROL CHARTS
The basic tool used in SPC is the control chart
There are various types of control charts
Variable Control Chart
Averages and range chart (X-Bar and R Bar Chart)
X bar and s chart
Moving Range Chart
Moving AveragendashMoving Range chart (also called MAndashMR chart)
p chart (also called proportion chart)
c chart (also called count chart)
np chart
u chart
27
POPULARITY OF CONTROL CHARTS
Control charts are a proven technique for improving productivity
Control charts are effective in defect prevention
Control charts prevent unnecessary process
adjustment
Control charts provide diagnostic information
Control charts provide information about process
capability
28
PROCEDURE FOR X ndashBAR AND R BAR CHART
1 Randomly sample ldquonrdquo units throughout the day (can be every 5
minutes every 30 minutes etc - whatever is appropriate for your
case)
2 For each sample calculate ldquoX-BARrdquo to estimate the mean and ldquoR
(range)rdquo to estimate variability NOTE THE RANGE CAN BE USED TO
ESTIMATE THE STANDARD DEVIATION
3 After collecting the 20-25 samples calculate X-BAR-BAR (the
average of all the X-BARs) and R-BAR (the average of all the ranges)
4 Using X-BAR-BAR and R-BAR calculate the control limits for your X-
BAR and R Control Charts
29
X-BAR CONTROL LIMITS
Upper Control Limit (UCL) = (X-BAR-BAR) + A2 (R-BAR)
Lower Control Limit(LCL) = (X-BAR-BAR) - A2 (R-BAR)
R CONTROL LIMITS
Upper Control Limit - D3 (R-BAR)
Lower Control Limit - D4 (R-BAR)
PROCEDURE FOR X ndashBAR AND R BAR CHART
30
CONTROL CHART CONSTANTS
sample size constant constant constant constant constant constant constant
n d2 A2 A3 B3 B4 D3 D4
2 1128 188 2659 0 3267 0 3267
3 1693 1023 1954 0 2568 0 2574
4 2059 0729 1628 0 2266 0 2282
5 2326 0577 1427 0 2089 0 2114
6 2534 0483 1287 003 197 0 2004
7 2704 0419 1182 0118 1882 0076 1924
8 2847 0373 1099 0185 1815 0136 1864
9 297 0337 1032 0239 1761 0184 1816
10 3078 0308 0975 0284 1716 0223 1777
31
5 For the R Control Chart plot all R values on the R Control Chart
to see if all the Ranges are ldquobetween the control limitsrdquo If they are
then your process is considered to be in a state of statistical control
(as far as the variability of the process is concerned)
6 For the X-BAR Control Chart plot all the X-BARs on the X-BAR
control chart to see if all the X-BARs are ldquobetween the control
limitsrdquo If they are then your process is considered in a state of
statistical control (as far as the average of the process is
concerned)
PROCEDURE FOR X ndashBAR AND R BAR CHART
32
SAMPLE DATA FOR X BAR ndashR CHART
Sub Group 1 2 3 4 5 X -Bar Range reg
1 1195 1191 1211 1203 1198 1200 02
2 1201 1198 1198 1197 12 1199 004
3 1193 1206 1198 1196 1202 1199 013
4 1205 1198 1205 1206 1198 1202 008
5 1198 1203 1206 1201 1199 1201 008
6 1202 1205 1196 1201 1195 1200 01
7 1199 1206 1201 1204 1201 1202 007
8 1201 1197 1198 1204 1198 1200 007
9 1198 1204 1198 1204 1204 1202 006
10 1205 1195 1198 1204 1196 1200 01
` X Bar-Bar 1200 009
X Bar Chart
UCL = X BAR-BAR + A2 R Bar
1200 +(0577009) 1205
LCL= X BAR-BAR - A2 R Bar
1200 - (0577009) 1195
R Chart
UCL = D4R Bar 211 009 021
LCL = D3 R Bar 0009 0
33
PLOT DATA ON CONTROL CHARTS
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1 2 3 4 5 6 7 8 9 10
Ave
rage
(X
ba
r)
X Bar Chart
UCL
LCL
X Bar
34
PLOT DATA ON CONTROL CHARTS
001
003
005
007
009
011
013
015
017
019
021
023
025
1 2 3 4 5 6 7 8 9 10
R Chart
UCL
LCL
35
PROCEDURE TO DETERMINE IF PROCESS IS IN A STATE OF
STATISTICAL CONTROL
7 If process is determined to be ldquoNOT STABLErdquo then stop and find out what
an assignable cause might be fix and then repeat the complete process of
collecting new data
8 If the process is determined to be ldquoSTABLErdquo then you may use the
control charts you developed to monitor future production to ensure that the
process REMAINS stable
More Samples for Control charts
36
READING OF CONTROL CHART
Control charts can determine whether a process is behaving in an unusual way The quality of the individual points of a subset is determined unstable if any of the
following occurs
Rule 1 Any point falls beyond 3σ from the centreline(this is represented by the upper and
lower control limits)
Rule 2 Two out of three consecutive points fall beyond 2σ on the same side of the
centreline
Rule 3 Four out of five consecutive points fall beyond 1σ on the same side of the
centreline
Rule 4 Nine or more consecutive points fall on the same side of the centreline
(Ref Next page for sample)
37
READING THE CONTROL CHART
38
CONTROL CHARTS FOR ATTRIBUTES ndashP-CHARTS amp C-CHARTS
Attributes are discrete events yesno or passfail
Use P-Charts for quality characteristics that are discrete and involve yesno or goodbad decisions
Eg
Number of leaking caulking tubes in a box of 48
Number of broken eggs in a carton
Use C-Charts for discrete defects when there can be more than one defect per unit
Eg
Number of stains in a carpet sample cut from a production run
Number of complaints per customer at a hotel
39
P-CHART EXAMPLE A PRODUCTION MANAGER FOR A TIRE COMPANY HAS INSPECTED THE NUMBER OF
DEFECTIVE TIRES IN FIVE RANDOM SAMPLES WITH 20 TIRES IN EACH SAMPLE THE TABLE BELOW SHOWS THE
NUMBER OF DEFECTIVE TIRES IN EACH SAMPLE OF 20 TIRES CALCULATE THE CONTROL LIMITS
Sample Number of
Defective Tires
Number of Tires in each
Sample
Proportion Defective
1 3 20 15
2 2 20 10
3 1 20 05
4 2 20 10
5 2 20 05
Total 9 100 09
01023(064)09σzpLCL
2823(064)09σzpUCL
06420
(09)(91)
n
)p(1pσ
09100
9
Inspected Total
DefectivespCL
p
p
p
Solution
40
P- CONTROL CHART
41
C-CHART EXAMPLE THE NUMBER OF WEEKLY CUSTOMER COMPLAINTS ARE MONITORED IN A LARGE HOTEL USING A C-CHART DEVELOP THREE SIGMA CONTROL LIMITS USING THE DATA TABLE BELOW
Week Number of Complaints
1 3
2 2
3 3
4 1
5 3
6 3
7 2
8 1
9 3
10 1
Total 22
022522322ccLCL
66522322ccUCL
2210
22
samples of
complaintsc
c
c
z
z
Solution
42
C- CONTROL CHART
43
The ability of a process to meet product designtechnical specifications
Assessing capability involves evaluating process variability relative to preset product or service specifications
Process Capability ndash Cp and Cpk
Cp assumes that the process is centered in the specification range
Cpk helps to address a possible lack of centering of the process
PROCESS CAPABILITY
6σ
LSLUSL
width process
width ionspecificatCp
3σ
LSLμ
3σ
μUSLminCpk
44
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
45
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
46
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
47
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
--and an individual part is measured at 520rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
48
GRAPHING THE TOLERANCE AND MEASUREMENTS
Suppose we made and measured several more
units and they were all EXACTLY the same
We wouldnrsquot have very many part problems
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
X
X
X
49
GRAPHING THE TOLERANCE AND MEASUREMENTS
In the real world units are NOT EXACTLY the same
Everything VARIES
The question isnrsquot IF units vary
Itrsquos how much when and why
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
XX
XXX
XXXXX
XXXXXXX
50
The ldquonormal bell curverdquo
Widths heights depths thicknesses weights speeds strengths
and many other types of measurements when charted as a
histogram often form the shape of a bell
A ldquoperfect bellrdquo like a ldquoperfect circlerdquo doesnrsquot occur in nature but
many processes are close enough to make the bell curve useful
(A number of common industrial measurements such as flatness and straightness do NOT tend to distribute in a bell shape their proper statistical analysis is performed using models other than the bell curve)
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
51
What is a ldquostandard deviationrdquo
If we measure the DISTANCE from the CENTER of the bell
to each individual measurement that makes up the bell curve
we can find a TYPICAL DISTANCE
The most commonly used statistic to estimate this distance is the
Standard Deviation (also called ldquoSigmardquo)
Because of the natural shape of the bell curve the area of +1 to ndash1
standard deviations includes about 68 of the curve
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
Typical distance
from the center +1
standard deviation
Typical distance
from the center -1
standard deviation
52
How much of the curve is included in how many standard
deviations
From ndash1 to +1 is about 68 of the bell curve
From ndash2 to +2 is about 95
From ndash3 to +3 is about 9973
From ndash4 to +4 is about 9999
(NOTE We usually show the bell from ndash3 to +3 to make it easier to draw but in concept the ldquotailsrdquo of the bell get very thin and go on forever)
-6 -5 -4 -3 -2 -1 +1 +2 +3 +4 +5 +6 0
53
A
B
What is Cpk It is a measure of how well a process is within a specification
Cpk = A divided by B
A = Distance from process mean to closest spec limit
B = 3 Standard Deviations (also called ldquo3 Sigmardquo)
A bigger Cpk is better because fewer units will be beyond spec
(A bigger ldquoArdquo and a smaller ldquoBrdquo are better)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
54
A
B
ldquoProcess Capabilityrdquo is the ability of a process
to fit its output within the tolerances
hellipa LARGER ldquoArdquo
hellipand a SMALLER ldquoBrdquo
hellipmeans BETTER ldquoProcess Capabilityrdquo
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
55
A
B
An Analogy
Analogy
The bell curve is your automobile
The spec limits are the edges of your garage door
If A = B you are hitting the frame of your garage door with your car
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
56
A
B
How can we make Cpk (A divided by B) better
1 Design the product so a wider tolerance is functional (ldquorobust designrdquo)
2 Choose equipment and methods for a good safety margin (ldquoprocess capabilityrdquo)
3 Correctly adjust but only when needed (ldquocontrolrdquo)
4 Discover ways to narrow the natural variation (ldquoimprovementrdquo)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
57
A
B
What does a very good Cpk do for us
This process is producing good units with a good safety margin
Note that when Cpk = 2 our process mean is 6 standard deviations from
the nearest spec so we say it has ldquo6 Sigma Capabilityrdquo
Specification
Limit
Specification
Limit
This Cpk is
about 2
Very good
Mean
58
A
B
What does a problem Cpk look like
This process is in danger of producing some defects
It is too close to the specification limits
(Remember the bell curve tail goes further than Bhellip hellipwe only show the bell to 3-sigma to make it easier to draw)
Specification
Limit
Specification
Limit
This Cpk is just
slightly greater
than 1 Not good
59
A
B
What does a very bad Cpk look like
A significant part of the ldquotailrdquo is hanging out beyond the spec limits
This process is producing scrap rework and customer rejects
Notice that if distance ldquoArdquo approaches zerohellip
hellipthe Cpk would approach zero andhellip
hellipthe process would become 50 defective
Specification
Limit
Specification
Limit
This Cpk is less
than 1 We desire
a minimum of 133
and ultimately we
want 2 or more
60
-
Q amp A
61
MEASUREMENT SYSTEM ANALYSIS (MSA)
An MSA is a statistical tool used to determine if a measurement system is capable of precise measurement
What is It
Objective or Purpose
bull To determine how much error is in the measurement due to the measurement process itself
bull Quantifies the variability added by the measurement system
bull Applicable to attribute data and variable data
When to Use It
bull On the critical inputs and outputs prior to collecting data for analysis
bull For any new or modified process in order to ensure the quality of the data
Measurement System Analysis is an analysis of the measurement process not an analysis of the people
IMPORTANT
Who Should be Involved
Everyone that measures and makes decisions about these measurements should be involved in the MSA
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The observed variation in process output measurements is not simply the variation in the process itself it is the variation in the process plus the variation in measurement that results from an inadequate measurement system
Conducting an MSA reduces the likelihood of passing a bad part or rejecting a good part
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The output of the process measured by bull Cycle time bull Dimensional data bull Number of defects and others
Observed Variation
Process Variation
Measurement System
Variation
Reproducibility
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Accuracy (Central Location)
OBSERVED VARIATION
Calibration addresses accuracy
Measurement System Analysis (MSA)
MEASUREMENT SYSTEM ERRORS
Accuracy difference between the observed measurement and the actual measurement
Precision variation that occurs when measuring the same part with the same instrument
MEASUREMENT SYSTEM ERROR
Precise but not
accurate
Accurate but not
precise
Not accurate or
precise
Accurate and
precise
ACCURACY OF MEASUREMENT
Broken down into three components
aStability
The consistency of measurements over time
bBias
A measure of the amount of partiality in the system
cLinearity
A measure of the bias values through the expected
range of measurements
OBSERVED VARIATION
Observed Variation
Process Variation
Measurement System
Variation
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Reproducibility
Accuracy (Central Location)
Calibration Addresses Accuracy
Letrsquos take a closer look at Precision
Measurement System Analysis (MSA)
Measurement System Analysis (MSA)
Error in Resolution The inability to detect small changes
Possible Cause
Wrong measurement device selected - divisions on scale not fine enough to detect changes
Resolution
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Repeatability The inability to get the same answer from repeated measurements made of the same item under absolutely identical conditions
Possible Cause
Lack of standard operating procedures (SOP) lack of training measuring system variablilty
Repeatability
Equipment Variation
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Reproducibility The inability to get the same answer from repeated measurements made under various conditions from different inspectors
Possible Cause
Lack of SOP lack of training
Reproducibility
Appraiser Variation
VARIABLE MSA ndash GAGE RampR STUDY
bull Gage RampR is the combined estimate of
measurement system Repeatability and
Reproducibility
bull Typically a 3-person study is performed Each person randomly measures 10 marked parts per trial
Each person can perform up to 3 trials
bull There are 3 key indicators EV or Equipment Variation
AV or Appraiser Variation
Overall GRR
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
TYPES OF DATA ndash ATTRIBUTE DATA
Attributes data Non-measurable characteristics Can be very subjective
Blush Scratched Color etc
Observations are counted YesNo PresentAbsent MeetsDoesnrsquot meet
Visually inspected Gono-go gauges
If color happens to be an attribute that is being inspected for Typically meet the expected color sample is given Maybe a light and dark compared to sample given The acceptable range is in between A reject is not measured just counted as one
14
Collected through measurement
Is very objective
Can be temperature length width weight force volts amps etc
Uses a measuring tool
Scale
Meters
Inspection should not be done to sort but for data collection and correction of the process
This will allow for quick response and rapid correction minimizing defect quantities
TYPES OF DATA ndash VARIABLE DATA
15
PARETO CHARTS
Vilfredo Pareto
Italyrsquos wealth
80 held by 20 of people
Used when analyzing attributes
Based on results of tally numbers in specific categories
What is a Pareto Chart used for
To display the relative importance of data
To direct efforts to the biggest improvement opportunity by highlighting the vital few in contrast to the useful many
16
CONSTRUCTING A PARETO CHART
Determine the categories and the units for comparison of the data such as frequency cost or time
Total the raw data in each category then determine the grand total by adding the totals of each category
Re-order the categories from largest to smallest
Determine the cumulative percent of each category (ie the sum of each category plus all categories that precede it in the rank order divided by the grand total and multiplied by 100)
17
CONSTRUCTING A PARETO CHART
Draw and label the left-hand vertical axis with the unit of comparison such as frequency cost or time
Draw and label the horizontal axis with the categories List from left to right in rank order
Draw and label the right-hand vertical axis from 0 to 100 percent The 100 percent should line up with the grand total on the left-hand vertical axis
Beginning with the largest category draw in bars for each category representing the total for that category
18
CONSTRUCTING A PARETO CHART
Draw a line graph beginning at the right-hand
corner of the first bar to represent the
cumulative percent for each category as
measured on the right-hand axis
Analyze the chart Usually the top 20 of the
categories will comprise roughly 80 of the
cumulative total
19
PARETO CHART - EXAMPLE
Lets assume we are listing all the rejected products that are removed from a candy manufacturing line in one week
First we put the rejects in specific categories
No wrapper - 10
No center - 37
Wrong shape - 53
Short shot - 6
Wrapper open - 132
Underweight - 4
Overweight ndash 17
Get the total rejects - 259
20
Develop a percentage for each category
No wrapper ndash 10259 = 39
No center ndash 37259 = 143
Wrong shape ndash 53259 = 205
Short shot ndash 6259 = 23
Wrapper open ndash 132259 = 51
Underweight ndash 4259 = 15
Overweight ndash 17259 = 66
PARETO CHART - EXAMPLE
21
Now place the counts in a histogram largest to smallest
0
10
20
30
40
50
60
Wrapper
Open
No Center No Wrapper Underweight
70
80
90
100
51
205
143
66 39
23 15
22
Finally add up each and plot as a line diagram
0
10
20
30
40
50
60
Wrapper
Open
No Center No Wrapper Underweight
70
80
90
100
715
51
205
143
858
66
924
39
963
23
986
15
1001
23
0
10
20
30
40
50
60
Wrapper
Open
No Center No Wrapper Underweight
70
80
90
100
715
51
205
143
858
66
924
39
963
23
986
15
1001
24
CONTROL CHARTS
Control charts are one of the most commonly used methods of Statistical Process Control (SPC) which
monitors the stability of a process
The main features of a control chart include the data points a centreline (mean value) and upper and
lower limits (bounds to indicate where a process output is considered out of control)They visually
display the fluctuations of a particular process variable that easily determine whether these variations
fall within the specified process limits
Control charts
a graphical method for detecting if the underlying distribution of variation of some measurable
characteristic of the product seems to have undergone a shift
monitor a process in real time
Map the output of a production process over time
A control chart always has a central line for the average an upper line for the upper control limit and a
lower line for the lower control limit These lines are determined from historical data
By comparing current data to these lines you can draw conclusions about whether the process
variation is consistent (in control) or is unpredictable
25
CONTROL CHART - PURPOSE
The main purpose of using a control chart is to monitor control and improve
process performance over time by studying variation and its source There are
several functions of a control chart
It centres attention on detecting and monitoring process variation over time
It provides a tool for on-going control of a process
It differentiates special from common causes of variation in order to be a guide for
local or management action
It helps improve a process to perform consistently and predictably to achieve higher
quality lower cost and higher effective capacity
It serves as a common language for discussing process performance
26
TYPES OF CONTROL CHARTS
The basic tool used in SPC is the control chart
There are various types of control charts
Variable Control Chart
Averages and range chart (X-Bar and R Bar Chart)
X bar and s chart
Moving Range Chart
Moving AveragendashMoving Range chart (also called MAndashMR chart)
p chart (also called proportion chart)
c chart (also called count chart)
np chart
u chart
27
POPULARITY OF CONTROL CHARTS
Control charts are a proven technique for improving productivity
Control charts are effective in defect prevention
Control charts prevent unnecessary process
adjustment
Control charts provide diagnostic information
Control charts provide information about process
capability
28
PROCEDURE FOR X ndashBAR AND R BAR CHART
1 Randomly sample ldquonrdquo units throughout the day (can be every 5
minutes every 30 minutes etc - whatever is appropriate for your
case)
2 For each sample calculate ldquoX-BARrdquo to estimate the mean and ldquoR
(range)rdquo to estimate variability NOTE THE RANGE CAN BE USED TO
ESTIMATE THE STANDARD DEVIATION
3 After collecting the 20-25 samples calculate X-BAR-BAR (the
average of all the X-BARs) and R-BAR (the average of all the ranges)
4 Using X-BAR-BAR and R-BAR calculate the control limits for your X-
BAR and R Control Charts
29
X-BAR CONTROL LIMITS
Upper Control Limit (UCL) = (X-BAR-BAR) + A2 (R-BAR)
Lower Control Limit(LCL) = (X-BAR-BAR) - A2 (R-BAR)
R CONTROL LIMITS
Upper Control Limit - D3 (R-BAR)
Lower Control Limit - D4 (R-BAR)
PROCEDURE FOR X ndashBAR AND R BAR CHART
30
CONTROL CHART CONSTANTS
sample size constant constant constant constant constant constant constant
n d2 A2 A3 B3 B4 D3 D4
2 1128 188 2659 0 3267 0 3267
3 1693 1023 1954 0 2568 0 2574
4 2059 0729 1628 0 2266 0 2282
5 2326 0577 1427 0 2089 0 2114
6 2534 0483 1287 003 197 0 2004
7 2704 0419 1182 0118 1882 0076 1924
8 2847 0373 1099 0185 1815 0136 1864
9 297 0337 1032 0239 1761 0184 1816
10 3078 0308 0975 0284 1716 0223 1777
31
5 For the R Control Chart plot all R values on the R Control Chart
to see if all the Ranges are ldquobetween the control limitsrdquo If they are
then your process is considered to be in a state of statistical control
(as far as the variability of the process is concerned)
6 For the X-BAR Control Chart plot all the X-BARs on the X-BAR
control chart to see if all the X-BARs are ldquobetween the control
limitsrdquo If they are then your process is considered in a state of
statistical control (as far as the average of the process is
concerned)
PROCEDURE FOR X ndashBAR AND R BAR CHART
32
SAMPLE DATA FOR X BAR ndashR CHART
Sub Group 1 2 3 4 5 X -Bar Range reg
1 1195 1191 1211 1203 1198 1200 02
2 1201 1198 1198 1197 12 1199 004
3 1193 1206 1198 1196 1202 1199 013
4 1205 1198 1205 1206 1198 1202 008
5 1198 1203 1206 1201 1199 1201 008
6 1202 1205 1196 1201 1195 1200 01
7 1199 1206 1201 1204 1201 1202 007
8 1201 1197 1198 1204 1198 1200 007
9 1198 1204 1198 1204 1204 1202 006
10 1205 1195 1198 1204 1196 1200 01
` X Bar-Bar 1200 009
X Bar Chart
UCL = X BAR-BAR + A2 R Bar
1200 +(0577009) 1205
LCL= X BAR-BAR - A2 R Bar
1200 - (0577009) 1195
R Chart
UCL = D4R Bar 211 009 021
LCL = D3 R Bar 0009 0
33
PLOT DATA ON CONTROL CHARTS
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1 2 3 4 5 6 7 8 9 10
Ave
rage
(X
ba
r)
X Bar Chart
UCL
LCL
X Bar
34
PLOT DATA ON CONTROL CHARTS
001
003
005
007
009
011
013
015
017
019
021
023
025
1 2 3 4 5 6 7 8 9 10
R Chart
UCL
LCL
35
PROCEDURE TO DETERMINE IF PROCESS IS IN A STATE OF
STATISTICAL CONTROL
7 If process is determined to be ldquoNOT STABLErdquo then stop and find out what
an assignable cause might be fix and then repeat the complete process of
collecting new data
8 If the process is determined to be ldquoSTABLErdquo then you may use the
control charts you developed to monitor future production to ensure that the
process REMAINS stable
More Samples for Control charts
36
READING OF CONTROL CHART
Control charts can determine whether a process is behaving in an unusual way The quality of the individual points of a subset is determined unstable if any of the
following occurs
Rule 1 Any point falls beyond 3σ from the centreline(this is represented by the upper and
lower control limits)
Rule 2 Two out of three consecutive points fall beyond 2σ on the same side of the
centreline
Rule 3 Four out of five consecutive points fall beyond 1σ on the same side of the
centreline
Rule 4 Nine or more consecutive points fall on the same side of the centreline
(Ref Next page for sample)
37
READING THE CONTROL CHART
38
CONTROL CHARTS FOR ATTRIBUTES ndashP-CHARTS amp C-CHARTS
Attributes are discrete events yesno or passfail
Use P-Charts for quality characteristics that are discrete and involve yesno or goodbad decisions
Eg
Number of leaking caulking tubes in a box of 48
Number of broken eggs in a carton
Use C-Charts for discrete defects when there can be more than one defect per unit
Eg
Number of stains in a carpet sample cut from a production run
Number of complaints per customer at a hotel
39
P-CHART EXAMPLE A PRODUCTION MANAGER FOR A TIRE COMPANY HAS INSPECTED THE NUMBER OF
DEFECTIVE TIRES IN FIVE RANDOM SAMPLES WITH 20 TIRES IN EACH SAMPLE THE TABLE BELOW SHOWS THE
NUMBER OF DEFECTIVE TIRES IN EACH SAMPLE OF 20 TIRES CALCULATE THE CONTROL LIMITS
Sample Number of
Defective Tires
Number of Tires in each
Sample
Proportion Defective
1 3 20 15
2 2 20 10
3 1 20 05
4 2 20 10
5 2 20 05
Total 9 100 09
01023(064)09σzpLCL
2823(064)09σzpUCL
06420
(09)(91)
n
)p(1pσ
09100
9
Inspected Total
DefectivespCL
p
p
p
Solution
40
P- CONTROL CHART
41
C-CHART EXAMPLE THE NUMBER OF WEEKLY CUSTOMER COMPLAINTS ARE MONITORED IN A LARGE HOTEL USING A C-CHART DEVELOP THREE SIGMA CONTROL LIMITS USING THE DATA TABLE BELOW
Week Number of Complaints
1 3
2 2
3 3
4 1
5 3
6 3
7 2
8 1
9 3
10 1
Total 22
022522322ccLCL
66522322ccUCL
2210
22
samples of
complaintsc
c
c
z
z
Solution
42
C- CONTROL CHART
43
The ability of a process to meet product designtechnical specifications
Assessing capability involves evaluating process variability relative to preset product or service specifications
Process Capability ndash Cp and Cpk
Cp assumes that the process is centered in the specification range
Cpk helps to address a possible lack of centering of the process
PROCESS CAPABILITY
6σ
LSLUSL
width process
width ionspecificatCp
3σ
LSLμ
3σ
μUSLminCpk
44
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
45
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
46
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
47
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
--and an individual part is measured at 520rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
48
GRAPHING THE TOLERANCE AND MEASUREMENTS
Suppose we made and measured several more
units and they were all EXACTLY the same
We wouldnrsquot have very many part problems
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
X
X
X
49
GRAPHING THE TOLERANCE AND MEASUREMENTS
In the real world units are NOT EXACTLY the same
Everything VARIES
The question isnrsquot IF units vary
Itrsquos how much when and why
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
XX
XXX
XXXXX
XXXXXXX
50
The ldquonormal bell curverdquo
Widths heights depths thicknesses weights speeds strengths
and many other types of measurements when charted as a
histogram often form the shape of a bell
A ldquoperfect bellrdquo like a ldquoperfect circlerdquo doesnrsquot occur in nature but
many processes are close enough to make the bell curve useful
(A number of common industrial measurements such as flatness and straightness do NOT tend to distribute in a bell shape their proper statistical analysis is performed using models other than the bell curve)
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
51
What is a ldquostandard deviationrdquo
If we measure the DISTANCE from the CENTER of the bell
to each individual measurement that makes up the bell curve
we can find a TYPICAL DISTANCE
The most commonly used statistic to estimate this distance is the
Standard Deviation (also called ldquoSigmardquo)
Because of the natural shape of the bell curve the area of +1 to ndash1
standard deviations includes about 68 of the curve
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
Typical distance
from the center +1
standard deviation
Typical distance
from the center -1
standard deviation
52
How much of the curve is included in how many standard
deviations
From ndash1 to +1 is about 68 of the bell curve
From ndash2 to +2 is about 95
From ndash3 to +3 is about 9973
From ndash4 to +4 is about 9999
(NOTE We usually show the bell from ndash3 to +3 to make it easier to draw but in concept the ldquotailsrdquo of the bell get very thin and go on forever)
-6 -5 -4 -3 -2 -1 +1 +2 +3 +4 +5 +6 0
53
A
B
What is Cpk It is a measure of how well a process is within a specification
Cpk = A divided by B
A = Distance from process mean to closest spec limit
B = 3 Standard Deviations (also called ldquo3 Sigmardquo)
A bigger Cpk is better because fewer units will be beyond spec
(A bigger ldquoArdquo and a smaller ldquoBrdquo are better)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
54
A
B
ldquoProcess Capabilityrdquo is the ability of a process
to fit its output within the tolerances
hellipa LARGER ldquoArdquo
hellipand a SMALLER ldquoBrdquo
hellipmeans BETTER ldquoProcess Capabilityrdquo
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
55
A
B
An Analogy
Analogy
The bell curve is your automobile
The spec limits are the edges of your garage door
If A = B you are hitting the frame of your garage door with your car
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
56
A
B
How can we make Cpk (A divided by B) better
1 Design the product so a wider tolerance is functional (ldquorobust designrdquo)
2 Choose equipment and methods for a good safety margin (ldquoprocess capabilityrdquo)
3 Correctly adjust but only when needed (ldquocontrolrdquo)
4 Discover ways to narrow the natural variation (ldquoimprovementrdquo)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
57
A
B
What does a very good Cpk do for us
This process is producing good units with a good safety margin
Note that when Cpk = 2 our process mean is 6 standard deviations from
the nearest spec so we say it has ldquo6 Sigma Capabilityrdquo
Specification
Limit
Specification
Limit
This Cpk is
about 2
Very good
Mean
58
A
B
What does a problem Cpk look like
This process is in danger of producing some defects
It is too close to the specification limits
(Remember the bell curve tail goes further than Bhellip hellipwe only show the bell to 3-sigma to make it easier to draw)
Specification
Limit
Specification
Limit
This Cpk is just
slightly greater
than 1 Not good
59
A
B
What does a very bad Cpk look like
A significant part of the ldquotailrdquo is hanging out beyond the spec limits
This process is producing scrap rework and customer rejects
Notice that if distance ldquoArdquo approaches zerohellip
hellipthe Cpk would approach zero andhellip
hellipthe process would become 50 defective
Specification
Limit
Specification
Limit
This Cpk is less
than 1 We desire
a minimum of 133
and ultimately we
want 2 or more
60
-
Q amp A
61
MEASUREMENT SYSTEM ANALYSIS (MSA)
An MSA is a statistical tool used to determine if a measurement system is capable of precise measurement
What is It
Objective or Purpose
bull To determine how much error is in the measurement due to the measurement process itself
bull Quantifies the variability added by the measurement system
bull Applicable to attribute data and variable data
When to Use It
bull On the critical inputs and outputs prior to collecting data for analysis
bull For any new or modified process in order to ensure the quality of the data
Measurement System Analysis is an analysis of the measurement process not an analysis of the people
IMPORTANT
Who Should be Involved
Everyone that measures and makes decisions about these measurements should be involved in the MSA
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The observed variation in process output measurements is not simply the variation in the process itself it is the variation in the process plus the variation in measurement that results from an inadequate measurement system
Conducting an MSA reduces the likelihood of passing a bad part or rejecting a good part
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The output of the process measured by bull Cycle time bull Dimensional data bull Number of defects and others
Observed Variation
Process Variation
Measurement System
Variation
Reproducibility
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Accuracy (Central Location)
OBSERVED VARIATION
Calibration addresses accuracy
Measurement System Analysis (MSA)
MEASUREMENT SYSTEM ERRORS
Accuracy difference between the observed measurement and the actual measurement
Precision variation that occurs when measuring the same part with the same instrument
MEASUREMENT SYSTEM ERROR
Precise but not
accurate
Accurate but not
precise
Not accurate or
precise
Accurate and
precise
ACCURACY OF MEASUREMENT
Broken down into three components
aStability
The consistency of measurements over time
bBias
A measure of the amount of partiality in the system
cLinearity
A measure of the bias values through the expected
range of measurements
OBSERVED VARIATION
Observed Variation
Process Variation
Measurement System
Variation
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Reproducibility
Accuracy (Central Location)
Calibration Addresses Accuracy
Letrsquos take a closer look at Precision
Measurement System Analysis (MSA)
Measurement System Analysis (MSA)
Error in Resolution The inability to detect small changes
Possible Cause
Wrong measurement device selected - divisions on scale not fine enough to detect changes
Resolution
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Repeatability The inability to get the same answer from repeated measurements made of the same item under absolutely identical conditions
Possible Cause
Lack of standard operating procedures (SOP) lack of training measuring system variablilty
Repeatability
Equipment Variation
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Reproducibility The inability to get the same answer from repeated measurements made under various conditions from different inspectors
Possible Cause
Lack of SOP lack of training
Reproducibility
Appraiser Variation
VARIABLE MSA ndash GAGE RampR STUDY
bull Gage RampR is the combined estimate of
measurement system Repeatability and
Reproducibility
bull Typically a 3-person study is performed Each person randomly measures 10 marked parts per trial
Each person can perform up to 3 trials
bull There are 3 key indicators EV or Equipment Variation
AV or Appraiser Variation
Overall GRR
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
Collected through measurement
Is very objective
Can be temperature length width weight force volts amps etc
Uses a measuring tool
Scale
Meters
Inspection should not be done to sort but for data collection and correction of the process
This will allow for quick response and rapid correction minimizing defect quantities
TYPES OF DATA ndash VARIABLE DATA
15
PARETO CHARTS
Vilfredo Pareto
Italyrsquos wealth
80 held by 20 of people
Used when analyzing attributes
Based on results of tally numbers in specific categories
What is a Pareto Chart used for
To display the relative importance of data
To direct efforts to the biggest improvement opportunity by highlighting the vital few in contrast to the useful many
16
CONSTRUCTING A PARETO CHART
Determine the categories and the units for comparison of the data such as frequency cost or time
Total the raw data in each category then determine the grand total by adding the totals of each category
Re-order the categories from largest to smallest
Determine the cumulative percent of each category (ie the sum of each category plus all categories that precede it in the rank order divided by the grand total and multiplied by 100)
17
CONSTRUCTING A PARETO CHART
Draw and label the left-hand vertical axis with the unit of comparison such as frequency cost or time
Draw and label the horizontal axis with the categories List from left to right in rank order
Draw and label the right-hand vertical axis from 0 to 100 percent The 100 percent should line up with the grand total on the left-hand vertical axis
Beginning with the largest category draw in bars for each category representing the total for that category
18
CONSTRUCTING A PARETO CHART
Draw a line graph beginning at the right-hand
corner of the first bar to represent the
cumulative percent for each category as
measured on the right-hand axis
Analyze the chart Usually the top 20 of the
categories will comprise roughly 80 of the
cumulative total
19
PARETO CHART - EXAMPLE
Lets assume we are listing all the rejected products that are removed from a candy manufacturing line in one week
First we put the rejects in specific categories
No wrapper - 10
No center - 37
Wrong shape - 53
Short shot - 6
Wrapper open - 132
Underweight - 4
Overweight ndash 17
Get the total rejects - 259
20
Develop a percentage for each category
No wrapper ndash 10259 = 39
No center ndash 37259 = 143
Wrong shape ndash 53259 = 205
Short shot ndash 6259 = 23
Wrapper open ndash 132259 = 51
Underweight ndash 4259 = 15
Overweight ndash 17259 = 66
PARETO CHART - EXAMPLE
21
Now place the counts in a histogram largest to smallest
0
10
20
30
40
50
60
Wrapper
Open
No Center No Wrapper Underweight
70
80
90
100
51
205
143
66 39
23 15
22
Finally add up each and plot as a line diagram
0
10
20
30
40
50
60
Wrapper
Open
No Center No Wrapper Underweight
70
80
90
100
715
51
205
143
858
66
924
39
963
23
986
15
1001
23
0
10
20
30
40
50
60
Wrapper
Open
No Center No Wrapper Underweight
70
80
90
100
715
51
205
143
858
66
924
39
963
23
986
15
1001
24
CONTROL CHARTS
Control charts are one of the most commonly used methods of Statistical Process Control (SPC) which
monitors the stability of a process
The main features of a control chart include the data points a centreline (mean value) and upper and
lower limits (bounds to indicate where a process output is considered out of control)They visually
display the fluctuations of a particular process variable that easily determine whether these variations
fall within the specified process limits
Control charts
a graphical method for detecting if the underlying distribution of variation of some measurable
characteristic of the product seems to have undergone a shift
monitor a process in real time
Map the output of a production process over time
A control chart always has a central line for the average an upper line for the upper control limit and a
lower line for the lower control limit These lines are determined from historical data
By comparing current data to these lines you can draw conclusions about whether the process
variation is consistent (in control) or is unpredictable
25
CONTROL CHART - PURPOSE
The main purpose of using a control chart is to monitor control and improve
process performance over time by studying variation and its source There are
several functions of a control chart
It centres attention on detecting and monitoring process variation over time
It provides a tool for on-going control of a process
It differentiates special from common causes of variation in order to be a guide for
local or management action
It helps improve a process to perform consistently and predictably to achieve higher
quality lower cost and higher effective capacity
It serves as a common language for discussing process performance
26
TYPES OF CONTROL CHARTS
The basic tool used in SPC is the control chart
There are various types of control charts
Variable Control Chart
Averages and range chart (X-Bar and R Bar Chart)
X bar and s chart
Moving Range Chart
Moving AveragendashMoving Range chart (also called MAndashMR chart)
p chart (also called proportion chart)
c chart (also called count chart)
np chart
u chart
27
POPULARITY OF CONTROL CHARTS
Control charts are a proven technique for improving productivity
Control charts are effective in defect prevention
Control charts prevent unnecessary process
adjustment
Control charts provide diagnostic information
Control charts provide information about process
capability
28
PROCEDURE FOR X ndashBAR AND R BAR CHART
1 Randomly sample ldquonrdquo units throughout the day (can be every 5
minutes every 30 minutes etc - whatever is appropriate for your
case)
2 For each sample calculate ldquoX-BARrdquo to estimate the mean and ldquoR
(range)rdquo to estimate variability NOTE THE RANGE CAN BE USED TO
ESTIMATE THE STANDARD DEVIATION
3 After collecting the 20-25 samples calculate X-BAR-BAR (the
average of all the X-BARs) and R-BAR (the average of all the ranges)
4 Using X-BAR-BAR and R-BAR calculate the control limits for your X-
BAR and R Control Charts
29
X-BAR CONTROL LIMITS
Upper Control Limit (UCL) = (X-BAR-BAR) + A2 (R-BAR)
Lower Control Limit(LCL) = (X-BAR-BAR) - A2 (R-BAR)
R CONTROL LIMITS
Upper Control Limit - D3 (R-BAR)
Lower Control Limit - D4 (R-BAR)
PROCEDURE FOR X ndashBAR AND R BAR CHART
30
CONTROL CHART CONSTANTS
sample size constant constant constant constant constant constant constant
n d2 A2 A3 B3 B4 D3 D4
2 1128 188 2659 0 3267 0 3267
3 1693 1023 1954 0 2568 0 2574
4 2059 0729 1628 0 2266 0 2282
5 2326 0577 1427 0 2089 0 2114
6 2534 0483 1287 003 197 0 2004
7 2704 0419 1182 0118 1882 0076 1924
8 2847 0373 1099 0185 1815 0136 1864
9 297 0337 1032 0239 1761 0184 1816
10 3078 0308 0975 0284 1716 0223 1777
31
5 For the R Control Chart plot all R values on the R Control Chart
to see if all the Ranges are ldquobetween the control limitsrdquo If they are
then your process is considered to be in a state of statistical control
(as far as the variability of the process is concerned)
6 For the X-BAR Control Chart plot all the X-BARs on the X-BAR
control chart to see if all the X-BARs are ldquobetween the control
limitsrdquo If they are then your process is considered in a state of
statistical control (as far as the average of the process is
concerned)
PROCEDURE FOR X ndashBAR AND R BAR CHART
32
SAMPLE DATA FOR X BAR ndashR CHART
Sub Group 1 2 3 4 5 X -Bar Range reg
1 1195 1191 1211 1203 1198 1200 02
2 1201 1198 1198 1197 12 1199 004
3 1193 1206 1198 1196 1202 1199 013
4 1205 1198 1205 1206 1198 1202 008
5 1198 1203 1206 1201 1199 1201 008
6 1202 1205 1196 1201 1195 1200 01
7 1199 1206 1201 1204 1201 1202 007
8 1201 1197 1198 1204 1198 1200 007
9 1198 1204 1198 1204 1204 1202 006
10 1205 1195 1198 1204 1196 1200 01
` X Bar-Bar 1200 009
X Bar Chart
UCL = X BAR-BAR + A2 R Bar
1200 +(0577009) 1205
LCL= X BAR-BAR - A2 R Bar
1200 - (0577009) 1195
R Chart
UCL = D4R Bar 211 009 021
LCL = D3 R Bar 0009 0
33
PLOT DATA ON CONTROL CHARTS
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1 2 3 4 5 6 7 8 9 10
Ave
rage
(X
ba
r)
X Bar Chart
UCL
LCL
X Bar
34
PLOT DATA ON CONTROL CHARTS
001
003
005
007
009
011
013
015
017
019
021
023
025
1 2 3 4 5 6 7 8 9 10
R Chart
UCL
LCL
35
PROCEDURE TO DETERMINE IF PROCESS IS IN A STATE OF
STATISTICAL CONTROL
7 If process is determined to be ldquoNOT STABLErdquo then stop and find out what
an assignable cause might be fix and then repeat the complete process of
collecting new data
8 If the process is determined to be ldquoSTABLErdquo then you may use the
control charts you developed to monitor future production to ensure that the
process REMAINS stable
More Samples for Control charts
36
READING OF CONTROL CHART
Control charts can determine whether a process is behaving in an unusual way The quality of the individual points of a subset is determined unstable if any of the
following occurs
Rule 1 Any point falls beyond 3σ from the centreline(this is represented by the upper and
lower control limits)
Rule 2 Two out of three consecutive points fall beyond 2σ on the same side of the
centreline
Rule 3 Four out of five consecutive points fall beyond 1σ on the same side of the
centreline
Rule 4 Nine or more consecutive points fall on the same side of the centreline
(Ref Next page for sample)
37
READING THE CONTROL CHART
38
CONTROL CHARTS FOR ATTRIBUTES ndashP-CHARTS amp C-CHARTS
Attributes are discrete events yesno or passfail
Use P-Charts for quality characteristics that are discrete and involve yesno or goodbad decisions
Eg
Number of leaking caulking tubes in a box of 48
Number of broken eggs in a carton
Use C-Charts for discrete defects when there can be more than one defect per unit
Eg
Number of stains in a carpet sample cut from a production run
Number of complaints per customer at a hotel
39
P-CHART EXAMPLE A PRODUCTION MANAGER FOR A TIRE COMPANY HAS INSPECTED THE NUMBER OF
DEFECTIVE TIRES IN FIVE RANDOM SAMPLES WITH 20 TIRES IN EACH SAMPLE THE TABLE BELOW SHOWS THE
NUMBER OF DEFECTIVE TIRES IN EACH SAMPLE OF 20 TIRES CALCULATE THE CONTROL LIMITS
Sample Number of
Defective Tires
Number of Tires in each
Sample
Proportion Defective
1 3 20 15
2 2 20 10
3 1 20 05
4 2 20 10
5 2 20 05
Total 9 100 09
01023(064)09σzpLCL
2823(064)09σzpUCL
06420
(09)(91)
n
)p(1pσ
09100
9
Inspected Total
DefectivespCL
p
p
p
Solution
40
P- CONTROL CHART
41
C-CHART EXAMPLE THE NUMBER OF WEEKLY CUSTOMER COMPLAINTS ARE MONITORED IN A LARGE HOTEL USING A C-CHART DEVELOP THREE SIGMA CONTROL LIMITS USING THE DATA TABLE BELOW
Week Number of Complaints
1 3
2 2
3 3
4 1
5 3
6 3
7 2
8 1
9 3
10 1
Total 22
022522322ccLCL
66522322ccUCL
2210
22
samples of
complaintsc
c
c
z
z
Solution
42
C- CONTROL CHART
43
The ability of a process to meet product designtechnical specifications
Assessing capability involves evaluating process variability relative to preset product or service specifications
Process Capability ndash Cp and Cpk
Cp assumes that the process is centered in the specification range
Cpk helps to address a possible lack of centering of the process
PROCESS CAPABILITY
6σ
LSLUSL
width process
width ionspecificatCp
3σ
LSLμ
3σ
μUSLminCpk
44
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
45
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
46
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
47
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
--and an individual part is measured at 520rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
48
GRAPHING THE TOLERANCE AND MEASUREMENTS
Suppose we made and measured several more
units and they were all EXACTLY the same
We wouldnrsquot have very many part problems
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
X
X
X
49
GRAPHING THE TOLERANCE AND MEASUREMENTS
In the real world units are NOT EXACTLY the same
Everything VARIES
The question isnrsquot IF units vary
Itrsquos how much when and why
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
XX
XXX
XXXXX
XXXXXXX
50
The ldquonormal bell curverdquo
Widths heights depths thicknesses weights speeds strengths
and many other types of measurements when charted as a
histogram often form the shape of a bell
A ldquoperfect bellrdquo like a ldquoperfect circlerdquo doesnrsquot occur in nature but
many processes are close enough to make the bell curve useful
(A number of common industrial measurements such as flatness and straightness do NOT tend to distribute in a bell shape their proper statistical analysis is performed using models other than the bell curve)
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
51
What is a ldquostandard deviationrdquo
If we measure the DISTANCE from the CENTER of the bell
to each individual measurement that makes up the bell curve
we can find a TYPICAL DISTANCE
The most commonly used statistic to estimate this distance is the
Standard Deviation (also called ldquoSigmardquo)
Because of the natural shape of the bell curve the area of +1 to ndash1
standard deviations includes about 68 of the curve
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
Typical distance
from the center +1
standard deviation
Typical distance
from the center -1
standard deviation
52
How much of the curve is included in how many standard
deviations
From ndash1 to +1 is about 68 of the bell curve
From ndash2 to +2 is about 95
From ndash3 to +3 is about 9973
From ndash4 to +4 is about 9999
(NOTE We usually show the bell from ndash3 to +3 to make it easier to draw but in concept the ldquotailsrdquo of the bell get very thin and go on forever)
-6 -5 -4 -3 -2 -1 +1 +2 +3 +4 +5 +6 0
53
A
B
What is Cpk It is a measure of how well a process is within a specification
Cpk = A divided by B
A = Distance from process mean to closest spec limit
B = 3 Standard Deviations (also called ldquo3 Sigmardquo)
A bigger Cpk is better because fewer units will be beyond spec
(A bigger ldquoArdquo and a smaller ldquoBrdquo are better)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
54
A
B
ldquoProcess Capabilityrdquo is the ability of a process
to fit its output within the tolerances
hellipa LARGER ldquoArdquo
hellipand a SMALLER ldquoBrdquo
hellipmeans BETTER ldquoProcess Capabilityrdquo
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
55
A
B
An Analogy
Analogy
The bell curve is your automobile
The spec limits are the edges of your garage door
If A = B you are hitting the frame of your garage door with your car
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
56
A
B
How can we make Cpk (A divided by B) better
1 Design the product so a wider tolerance is functional (ldquorobust designrdquo)
2 Choose equipment and methods for a good safety margin (ldquoprocess capabilityrdquo)
3 Correctly adjust but only when needed (ldquocontrolrdquo)
4 Discover ways to narrow the natural variation (ldquoimprovementrdquo)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
57
A
B
What does a very good Cpk do for us
This process is producing good units with a good safety margin
Note that when Cpk = 2 our process mean is 6 standard deviations from
the nearest spec so we say it has ldquo6 Sigma Capabilityrdquo
Specification
Limit
Specification
Limit
This Cpk is
about 2
Very good
Mean
58
A
B
What does a problem Cpk look like
This process is in danger of producing some defects
It is too close to the specification limits
(Remember the bell curve tail goes further than Bhellip hellipwe only show the bell to 3-sigma to make it easier to draw)
Specification
Limit
Specification
Limit
This Cpk is just
slightly greater
than 1 Not good
59
A
B
What does a very bad Cpk look like
A significant part of the ldquotailrdquo is hanging out beyond the spec limits
This process is producing scrap rework and customer rejects
Notice that if distance ldquoArdquo approaches zerohellip
hellipthe Cpk would approach zero andhellip
hellipthe process would become 50 defective
Specification
Limit
Specification
Limit
This Cpk is less
than 1 We desire
a minimum of 133
and ultimately we
want 2 or more
60
-
Q amp A
61
MEASUREMENT SYSTEM ANALYSIS (MSA)
An MSA is a statistical tool used to determine if a measurement system is capable of precise measurement
What is It
Objective or Purpose
bull To determine how much error is in the measurement due to the measurement process itself
bull Quantifies the variability added by the measurement system
bull Applicable to attribute data and variable data
When to Use It
bull On the critical inputs and outputs prior to collecting data for analysis
bull For any new or modified process in order to ensure the quality of the data
Measurement System Analysis is an analysis of the measurement process not an analysis of the people
IMPORTANT
Who Should be Involved
Everyone that measures and makes decisions about these measurements should be involved in the MSA
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The observed variation in process output measurements is not simply the variation in the process itself it is the variation in the process plus the variation in measurement that results from an inadequate measurement system
Conducting an MSA reduces the likelihood of passing a bad part or rejecting a good part
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The output of the process measured by bull Cycle time bull Dimensional data bull Number of defects and others
Observed Variation
Process Variation
Measurement System
Variation
Reproducibility
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Accuracy (Central Location)
OBSERVED VARIATION
Calibration addresses accuracy
Measurement System Analysis (MSA)
MEASUREMENT SYSTEM ERRORS
Accuracy difference between the observed measurement and the actual measurement
Precision variation that occurs when measuring the same part with the same instrument
MEASUREMENT SYSTEM ERROR
Precise but not
accurate
Accurate but not
precise
Not accurate or
precise
Accurate and
precise
ACCURACY OF MEASUREMENT
Broken down into three components
aStability
The consistency of measurements over time
bBias
A measure of the amount of partiality in the system
cLinearity
A measure of the bias values through the expected
range of measurements
OBSERVED VARIATION
Observed Variation
Process Variation
Measurement System
Variation
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Reproducibility
Accuracy (Central Location)
Calibration Addresses Accuracy
Letrsquos take a closer look at Precision
Measurement System Analysis (MSA)
Measurement System Analysis (MSA)
Error in Resolution The inability to detect small changes
Possible Cause
Wrong measurement device selected - divisions on scale not fine enough to detect changes
Resolution
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Repeatability The inability to get the same answer from repeated measurements made of the same item under absolutely identical conditions
Possible Cause
Lack of standard operating procedures (SOP) lack of training measuring system variablilty
Repeatability
Equipment Variation
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Reproducibility The inability to get the same answer from repeated measurements made under various conditions from different inspectors
Possible Cause
Lack of SOP lack of training
Reproducibility
Appraiser Variation
VARIABLE MSA ndash GAGE RampR STUDY
bull Gage RampR is the combined estimate of
measurement system Repeatability and
Reproducibility
bull Typically a 3-person study is performed Each person randomly measures 10 marked parts per trial
Each person can perform up to 3 trials
bull There are 3 key indicators EV or Equipment Variation
AV or Appraiser Variation
Overall GRR
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
PARETO CHARTS
Vilfredo Pareto
Italyrsquos wealth
80 held by 20 of people
Used when analyzing attributes
Based on results of tally numbers in specific categories
What is a Pareto Chart used for
To display the relative importance of data
To direct efforts to the biggest improvement opportunity by highlighting the vital few in contrast to the useful many
16
CONSTRUCTING A PARETO CHART
Determine the categories and the units for comparison of the data such as frequency cost or time
Total the raw data in each category then determine the grand total by adding the totals of each category
Re-order the categories from largest to smallest
Determine the cumulative percent of each category (ie the sum of each category plus all categories that precede it in the rank order divided by the grand total and multiplied by 100)
17
CONSTRUCTING A PARETO CHART
Draw and label the left-hand vertical axis with the unit of comparison such as frequency cost or time
Draw and label the horizontal axis with the categories List from left to right in rank order
Draw and label the right-hand vertical axis from 0 to 100 percent The 100 percent should line up with the grand total on the left-hand vertical axis
Beginning with the largest category draw in bars for each category representing the total for that category
18
CONSTRUCTING A PARETO CHART
Draw a line graph beginning at the right-hand
corner of the first bar to represent the
cumulative percent for each category as
measured on the right-hand axis
Analyze the chart Usually the top 20 of the
categories will comprise roughly 80 of the
cumulative total
19
PARETO CHART - EXAMPLE
Lets assume we are listing all the rejected products that are removed from a candy manufacturing line in one week
First we put the rejects in specific categories
No wrapper - 10
No center - 37
Wrong shape - 53
Short shot - 6
Wrapper open - 132
Underweight - 4
Overweight ndash 17
Get the total rejects - 259
20
Develop a percentage for each category
No wrapper ndash 10259 = 39
No center ndash 37259 = 143
Wrong shape ndash 53259 = 205
Short shot ndash 6259 = 23
Wrapper open ndash 132259 = 51
Underweight ndash 4259 = 15
Overweight ndash 17259 = 66
PARETO CHART - EXAMPLE
21
Now place the counts in a histogram largest to smallest
0
10
20
30
40
50
60
Wrapper
Open
No Center No Wrapper Underweight
70
80
90
100
51
205
143
66 39
23 15
22
Finally add up each and plot as a line diagram
0
10
20
30
40
50
60
Wrapper
Open
No Center No Wrapper Underweight
70
80
90
100
715
51
205
143
858
66
924
39
963
23
986
15
1001
23
0
10
20
30
40
50
60
Wrapper
Open
No Center No Wrapper Underweight
70
80
90
100
715
51
205
143
858
66
924
39
963
23
986
15
1001
24
CONTROL CHARTS
Control charts are one of the most commonly used methods of Statistical Process Control (SPC) which
monitors the stability of a process
The main features of a control chart include the data points a centreline (mean value) and upper and
lower limits (bounds to indicate where a process output is considered out of control)They visually
display the fluctuations of a particular process variable that easily determine whether these variations
fall within the specified process limits
Control charts
a graphical method for detecting if the underlying distribution of variation of some measurable
characteristic of the product seems to have undergone a shift
monitor a process in real time
Map the output of a production process over time
A control chart always has a central line for the average an upper line for the upper control limit and a
lower line for the lower control limit These lines are determined from historical data
By comparing current data to these lines you can draw conclusions about whether the process
variation is consistent (in control) or is unpredictable
25
CONTROL CHART - PURPOSE
The main purpose of using a control chart is to monitor control and improve
process performance over time by studying variation and its source There are
several functions of a control chart
It centres attention on detecting and monitoring process variation over time
It provides a tool for on-going control of a process
It differentiates special from common causes of variation in order to be a guide for
local or management action
It helps improve a process to perform consistently and predictably to achieve higher
quality lower cost and higher effective capacity
It serves as a common language for discussing process performance
26
TYPES OF CONTROL CHARTS
The basic tool used in SPC is the control chart
There are various types of control charts
Variable Control Chart
Averages and range chart (X-Bar and R Bar Chart)
X bar and s chart
Moving Range Chart
Moving AveragendashMoving Range chart (also called MAndashMR chart)
p chart (also called proportion chart)
c chart (also called count chart)
np chart
u chart
27
POPULARITY OF CONTROL CHARTS
Control charts are a proven technique for improving productivity
Control charts are effective in defect prevention
Control charts prevent unnecessary process
adjustment
Control charts provide diagnostic information
Control charts provide information about process
capability
28
PROCEDURE FOR X ndashBAR AND R BAR CHART
1 Randomly sample ldquonrdquo units throughout the day (can be every 5
minutes every 30 minutes etc - whatever is appropriate for your
case)
2 For each sample calculate ldquoX-BARrdquo to estimate the mean and ldquoR
(range)rdquo to estimate variability NOTE THE RANGE CAN BE USED TO
ESTIMATE THE STANDARD DEVIATION
3 After collecting the 20-25 samples calculate X-BAR-BAR (the
average of all the X-BARs) and R-BAR (the average of all the ranges)
4 Using X-BAR-BAR and R-BAR calculate the control limits for your X-
BAR and R Control Charts
29
X-BAR CONTROL LIMITS
Upper Control Limit (UCL) = (X-BAR-BAR) + A2 (R-BAR)
Lower Control Limit(LCL) = (X-BAR-BAR) - A2 (R-BAR)
R CONTROL LIMITS
Upper Control Limit - D3 (R-BAR)
Lower Control Limit - D4 (R-BAR)
PROCEDURE FOR X ndashBAR AND R BAR CHART
30
CONTROL CHART CONSTANTS
sample size constant constant constant constant constant constant constant
n d2 A2 A3 B3 B4 D3 D4
2 1128 188 2659 0 3267 0 3267
3 1693 1023 1954 0 2568 0 2574
4 2059 0729 1628 0 2266 0 2282
5 2326 0577 1427 0 2089 0 2114
6 2534 0483 1287 003 197 0 2004
7 2704 0419 1182 0118 1882 0076 1924
8 2847 0373 1099 0185 1815 0136 1864
9 297 0337 1032 0239 1761 0184 1816
10 3078 0308 0975 0284 1716 0223 1777
31
5 For the R Control Chart plot all R values on the R Control Chart
to see if all the Ranges are ldquobetween the control limitsrdquo If they are
then your process is considered to be in a state of statistical control
(as far as the variability of the process is concerned)
6 For the X-BAR Control Chart plot all the X-BARs on the X-BAR
control chart to see if all the X-BARs are ldquobetween the control
limitsrdquo If they are then your process is considered in a state of
statistical control (as far as the average of the process is
concerned)
PROCEDURE FOR X ndashBAR AND R BAR CHART
32
SAMPLE DATA FOR X BAR ndashR CHART
Sub Group 1 2 3 4 5 X -Bar Range reg
1 1195 1191 1211 1203 1198 1200 02
2 1201 1198 1198 1197 12 1199 004
3 1193 1206 1198 1196 1202 1199 013
4 1205 1198 1205 1206 1198 1202 008
5 1198 1203 1206 1201 1199 1201 008
6 1202 1205 1196 1201 1195 1200 01
7 1199 1206 1201 1204 1201 1202 007
8 1201 1197 1198 1204 1198 1200 007
9 1198 1204 1198 1204 1204 1202 006
10 1205 1195 1198 1204 1196 1200 01
` X Bar-Bar 1200 009
X Bar Chart
UCL = X BAR-BAR + A2 R Bar
1200 +(0577009) 1205
LCL= X BAR-BAR - A2 R Bar
1200 - (0577009) 1195
R Chart
UCL = D4R Bar 211 009 021
LCL = D3 R Bar 0009 0
33
PLOT DATA ON CONTROL CHARTS
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1 2 3 4 5 6 7 8 9 10
Ave
rage
(X
ba
r)
X Bar Chart
UCL
LCL
X Bar
34
PLOT DATA ON CONTROL CHARTS
001
003
005
007
009
011
013
015
017
019
021
023
025
1 2 3 4 5 6 7 8 9 10
R Chart
UCL
LCL
35
PROCEDURE TO DETERMINE IF PROCESS IS IN A STATE OF
STATISTICAL CONTROL
7 If process is determined to be ldquoNOT STABLErdquo then stop and find out what
an assignable cause might be fix and then repeat the complete process of
collecting new data
8 If the process is determined to be ldquoSTABLErdquo then you may use the
control charts you developed to monitor future production to ensure that the
process REMAINS stable
More Samples for Control charts
36
READING OF CONTROL CHART
Control charts can determine whether a process is behaving in an unusual way The quality of the individual points of a subset is determined unstable if any of the
following occurs
Rule 1 Any point falls beyond 3σ from the centreline(this is represented by the upper and
lower control limits)
Rule 2 Two out of three consecutive points fall beyond 2σ on the same side of the
centreline
Rule 3 Four out of five consecutive points fall beyond 1σ on the same side of the
centreline
Rule 4 Nine or more consecutive points fall on the same side of the centreline
(Ref Next page for sample)
37
READING THE CONTROL CHART
38
CONTROL CHARTS FOR ATTRIBUTES ndashP-CHARTS amp C-CHARTS
Attributes are discrete events yesno or passfail
Use P-Charts for quality characteristics that are discrete and involve yesno or goodbad decisions
Eg
Number of leaking caulking tubes in a box of 48
Number of broken eggs in a carton
Use C-Charts for discrete defects when there can be more than one defect per unit
Eg
Number of stains in a carpet sample cut from a production run
Number of complaints per customer at a hotel
39
P-CHART EXAMPLE A PRODUCTION MANAGER FOR A TIRE COMPANY HAS INSPECTED THE NUMBER OF
DEFECTIVE TIRES IN FIVE RANDOM SAMPLES WITH 20 TIRES IN EACH SAMPLE THE TABLE BELOW SHOWS THE
NUMBER OF DEFECTIVE TIRES IN EACH SAMPLE OF 20 TIRES CALCULATE THE CONTROL LIMITS
Sample Number of
Defective Tires
Number of Tires in each
Sample
Proportion Defective
1 3 20 15
2 2 20 10
3 1 20 05
4 2 20 10
5 2 20 05
Total 9 100 09
01023(064)09σzpLCL
2823(064)09σzpUCL
06420
(09)(91)
n
)p(1pσ
09100
9
Inspected Total
DefectivespCL
p
p
p
Solution
40
P- CONTROL CHART
41
C-CHART EXAMPLE THE NUMBER OF WEEKLY CUSTOMER COMPLAINTS ARE MONITORED IN A LARGE HOTEL USING A C-CHART DEVELOP THREE SIGMA CONTROL LIMITS USING THE DATA TABLE BELOW
Week Number of Complaints
1 3
2 2
3 3
4 1
5 3
6 3
7 2
8 1
9 3
10 1
Total 22
022522322ccLCL
66522322ccUCL
2210
22
samples of
complaintsc
c
c
z
z
Solution
42
C- CONTROL CHART
43
The ability of a process to meet product designtechnical specifications
Assessing capability involves evaluating process variability relative to preset product or service specifications
Process Capability ndash Cp and Cpk
Cp assumes that the process is centered in the specification range
Cpk helps to address a possible lack of centering of the process
PROCESS CAPABILITY
6σ
LSLUSL
width process
width ionspecificatCp
3σ
LSLμ
3σ
μUSLminCpk
44
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
45
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
46
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
47
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
--and an individual part is measured at 520rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
48
GRAPHING THE TOLERANCE AND MEASUREMENTS
Suppose we made and measured several more
units and they were all EXACTLY the same
We wouldnrsquot have very many part problems
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
X
X
X
49
GRAPHING THE TOLERANCE AND MEASUREMENTS
In the real world units are NOT EXACTLY the same
Everything VARIES
The question isnrsquot IF units vary
Itrsquos how much when and why
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
XX
XXX
XXXXX
XXXXXXX
50
The ldquonormal bell curverdquo
Widths heights depths thicknesses weights speeds strengths
and many other types of measurements when charted as a
histogram often form the shape of a bell
A ldquoperfect bellrdquo like a ldquoperfect circlerdquo doesnrsquot occur in nature but
many processes are close enough to make the bell curve useful
(A number of common industrial measurements such as flatness and straightness do NOT tend to distribute in a bell shape their proper statistical analysis is performed using models other than the bell curve)
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
51
What is a ldquostandard deviationrdquo
If we measure the DISTANCE from the CENTER of the bell
to each individual measurement that makes up the bell curve
we can find a TYPICAL DISTANCE
The most commonly used statistic to estimate this distance is the
Standard Deviation (also called ldquoSigmardquo)
Because of the natural shape of the bell curve the area of +1 to ndash1
standard deviations includes about 68 of the curve
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
Typical distance
from the center +1
standard deviation
Typical distance
from the center -1
standard deviation
52
How much of the curve is included in how many standard
deviations
From ndash1 to +1 is about 68 of the bell curve
From ndash2 to +2 is about 95
From ndash3 to +3 is about 9973
From ndash4 to +4 is about 9999
(NOTE We usually show the bell from ndash3 to +3 to make it easier to draw but in concept the ldquotailsrdquo of the bell get very thin and go on forever)
-6 -5 -4 -3 -2 -1 +1 +2 +3 +4 +5 +6 0
53
A
B
What is Cpk It is a measure of how well a process is within a specification
Cpk = A divided by B
A = Distance from process mean to closest spec limit
B = 3 Standard Deviations (also called ldquo3 Sigmardquo)
A bigger Cpk is better because fewer units will be beyond spec
(A bigger ldquoArdquo and a smaller ldquoBrdquo are better)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
54
A
B
ldquoProcess Capabilityrdquo is the ability of a process
to fit its output within the tolerances
hellipa LARGER ldquoArdquo
hellipand a SMALLER ldquoBrdquo
hellipmeans BETTER ldquoProcess Capabilityrdquo
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
55
A
B
An Analogy
Analogy
The bell curve is your automobile
The spec limits are the edges of your garage door
If A = B you are hitting the frame of your garage door with your car
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
56
A
B
How can we make Cpk (A divided by B) better
1 Design the product so a wider tolerance is functional (ldquorobust designrdquo)
2 Choose equipment and methods for a good safety margin (ldquoprocess capabilityrdquo)
3 Correctly adjust but only when needed (ldquocontrolrdquo)
4 Discover ways to narrow the natural variation (ldquoimprovementrdquo)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
57
A
B
What does a very good Cpk do for us
This process is producing good units with a good safety margin
Note that when Cpk = 2 our process mean is 6 standard deviations from
the nearest spec so we say it has ldquo6 Sigma Capabilityrdquo
Specification
Limit
Specification
Limit
This Cpk is
about 2
Very good
Mean
58
A
B
What does a problem Cpk look like
This process is in danger of producing some defects
It is too close to the specification limits
(Remember the bell curve tail goes further than Bhellip hellipwe only show the bell to 3-sigma to make it easier to draw)
Specification
Limit
Specification
Limit
This Cpk is just
slightly greater
than 1 Not good
59
A
B
What does a very bad Cpk look like
A significant part of the ldquotailrdquo is hanging out beyond the spec limits
This process is producing scrap rework and customer rejects
Notice that if distance ldquoArdquo approaches zerohellip
hellipthe Cpk would approach zero andhellip
hellipthe process would become 50 defective
Specification
Limit
Specification
Limit
This Cpk is less
than 1 We desire
a minimum of 133
and ultimately we
want 2 or more
60
-
Q amp A
61
MEASUREMENT SYSTEM ANALYSIS (MSA)
An MSA is a statistical tool used to determine if a measurement system is capable of precise measurement
What is It
Objective or Purpose
bull To determine how much error is in the measurement due to the measurement process itself
bull Quantifies the variability added by the measurement system
bull Applicable to attribute data and variable data
When to Use It
bull On the critical inputs and outputs prior to collecting data for analysis
bull For any new or modified process in order to ensure the quality of the data
Measurement System Analysis is an analysis of the measurement process not an analysis of the people
IMPORTANT
Who Should be Involved
Everyone that measures and makes decisions about these measurements should be involved in the MSA
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The observed variation in process output measurements is not simply the variation in the process itself it is the variation in the process plus the variation in measurement that results from an inadequate measurement system
Conducting an MSA reduces the likelihood of passing a bad part or rejecting a good part
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The output of the process measured by bull Cycle time bull Dimensional data bull Number of defects and others
Observed Variation
Process Variation
Measurement System
Variation
Reproducibility
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Accuracy (Central Location)
OBSERVED VARIATION
Calibration addresses accuracy
Measurement System Analysis (MSA)
MEASUREMENT SYSTEM ERRORS
Accuracy difference between the observed measurement and the actual measurement
Precision variation that occurs when measuring the same part with the same instrument
MEASUREMENT SYSTEM ERROR
Precise but not
accurate
Accurate but not
precise
Not accurate or
precise
Accurate and
precise
ACCURACY OF MEASUREMENT
Broken down into three components
aStability
The consistency of measurements over time
bBias
A measure of the amount of partiality in the system
cLinearity
A measure of the bias values through the expected
range of measurements
OBSERVED VARIATION
Observed Variation
Process Variation
Measurement System
Variation
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Reproducibility
Accuracy (Central Location)
Calibration Addresses Accuracy
Letrsquos take a closer look at Precision
Measurement System Analysis (MSA)
Measurement System Analysis (MSA)
Error in Resolution The inability to detect small changes
Possible Cause
Wrong measurement device selected - divisions on scale not fine enough to detect changes
Resolution
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Repeatability The inability to get the same answer from repeated measurements made of the same item under absolutely identical conditions
Possible Cause
Lack of standard operating procedures (SOP) lack of training measuring system variablilty
Repeatability
Equipment Variation
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Reproducibility The inability to get the same answer from repeated measurements made under various conditions from different inspectors
Possible Cause
Lack of SOP lack of training
Reproducibility
Appraiser Variation
VARIABLE MSA ndash GAGE RampR STUDY
bull Gage RampR is the combined estimate of
measurement system Repeatability and
Reproducibility
bull Typically a 3-person study is performed Each person randomly measures 10 marked parts per trial
Each person can perform up to 3 trials
bull There are 3 key indicators EV or Equipment Variation
AV or Appraiser Variation
Overall GRR
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
CONSTRUCTING A PARETO CHART
Determine the categories and the units for comparison of the data such as frequency cost or time
Total the raw data in each category then determine the grand total by adding the totals of each category
Re-order the categories from largest to smallest
Determine the cumulative percent of each category (ie the sum of each category plus all categories that precede it in the rank order divided by the grand total and multiplied by 100)
17
CONSTRUCTING A PARETO CHART
Draw and label the left-hand vertical axis with the unit of comparison such as frequency cost or time
Draw and label the horizontal axis with the categories List from left to right in rank order
Draw and label the right-hand vertical axis from 0 to 100 percent The 100 percent should line up with the grand total on the left-hand vertical axis
Beginning with the largest category draw in bars for each category representing the total for that category
18
CONSTRUCTING A PARETO CHART
Draw a line graph beginning at the right-hand
corner of the first bar to represent the
cumulative percent for each category as
measured on the right-hand axis
Analyze the chart Usually the top 20 of the
categories will comprise roughly 80 of the
cumulative total
19
PARETO CHART - EXAMPLE
Lets assume we are listing all the rejected products that are removed from a candy manufacturing line in one week
First we put the rejects in specific categories
No wrapper - 10
No center - 37
Wrong shape - 53
Short shot - 6
Wrapper open - 132
Underweight - 4
Overweight ndash 17
Get the total rejects - 259
20
Develop a percentage for each category
No wrapper ndash 10259 = 39
No center ndash 37259 = 143
Wrong shape ndash 53259 = 205
Short shot ndash 6259 = 23
Wrapper open ndash 132259 = 51
Underweight ndash 4259 = 15
Overweight ndash 17259 = 66
PARETO CHART - EXAMPLE
21
Now place the counts in a histogram largest to smallest
0
10
20
30
40
50
60
Wrapper
Open
No Center No Wrapper Underweight
70
80
90
100
51
205
143
66 39
23 15
22
Finally add up each and plot as a line diagram
0
10
20
30
40
50
60
Wrapper
Open
No Center No Wrapper Underweight
70
80
90
100
715
51
205
143
858
66
924
39
963
23
986
15
1001
23
0
10
20
30
40
50
60
Wrapper
Open
No Center No Wrapper Underweight
70
80
90
100
715
51
205
143
858
66
924
39
963
23
986
15
1001
24
CONTROL CHARTS
Control charts are one of the most commonly used methods of Statistical Process Control (SPC) which
monitors the stability of a process
The main features of a control chart include the data points a centreline (mean value) and upper and
lower limits (bounds to indicate where a process output is considered out of control)They visually
display the fluctuations of a particular process variable that easily determine whether these variations
fall within the specified process limits
Control charts
a graphical method for detecting if the underlying distribution of variation of some measurable
characteristic of the product seems to have undergone a shift
monitor a process in real time
Map the output of a production process over time
A control chart always has a central line for the average an upper line for the upper control limit and a
lower line for the lower control limit These lines are determined from historical data
By comparing current data to these lines you can draw conclusions about whether the process
variation is consistent (in control) or is unpredictable
25
CONTROL CHART - PURPOSE
The main purpose of using a control chart is to monitor control and improve
process performance over time by studying variation and its source There are
several functions of a control chart
It centres attention on detecting and monitoring process variation over time
It provides a tool for on-going control of a process
It differentiates special from common causes of variation in order to be a guide for
local or management action
It helps improve a process to perform consistently and predictably to achieve higher
quality lower cost and higher effective capacity
It serves as a common language for discussing process performance
26
TYPES OF CONTROL CHARTS
The basic tool used in SPC is the control chart
There are various types of control charts
Variable Control Chart
Averages and range chart (X-Bar and R Bar Chart)
X bar and s chart
Moving Range Chart
Moving AveragendashMoving Range chart (also called MAndashMR chart)
p chart (also called proportion chart)
c chart (also called count chart)
np chart
u chart
27
POPULARITY OF CONTROL CHARTS
Control charts are a proven technique for improving productivity
Control charts are effective in defect prevention
Control charts prevent unnecessary process
adjustment
Control charts provide diagnostic information
Control charts provide information about process
capability
28
PROCEDURE FOR X ndashBAR AND R BAR CHART
1 Randomly sample ldquonrdquo units throughout the day (can be every 5
minutes every 30 minutes etc - whatever is appropriate for your
case)
2 For each sample calculate ldquoX-BARrdquo to estimate the mean and ldquoR
(range)rdquo to estimate variability NOTE THE RANGE CAN BE USED TO
ESTIMATE THE STANDARD DEVIATION
3 After collecting the 20-25 samples calculate X-BAR-BAR (the
average of all the X-BARs) and R-BAR (the average of all the ranges)
4 Using X-BAR-BAR and R-BAR calculate the control limits for your X-
BAR and R Control Charts
29
X-BAR CONTROL LIMITS
Upper Control Limit (UCL) = (X-BAR-BAR) + A2 (R-BAR)
Lower Control Limit(LCL) = (X-BAR-BAR) - A2 (R-BAR)
R CONTROL LIMITS
Upper Control Limit - D3 (R-BAR)
Lower Control Limit - D4 (R-BAR)
PROCEDURE FOR X ndashBAR AND R BAR CHART
30
CONTROL CHART CONSTANTS
sample size constant constant constant constant constant constant constant
n d2 A2 A3 B3 B4 D3 D4
2 1128 188 2659 0 3267 0 3267
3 1693 1023 1954 0 2568 0 2574
4 2059 0729 1628 0 2266 0 2282
5 2326 0577 1427 0 2089 0 2114
6 2534 0483 1287 003 197 0 2004
7 2704 0419 1182 0118 1882 0076 1924
8 2847 0373 1099 0185 1815 0136 1864
9 297 0337 1032 0239 1761 0184 1816
10 3078 0308 0975 0284 1716 0223 1777
31
5 For the R Control Chart plot all R values on the R Control Chart
to see if all the Ranges are ldquobetween the control limitsrdquo If they are
then your process is considered to be in a state of statistical control
(as far as the variability of the process is concerned)
6 For the X-BAR Control Chart plot all the X-BARs on the X-BAR
control chart to see if all the X-BARs are ldquobetween the control
limitsrdquo If they are then your process is considered in a state of
statistical control (as far as the average of the process is
concerned)
PROCEDURE FOR X ndashBAR AND R BAR CHART
32
SAMPLE DATA FOR X BAR ndashR CHART
Sub Group 1 2 3 4 5 X -Bar Range reg
1 1195 1191 1211 1203 1198 1200 02
2 1201 1198 1198 1197 12 1199 004
3 1193 1206 1198 1196 1202 1199 013
4 1205 1198 1205 1206 1198 1202 008
5 1198 1203 1206 1201 1199 1201 008
6 1202 1205 1196 1201 1195 1200 01
7 1199 1206 1201 1204 1201 1202 007
8 1201 1197 1198 1204 1198 1200 007
9 1198 1204 1198 1204 1204 1202 006
10 1205 1195 1198 1204 1196 1200 01
` X Bar-Bar 1200 009
X Bar Chart
UCL = X BAR-BAR + A2 R Bar
1200 +(0577009) 1205
LCL= X BAR-BAR - A2 R Bar
1200 - (0577009) 1195
R Chart
UCL = D4R Bar 211 009 021
LCL = D3 R Bar 0009 0
33
PLOT DATA ON CONTROL CHARTS
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1 2 3 4 5 6 7 8 9 10
Ave
rage
(X
ba
r)
X Bar Chart
UCL
LCL
X Bar
34
PLOT DATA ON CONTROL CHARTS
001
003
005
007
009
011
013
015
017
019
021
023
025
1 2 3 4 5 6 7 8 9 10
R Chart
UCL
LCL
35
PROCEDURE TO DETERMINE IF PROCESS IS IN A STATE OF
STATISTICAL CONTROL
7 If process is determined to be ldquoNOT STABLErdquo then stop and find out what
an assignable cause might be fix and then repeat the complete process of
collecting new data
8 If the process is determined to be ldquoSTABLErdquo then you may use the
control charts you developed to monitor future production to ensure that the
process REMAINS stable
More Samples for Control charts
36
READING OF CONTROL CHART
Control charts can determine whether a process is behaving in an unusual way The quality of the individual points of a subset is determined unstable if any of the
following occurs
Rule 1 Any point falls beyond 3σ from the centreline(this is represented by the upper and
lower control limits)
Rule 2 Two out of three consecutive points fall beyond 2σ on the same side of the
centreline
Rule 3 Four out of five consecutive points fall beyond 1σ on the same side of the
centreline
Rule 4 Nine or more consecutive points fall on the same side of the centreline
(Ref Next page for sample)
37
READING THE CONTROL CHART
38
CONTROL CHARTS FOR ATTRIBUTES ndashP-CHARTS amp C-CHARTS
Attributes are discrete events yesno or passfail
Use P-Charts for quality characteristics that are discrete and involve yesno or goodbad decisions
Eg
Number of leaking caulking tubes in a box of 48
Number of broken eggs in a carton
Use C-Charts for discrete defects when there can be more than one defect per unit
Eg
Number of stains in a carpet sample cut from a production run
Number of complaints per customer at a hotel
39
P-CHART EXAMPLE A PRODUCTION MANAGER FOR A TIRE COMPANY HAS INSPECTED THE NUMBER OF
DEFECTIVE TIRES IN FIVE RANDOM SAMPLES WITH 20 TIRES IN EACH SAMPLE THE TABLE BELOW SHOWS THE
NUMBER OF DEFECTIVE TIRES IN EACH SAMPLE OF 20 TIRES CALCULATE THE CONTROL LIMITS
Sample Number of
Defective Tires
Number of Tires in each
Sample
Proportion Defective
1 3 20 15
2 2 20 10
3 1 20 05
4 2 20 10
5 2 20 05
Total 9 100 09
01023(064)09σzpLCL
2823(064)09σzpUCL
06420
(09)(91)
n
)p(1pσ
09100
9
Inspected Total
DefectivespCL
p
p
p
Solution
40
P- CONTROL CHART
41
C-CHART EXAMPLE THE NUMBER OF WEEKLY CUSTOMER COMPLAINTS ARE MONITORED IN A LARGE HOTEL USING A C-CHART DEVELOP THREE SIGMA CONTROL LIMITS USING THE DATA TABLE BELOW
Week Number of Complaints
1 3
2 2
3 3
4 1
5 3
6 3
7 2
8 1
9 3
10 1
Total 22
022522322ccLCL
66522322ccUCL
2210
22
samples of
complaintsc
c
c
z
z
Solution
42
C- CONTROL CHART
43
The ability of a process to meet product designtechnical specifications
Assessing capability involves evaluating process variability relative to preset product or service specifications
Process Capability ndash Cp and Cpk
Cp assumes that the process is centered in the specification range
Cpk helps to address a possible lack of centering of the process
PROCESS CAPABILITY
6σ
LSLUSL
width process
width ionspecificatCp
3σ
LSLμ
3σ
μUSLminCpk
44
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
45
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
46
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
47
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
--and an individual part is measured at 520rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
48
GRAPHING THE TOLERANCE AND MEASUREMENTS
Suppose we made and measured several more
units and they were all EXACTLY the same
We wouldnrsquot have very many part problems
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
X
X
X
49
GRAPHING THE TOLERANCE AND MEASUREMENTS
In the real world units are NOT EXACTLY the same
Everything VARIES
The question isnrsquot IF units vary
Itrsquos how much when and why
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
XX
XXX
XXXXX
XXXXXXX
50
The ldquonormal bell curverdquo
Widths heights depths thicknesses weights speeds strengths
and many other types of measurements when charted as a
histogram often form the shape of a bell
A ldquoperfect bellrdquo like a ldquoperfect circlerdquo doesnrsquot occur in nature but
many processes are close enough to make the bell curve useful
(A number of common industrial measurements such as flatness and straightness do NOT tend to distribute in a bell shape their proper statistical analysis is performed using models other than the bell curve)
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
51
What is a ldquostandard deviationrdquo
If we measure the DISTANCE from the CENTER of the bell
to each individual measurement that makes up the bell curve
we can find a TYPICAL DISTANCE
The most commonly used statistic to estimate this distance is the
Standard Deviation (also called ldquoSigmardquo)
Because of the natural shape of the bell curve the area of +1 to ndash1
standard deviations includes about 68 of the curve
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
Typical distance
from the center +1
standard deviation
Typical distance
from the center -1
standard deviation
52
How much of the curve is included in how many standard
deviations
From ndash1 to +1 is about 68 of the bell curve
From ndash2 to +2 is about 95
From ndash3 to +3 is about 9973
From ndash4 to +4 is about 9999
(NOTE We usually show the bell from ndash3 to +3 to make it easier to draw but in concept the ldquotailsrdquo of the bell get very thin and go on forever)
-6 -5 -4 -3 -2 -1 +1 +2 +3 +4 +5 +6 0
53
A
B
What is Cpk It is a measure of how well a process is within a specification
Cpk = A divided by B
A = Distance from process mean to closest spec limit
B = 3 Standard Deviations (also called ldquo3 Sigmardquo)
A bigger Cpk is better because fewer units will be beyond spec
(A bigger ldquoArdquo and a smaller ldquoBrdquo are better)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
54
A
B
ldquoProcess Capabilityrdquo is the ability of a process
to fit its output within the tolerances
hellipa LARGER ldquoArdquo
hellipand a SMALLER ldquoBrdquo
hellipmeans BETTER ldquoProcess Capabilityrdquo
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
55
A
B
An Analogy
Analogy
The bell curve is your automobile
The spec limits are the edges of your garage door
If A = B you are hitting the frame of your garage door with your car
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
56
A
B
How can we make Cpk (A divided by B) better
1 Design the product so a wider tolerance is functional (ldquorobust designrdquo)
2 Choose equipment and methods for a good safety margin (ldquoprocess capabilityrdquo)
3 Correctly adjust but only when needed (ldquocontrolrdquo)
4 Discover ways to narrow the natural variation (ldquoimprovementrdquo)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
57
A
B
What does a very good Cpk do for us
This process is producing good units with a good safety margin
Note that when Cpk = 2 our process mean is 6 standard deviations from
the nearest spec so we say it has ldquo6 Sigma Capabilityrdquo
Specification
Limit
Specification
Limit
This Cpk is
about 2
Very good
Mean
58
A
B
What does a problem Cpk look like
This process is in danger of producing some defects
It is too close to the specification limits
(Remember the bell curve tail goes further than Bhellip hellipwe only show the bell to 3-sigma to make it easier to draw)
Specification
Limit
Specification
Limit
This Cpk is just
slightly greater
than 1 Not good
59
A
B
What does a very bad Cpk look like
A significant part of the ldquotailrdquo is hanging out beyond the spec limits
This process is producing scrap rework and customer rejects
Notice that if distance ldquoArdquo approaches zerohellip
hellipthe Cpk would approach zero andhellip
hellipthe process would become 50 defective
Specification
Limit
Specification
Limit
This Cpk is less
than 1 We desire
a minimum of 133
and ultimately we
want 2 or more
60
-
Q amp A
61
MEASUREMENT SYSTEM ANALYSIS (MSA)
An MSA is a statistical tool used to determine if a measurement system is capable of precise measurement
What is It
Objective or Purpose
bull To determine how much error is in the measurement due to the measurement process itself
bull Quantifies the variability added by the measurement system
bull Applicable to attribute data and variable data
When to Use It
bull On the critical inputs and outputs prior to collecting data for analysis
bull For any new or modified process in order to ensure the quality of the data
Measurement System Analysis is an analysis of the measurement process not an analysis of the people
IMPORTANT
Who Should be Involved
Everyone that measures and makes decisions about these measurements should be involved in the MSA
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The observed variation in process output measurements is not simply the variation in the process itself it is the variation in the process plus the variation in measurement that results from an inadequate measurement system
Conducting an MSA reduces the likelihood of passing a bad part or rejecting a good part
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The output of the process measured by bull Cycle time bull Dimensional data bull Number of defects and others
Observed Variation
Process Variation
Measurement System
Variation
Reproducibility
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Accuracy (Central Location)
OBSERVED VARIATION
Calibration addresses accuracy
Measurement System Analysis (MSA)
MEASUREMENT SYSTEM ERRORS
Accuracy difference between the observed measurement and the actual measurement
Precision variation that occurs when measuring the same part with the same instrument
MEASUREMENT SYSTEM ERROR
Precise but not
accurate
Accurate but not
precise
Not accurate or
precise
Accurate and
precise
ACCURACY OF MEASUREMENT
Broken down into three components
aStability
The consistency of measurements over time
bBias
A measure of the amount of partiality in the system
cLinearity
A measure of the bias values through the expected
range of measurements
OBSERVED VARIATION
Observed Variation
Process Variation
Measurement System
Variation
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Reproducibility
Accuracy (Central Location)
Calibration Addresses Accuracy
Letrsquos take a closer look at Precision
Measurement System Analysis (MSA)
Measurement System Analysis (MSA)
Error in Resolution The inability to detect small changes
Possible Cause
Wrong measurement device selected - divisions on scale not fine enough to detect changes
Resolution
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Repeatability The inability to get the same answer from repeated measurements made of the same item under absolutely identical conditions
Possible Cause
Lack of standard operating procedures (SOP) lack of training measuring system variablilty
Repeatability
Equipment Variation
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Reproducibility The inability to get the same answer from repeated measurements made under various conditions from different inspectors
Possible Cause
Lack of SOP lack of training
Reproducibility
Appraiser Variation
VARIABLE MSA ndash GAGE RampR STUDY
bull Gage RampR is the combined estimate of
measurement system Repeatability and
Reproducibility
bull Typically a 3-person study is performed Each person randomly measures 10 marked parts per trial
Each person can perform up to 3 trials
bull There are 3 key indicators EV or Equipment Variation
AV or Appraiser Variation
Overall GRR
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
CONSTRUCTING A PARETO CHART
Draw and label the left-hand vertical axis with the unit of comparison such as frequency cost or time
Draw and label the horizontal axis with the categories List from left to right in rank order
Draw and label the right-hand vertical axis from 0 to 100 percent The 100 percent should line up with the grand total on the left-hand vertical axis
Beginning with the largest category draw in bars for each category representing the total for that category
18
CONSTRUCTING A PARETO CHART
Draw a line graph beginning at the right-hand
corner of the first bar to represent the
cumulative percent for each category as
measured on the right-hand axis
Analyze the chart Usually the top 20 of the
categories will comprise roughly 80 of the
cumulative total
19
PARETO CHART - EXAMPLE
Lets assume we are listing all the rejected products that are removed from a candy manufacturing line in one week
First we put the rejects in specific categories
No wrapper - 10
No center - 37
Wrong shape - 53
Short shot - 6
Wrapper open - 132
Underweight - 4
Overweight ndash 17
Get the total rejects - 259
20
Develop a percentage for each category
No wrapper ndash 10259 = 39
No center ndash 37259 = 143
Wrong shape ndash 53259 = 205
Short shot ndash 6259 = 23
Wrapper open ndash 132259 = 51
Underweight ndash 4259 = 15
Overweight ndash 17259 = 66
PARETO CHART - EXAMPLE
21
Now place the counts in a histogram largest to smallest
0
10
20
30
40
50
60
Wrapper
Open
No Center No Wrapper Underweight
70
80
90
100
51
205
143
66 39
23 15
22
Finally add up each and plot as a line diagram
0
10
20
30
40
50
60
Wrapper
Open
No Center No Wrapper Underweight
70
80
90
100
715
51
205
143
858
66
924
39
963
23
986
15
1001
23
0
10
20
30
40
50
60
Wrapper
Open
No Center No Wrapper Underweight
70
80
90
100
715
51
205
143
858
66
924
39
963
23
986
15
1001
24
CONTROL CHARTS
Control charts are one of the most commonly used methods of Statistical Process Control (SPC) which
monitors the stability of a process
The main features of a control chart include the data points a centreline (mean value) and upper and
lower limits (bounds to indicate where a process output is considered out of control)They visually
display the fluctuations of a particular process variable that easily determine whether these variations
fall within the specified process limits
Control charts
a graphical method for detecting if the underlying distribution of variation of some measurable
characteristic of the product seems to have undergone a shift
monitor a process in real time
Map the output of a production process over time
A control chart always has a central line for the average an upper line for the upper control limit and a
lower line for the lower control limit These lines are determined from historical data
By comparing current data to these lines you can draw conclusions about whether the process
variation is consistent (in control) or is unpredictable
25
CONTROL CHART - PURPOSE
The main purpose of using a control chart is to monitor control and improve
process performance over time by studying variation and its source There are
several functions of a control chart
It centres attention on detecting and monitoring process variation over time
It provides a tool for on-going control of a process
It differentiates special from common causes of variation in order to be a guide for
local or management action
It helps improve a process to perform consistently and predictably to achieve higher
quality lower cost and higher effective capacity
It serves as a common language for discussing process performance
26
TYPES OF CONTROL CHARTS
The basic tool used in SPC is the control chart
There are various types of control charts
Variable Control Chart
Averages and range chart (X-Bar and R Bar Chart)
X bar and s chart
Moving Range Chart
Moving AveragendashMoving Range chart (also called MAndashMR chart)
p chart (also called proportion chart)
c chart (also called count chart)
np chart
u chart
27
POPULARITY OF CONTROL CHARTS
Control charts are a proven technique for improving productivity
Control charts are effective in defect prevention
Control charts prevent unnecessary process
adjustment
Control charts provide diagnostic information
Control charts provide information about process
capability
28
PROCEDURE FOR X ndashBAR AND R BAR CHART
1 Randomly sample ldquonrdquo units throughout the day (can be every 5
minutes every 30 minutes etc - whatever is appropriate for your
case)
2 For each sample calculate ldquoX-BARrdquo to estimate the mean and ldquoR
(range)rdquo to estimate variability NOTE THE RANGE CAN BE USED TO
ESTIMATE THE STANDARD DEVIATION
3 After collecting the 20-25 samples calculate X-BAR-BAR (the
average of all the X-BARs) and R-BAR (the average of all the ranges)
4 Using X-BAR-BAR and R-BAR calculate the control limits for your X-
BAR and R Control Charts
29
X-BAR CONTROL LIMITS
Upper Control Limit (UCL) = (X-BAR-BAR) + A2 (R-BAR)
Lower Control Limit(LCL) = (X-BAR-BAR) - A2 (R-BAR)
R CONTROL LIMITS
Upper Control Limit - D3 (R-BAR)
Lower Control Limit - D4 (R-BAR)
PROCEDURE FOR X ndashBAR AND R BAR CHART
30
CONTROL CHART CONSTANTS
sample size constant constant constant constant constant constant constant
n d2 A2 A3 B3 B4 D3 D4
2 1128 188 2659 0 3267 0 3267
3 1693 1023 1954 0 2568 0 2574
4 2059 0729 1628 0 2266 0 2282
5 2326 0577 1427 0 2089 0 2114
6 2534 0483 1287 003 197 0 2004
7 2704 0419 1182 0118 1882 0076 1924
8 2847 0373 1099 0185 1815 0136 1864
9 297 0337 1032 0239 1761 0184 1816
10 3078 0308 0975 0284 1716 0223 1777
31
5 For the R Control Chart plot all R values on the R Control Chart
to see if all the Ranges are ldquobetween the control limitsrdquo If they are
then your process is considered to be in a state of statistical control
(as far as the variability of the process is concerned)
6 For the X-BAR Control Chart plot all the X-BARs on the X-BAR
control chart to see if all the X-BARs are ldquobetween the control
limitsrdquo If they are then your process is considered in a state of
statistical control (as far as the average of the process is
concerned)
PROCEDURE FOR X ndashBAR AND R BAR CHART
32
SAMPLE DATA FOR X BAR ndashR CHART
Sub Group 1 2 3 4 5 X -Bar Range reg
1 1195 1191 1211 1203 1198 1200 02
2 1201 1198 1198 1197 12 1199 004
3 1193 1206 1198 1196 1202 1199 013
4 1205 1198 1205 1206 1198 1202 008
5 1198 1203 1206 1201 1199 1201 008
6 1202 1205 1196 1201 1195 1200 01
7 1199 1206 1201 1204 1201 1202 007
8 1201 1197 1198 1204 1198 1200 007
9 1198 1204 1198 1204 1204 1202 006
10 1205 1195 1198 1204 1196 1200 01
` X Bar-Bar 1200 009
X Bar Chart
UCL = X BAR-BAR + A2 R Bar
1200 +(0577009) 1205
LCL= X BAR-BAR - A2 R Bar
1200 - (0577009) 1195
R Chart
UCL = D4R Bar 211 009 021
LCL = D3 R Bar 0009 0
33
PLOT DATA ON CONTROL CHARTS
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1 2 3 4 5 6 7 8 9 10
Ave
rage
(X
ba
r)
X Bar Chart
UCL
LCL
X Bar
34
PLOT DATA ON CONTROL CHARTS
001
003
005
007
009
011
013
015
017
019
021
023
025
1 2 3 4 5 6 7 8 9 10
R Chart
UCL
LCL
35
PROCEDURE TO DETERMINE IF PROCESS IS IN A STATE OF
STATISTICAL CONTROL
7 If process is determined to be ldquoNOT STABLErdquo then stop and find out what
an assignable cause might be fix and then repeat the complete process of
collecting new data
8 If the process is determined to be ldquoSTABLErdquo then you may use the
control charts you developed to monitor future production to ensure that the
process REMAINS stable
More Samples for Control charts
36
READING OF CONTROL CHART
Control charts can determine whether a process is behaving in an unusual way The quality of the individual points of a subset is determined unstable if any of the
following occurs
Rule 1 Any point falls beyond 3σ from the centreline(this is represented by the upper and
lower control limits)
Rule 2 Two out of three consecutive points fall beyond 2σ on the same side of the
centreline
Rule 3 Four out of five consecutive points fall beyond 1σ on the same side of the
centreline
Rule 4 Nine or more consecutive points fall on the same side of the centreline
(Ref Next page for sample)
37
READING THE CONTROL CHART
38
CONTROL CHARTS FOR ATTRIBUTES ndashP-CHARTS amp C-CHARTS
Attributes are discrete events yesno or passfail
Use P-Charts for quality characteristics that are discrete and involve yesno or goodbad decisions
Eg
Number of leaking caulking tubes in a box of 48
Number of broken eggs in a carton
Use C-Charts for discrete defects when there can be more than one defect per unit
Eg
Number of stains in a carpet sample cut from a production run
Number of complaints per customer at a hotel
39
P-CHART EXAMPLE A PRODUCTION MANAGER FOR A TIRE COMPANY HAS INSPECTED THE NUMBER OF
DEFECTIVE TIRES IN FIVE RANDOM SAMPLES WITH 20 TIRES IN EACH SAMPLE THE TABLE BELOW SHOWS THE
NUMBER OF DEFECTIVE TIRES IN EACH SAMPLE OF 20 TIRES CALCULATE THE CONTROL LIMITS
Sample Number of
Defective Tires
Number of Tires in each
Sample
Proportion Defective
1 3 20 15
2 2 20 10
3 1 20 05
4 2 20 10
5 2 20 05
Total 9 100 09
01023(064)09σzpLCL
2823(064)09σzpUCL
06420
(09)(91)
n
)p(1pσ
09100
9
Inspected Total
DefectivespCL
p
p
p
Solution
40
P- CONTROL CHART
41
C-CHART EXAMPLE THE NUMBER OF WEEKLY CUSTOMER COMPLAINTS ARE MONITORED IN A LARGE HOTEL USING A C-CHART DEVELOP THREE SIGMA CONTROL LIMITS USING THE DATA TABLE BELOW
Week Number of Complaints
1 3
2 2
3 3
4 1
5 3
6 3
7 2
8 1
9 3
10 1
Total 22
022522322ccLCL
66522322ccUCL
2210
22
samples of
complaintsc
c
c
z
z
Solution
42
C- CONTROL CHART
43
The ability of a process to meet product designtechnical specifications
Assessing capability involves evaluating process variability relative to preset product or service specifications
Process Capability ndash Cp and Cpk
Cp assumes that the process is centered in the specification range
Cpk helps to address a possible lack of centering of the process
PROCESS CAPABILITY
6σ
LSLUSL
width process
width ionspecificatCp
3σ
LSLμ
3σ
μUSLminCpk
44
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
45
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
46
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
47
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
--and an individual part is measured at 520rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
48
GRAPHING THE TOLERANCE AND MEASUREMENTS
Suppose we made and measured several more
units and they were all EXACTLY the same
We wouldnrsquot have very many part problems
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
X
X
X
49
GRAPHING THE TOLERANCE AND MEASUREMENTS
In the real world units are NOT EXACTLY the same
Everything VARIES
The question isnrsquot IF units vary
Itrsquos how much when and why
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
XX
XXX
XXXXX
XXXXXXX
50
The ldquonormal bell curverdquo
Widths heights depths thicknesses weights speeds strengths
and many other types of measurements when charted as a
histogram often form the shape of a bell
A ldquoperfect bellrdquo like a ldquoperfect circlerdquo doesnrsquot occur in nature but
many processes are close enough to make the bell curve useful
(A number of common industrial measurements such as flatness and straightness do NOT tend to distribute in a bell shape their proper statistical analysis is performed using models other than the bell curve)
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
51
What is a ldquostandard deviationrdquo
If we measure the DISTANCE from the CENTER of the bell
to each individual measurement that makes up the bell curve
we can find a TYPICAL DISTANCE
The most commonly used statistic to estimate this distance is the
Standard Deviation (also called ldquoSigmardquo)
Because of the natural shape of the bell curve the area of +1 to ndash1
standard deviations includes about 68 of the curve
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
Typical distance
from the center +1
standard deviation
Typical distance
from the center -1
standard deviation
52
How much of the curve is included in how many standard
deviations
From ndash1 to +1 is about 68 of the bell curve
From ndash2 to +2 is about 95
From ndash3 to +3 is about 9973
From ndash4 to +4 is about 9999
(NOTE We usually show the bell from ndash3 to +3 to make it easier to draw but in concept the ldquotailsrdquo of the bell get very thin and go on forever)
-6 -5 -4 -3 -2 -1 +1 +2 +3 +4 +5 +6 0
53
A
B
What is Cpk It is a measure of how well a process is within a specification
Cpk = A divided by B
A = Distance from process mean to closest spec limit
B = 3 Standard Deviations (also called ldquo3 Sigmardquo)
A bigger Cpk is better because fewer units will be beyond spec
(A bigger ldquoArdquo and a smaller ldquoBrdquo are better)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
54
A
B
ldquoProcess Capabilityrdquo is the ability of a process
to fit its output within the tolerances
hellipa LARGER ldquoArdquo
hellipand a SMALLER ldquoBrdquo
hellipmeans BETTER ldquoProcess Capabilityrdquo
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
55
A
B
An Analogy
Analogy
The bell curve is your automobile
The spec limits are the edges of your garage door
If A = B you are hitting the frame of your garage door with your car
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
56
A
B
How can we make Cpk (A divided by B) better
1 Design the product so a wider tolerance is functional (ldquorobust designrdquo)
2 Choose equipment and methods for a good safety margin (ldquoprocess capabilityrdquo)
3 Correctly adjust but only when needed (ldquocontrolrdquo)
4 Discover ways to narrow the natural variation (ldquoimprovementrdquo)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
57
A
B
What does a very good Cpk do for us
This process is producing good units with a good safety margin
Note that when Cpk = 2 our process mean is 6 standard deviations from
the nearest spec so we say it has ldquo6 Sigma Capabilityrdquo
Specification
Limit
Specification
Limit
This Cpk is
about 2
Very good
Mean
58
A
B
What does a problem Cpk look like
This process is in danger of producing some defects
It is too close to the specification limits
(Remember the bell curve tail goes further than Bhellip hellipwe only show the bell to 3-sigma to make it easier to draw)
Specification
Limit
Specification
Limit
This Cpk is just
slightly greater
than 1 Not good
59
A
B
What does a very bad Cpk look like
A significant part of the ldquotailrdquo is hanging out beyond the spec limits
This process is producing scrap rework and customer rejects
Notice that if distance ldquoArdquo approaches zerohellip
hellipthe Cpk would approach zero andhellip
hellipthe process would become 50 defective
Specification
Limit
Specification
Limit
This Cpk is less
than 1 We desire
a minimum of 133
and ultimately we
want 2 or more
60
-
Q amp A
61
MEASUREMENT SYSTEM ANALYSIS (MSA)
An MSA is a statistical tool used to determine if a measurement system is capable of precise measurement
What is It
Objective or Purpose
bull To determine how much error is in the measurement due to the measurement process itself
bull Quantifies the variability added by the measurement system
bull Applicable to attribute data and variable data
When to Use It
bull On the critical inputs and outputs prior to collecting data for analysis
bull For any new or modified process in order to ensure the quality of the data
Measurement System Analysis is an analysis of the measurement process not an analysis of the people
IMPORTANT
Who Should be Involved
Everyone that measures and makes decisions about these measurements should be involved in the MSA
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The observed variation in process output measurements is not simply the variation in the process itself it is the variation in the process plus the variation in measurement that results from an inadequate measurement system
Conducting an MSA reduces the likelihood of passing a bad part or rejecting a good part
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The output of the process measured by bull Cycle time bull Dimensional data bull Number of defects and others
Observed Variation
Process Variation
Measurement System
Variation
Reproducibility
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Accuracy (Central Location)
OBSERVED VARIATION
Calibration addresses accuracy
Measurement System Analysis (MSA)
MEASUREMENT SYSTEM ERRORS
Accuracy difference between the observed measurement and the actual measurement
Precision variation that occurs when measuring the same part with the same instrument
MEASUREMENT SYSTEM ERROR
Precise but not
accurate
Accurate but not
precise
Not accurate or
precise
Accurate and
precise
ACCURACY OF MEASUREMENT
Broken down into three components
aStability
The consistency of measurements over time
bBias
A measure of the amount of partiality in the system
cLinearity
A measure of the bias values through the expected
range of measurements
OBSERVED VARIATION
Observed Variation
Process Variation
Measurement System
Variation
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Reproducibility
Accuracy (Central Location)
Calibration Addresses Accuracy
Letrsquos take a closer look at Precision
Measurement System Analysis (MSA)
Measurement System Analysis (MSA)
Error in Resolution The inability to detect small changes
Possible Cause
Wrong measurement device selected - divisions on scale not fine enough to detect changes
Resolution
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Repeatability The inability to get the same answer from repeated measurements made of the same item under absolutely identical conditions
Possible Cause
Lack of standard operating procedures (SOP) lack of training measuring system variablilty
Repeatability
Equipment Variation
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Reproducibility The inability to get the same answer from repeated measurements made under various conditions from different inspectors
Possible Cause
Lack of SOP lack of training
Reproducibility
Appraiser Variation
VARIABLE MSA ndash GAGE RampR STUDY
bull Gage RampR is the combined estimate of
measurement system Repeatability and
Reproducibility
bull Typically a 3-person study is performed Each person randomly measures 10 marked parts per trial
Each person can perform up to 3 trials
bull There are 3 key indicators EV or Equipment Variation
AV or Appraiser Variation
Overall GRR
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
CONSTRUCTING A PARETO CHART
Draw a line graph beginning at the right-hand
corner of the first bar to represent the
cumulative percent for each category as
measured on the right-hand axis
Analyze the chart Usually the top 20 of the
categories will comprise roughly 80 of the
cumulative total
19
PARETO CHART - EXAMPLE
Lets assume we are listing all the rejected products that are removed from a candy manufacturing line in one week
First we put the rejects in specific categories
No wrapper - 10
No center - 37
Wrong shape - 53
Short shot - 6
Wrapper open - 132
Underweight - 4
Overweight ndash 17
Get the total rejects - 259
20
Develop a percentage for each category
No wrapper ndash 10259 = 39
No center ndash 37259 = 143
Wrong shape ndash 53259 = 205
Short shot ndash 6259 = 23
Wrapper open ndash 132259 = 51
Underweight ndash 4259 = 15
Overweight ndash 17259 = 66
PARETO CHART - EXAMPLE
21
Now place the counts in a histogram largest to smallest
0
10
20
30
40
50
60
Wrapper
Open
No Center No Wrapper Underweight
70
80
90
100
51
205
143
66 39
23 15
22
Finally add up each and plot as a line diagram
0
10
20
30
40
50
60
Wrapper
Open
No Center No Wrapper Underweight
70
80
90
100
715
51
205
143
858
66
924
39
963
23
986
15
1001
23
0
10
20
30
40
50
60
Wrapper
Open
No Center No Wrapper Underweight
70
80
90
100
715
51
205
143
858
66
924
39
963
23
986
15
1001
24
CONTROL CHARTS
Control charts are one of the most commonly used methods of Statistical Process Control (SPC) which
monitors the stability of a process
The main features of a control chart include the data points a centreline (mean value) and upper and
lower limits (bounds to indicate where a process output is considered out of control)They visually
display the fluctuations of a particular process variable that easily determine whether these variations
fall within the specified process limits
Control charts
a graphical method for detecting if the underlying distribution of variation of some measurable
characteristic of the product seems to have undergone a shift
monitor a process in real time
Map the output of a production process over time
A control chart always has a central line for the average an upper line for the upper control limit and a
lower line for the lower control limit These lines are determined from historical data
By comparing current data to these lines you can draw conclusions about whether the process
variation is consistent (in control) or is unpredictable
25
CONTROL CHART - PURPOSE
The main purpose of using a control chart is to monitor control and improve
process performance over time by studying variation and its source There are
several functions of a control chart
It centres attention on detecting and monitoring process variation over time
It provides a tool for on-going control of a process
It differentiates special from common causes of variation in order to be a guide for
local or management action
It helps improve a process to perform consistently and predictably to achieve higher
quality lower cost and higher effective capacity
It serves as a common language for discussing process performance
26
TYPES OF CONTROL CHARTS
The basic tool used in SPC is the control chart
There are various types of control charts
Variable Control Chart
Averages and range chart (X-Bar and R Bar Chart)
X bar and s chart
Moving Range Chart
Moving AveragendashMoving Range chart (also called MAndashMR chart)
p chart (also called proportion chart)
c chart (also called count chart)
np chart
u chart
27
POPULARITY OF CONTROL CHARTS
Control charts are a proven technique for improving productivity
Control charts are effective in defect prevention
Control charts prevent unnecessary process
adjustment
Control charts provide diagnostic information
Control charts provide information about process
capability
28
PROCEDURE FOR X ndashBAR AND R BAR CHART
1 Randomly sample ldquonrdquo units throughout the day (can be every 5
minutes every 30 minutes etc - whatever is appropriate for your
case)
2 For each sample calculate ldquoX-BARrdquo to estimate the mean and ldquoR
(range)rdquo to estimate variability NOTE THE RANGE CAN BE USED TO
ESTIMATE THE STANDARD DEVIATION
3 After collecting the 20-25 samples calculate X-BAR-BAR (the
average of all the X-BARs) and R-BAR (the average of all the ranges)
4 Using X-BAR-BAR and R-BAR calculate the control limits for your X-
BAR and R Control Charts
29
X-BAR CONTROL LIMITS
Upper Control Limit (UCL) = (X-BAR-BAR) + A2 (R-BAR)
Lower Control Limit(LCL) = (X-BAR-BAR) - A2 (R-BAR)
R CONTROL LIMITS
Upper Control Limit - D3 (R-BAR)
Lower Control Limit - D4 (R-BAR)
PROCEDURE FOR X ndashBAR AND R BAR CHART
30
CONTROL CHART CONSTANTS
sample size constant constant constant constant constant constant constant
n d2 A2 A3 B3 B4 D3 D4
2 1128 188 2659 0 3267 0 3267
3 1693 1023 1954 0 2568 0 2574
4 2059 0729 1628 0 2266 0 2282
5 2326 0577 1427 0 2089 0 2114
6 2534 0483 1287 003 197 0 2004
7 2704 0419 1182 0118 1882 0076 1924
8 2847 0373 1099 0185 1815 0136 1864
9 297 0337 1032 0239 1761 0184 1816
10 3078 0308 0975 0284 1716 0223 1777
31
5 For the R Control Chart plot all R values on the R Control Chart
to see if all the Ranges are ldquobetween the control limitsrdquo If they are
then your process is considered to be in a state of statistical control
(as far as the variability of the process is concerned)
6 For the X-BAR Control Chart plot all the X-BARs on the X-BAR
control chart to see if all the X-BARs are ldquobetween the control
limitsrdquo If they are then your process is considered in a state of
statistical control (as far as the average of the process is
concerned)
PROCEDURE FOR X ndashBAR AND R BAR CHART
32
SAMPLE DATA FOR X BAR ndashR CHART
Sub Group 1 2 3 4 5 X -Bar Range reg
1 1195 1191 1211 1203 1198 1200 02
2 1201 1198 1198 1197 12 1199 004
3 1193 1206 1198 1196 1202 1199 013
4 1205 1198 1205 1206 1198 1202 008
5 1198 1203 1206 1201 1199 1201 008
6 1202 1205 1196 1201 1195 1200 01
7 1199 1206 1201 1204 1201 1202 007
8 1201 1197 1198 1204 1198 1200 007
9 1198 1204 1198 1204 1204 1202 006
10 1205 1195 1198 1204 1196 1200 01
` X Bar-Bar 1200 009
X Bar Chart
UCL = X BAR-BAR + A2 R Bar
1200 +(0577009) 1205
LCL= X BAR-BAR - A2 R Bar
1200 - (0577009) 1195
R Chart
UCL = D4R Bar 211 009 021
LCL = D3 R Bar 0009 0
33
PLOT DATA ON CONTROL CHARTS
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1 2 3 4 5 6 7 8 9 10
Ave
rage
(X
ba
r)
X Bar Chart
UCL
LCL
X Bar
34
PLOT DATA ON CONTROL CHARTS
001
003
005
007
009
011
013
015
017
019
021
023
025
1 2 3 4 5 6 7 8 9 10
R Chart
UCL
LCL
35
PROCEDURE TO DETERMINE IF PROCESS IS IN A STATE OF
STATISTICAL CONTROL
7 If process is determined to be ldquoNOT STABLErdquo then stop and find out what
an assignable cause might be fix and then repeat the complete process of
collecting new data
8 If the process is determined to be ldquoSTABLErdquo then you may use the
control charts you developed to monitor future production to ensure that the
process REMAINS stable
More Samples for Control charts
36
READING OF CONTROL CHART
Control charts can determine whether a process is behaving in an unusual way The quality of the individual points of a subset is determined unstable if any of the
following occurs
Rule 1 Any point falls beyond 3σ from the centreline(this is represented by the upper and
lower control limits)
Rule 2 Two out of three consecutive points fall beyond 2σ on the same side of the
centreline
Rule 3 Four out of five consecutive points fall beyond 1σ on the same side of the
centreline
Rule 4 Nine or more consecutive points fall on the same side of the centreline
(Ref Next page for sample)
37
READING THE CONTROL CHART
38
CONTROL CHARTS FOR ATTRIBUTES ndashP-CHARTS amp C-CHARTS
Attributes are discrete events yesno or passfail
Use P-Charts for quality characteristics that are discrete and involve yesno or goodbad decisions
Eg
Number of leaking caulking tubes in a box of 48
Number of broken eggs in a carton
Use C-Charts for discrete defects when there can be more than one defect per unit
Eg
Number of stains in a carpet sample cut from a production run
Number of complaints per customer at a hotel
39
P-CHART EXAMPLE A PRODUCTION MANAGER FOR A TIRE COMPANY HAS INSPECTED THE NUMBER OF
DEFECTIVE TIRES IN FIVE RANDOM SAMPLES WITH 20 TIRES IN EACH SAMPLE THE TABLE BELOW SHOWS THE
NUMBER OF DEFECTIVE TIRES IN EACH SAMPLE OF 20 TIRES CALCULATE THE CONTROL LIMITS
Sample Number of
Defective Tires
Number of Tires in each
Sample
Proportion Defective
1 3 20 15
2 2 20 10
3 1 20 05
4 2 20 10
5 2 20 05
Total 9 100 09
01023(064)09σzpLCL
2823(064)09σzpUCL
06420
(09)(91)
n
)p(1pσ
09100
9
Inspected Total
DefectivespCL
p
p
p
Solution
40
P- CONTROL CHART
41
C-CHART EXAMPLE THE NUMBER OF WEEKLY CUSTOMER COMPLAINTS ARE MONITORED IN A LARGE HOTEL USING A C-CHART DEVELOP THREE SIGMA CONTROL LIMITS USING THE DATA TABLE BELOW
Week Number of Complaints
1 3
2 2
3 3
4 1
5 3
6 3
7 2
8 1
9 3
10 1
Total 22
022522322ccLCL
66522322ccUCL
2210
22
samples of
complaintsc
c
c
z
z
Solution
42
C- CONTROL CHART
43
The ability of a process to meet product designtechnical specifications
Assessing capability involves evaluating process variability relative to preset product or service specifications
Process Capability ndash Cp and Cpk
Cp assumes that the process is centered in the specification range
Cpk helps to address a possible lack of centering of the process
PROCESS CAPABILITY
6σ
LSLUSL
width process
width ionspecificatCp
3σ
LSLμ
3σ
μUSLminCpk
44
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
45
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
46
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
47
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
--and an individual part is measured at 520rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
48
GRAPHING THE TOLERANCE AND MEASUREMENTS
Suppose we made and measured several more
units and they were all EXACTLY the same
We wouldnrsquot have very many part problems
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
X
X
X
49
GRAPHING THE TOLERANCE AND MEASUREMENTS
In the real world units are NOT EXACTLY the same
Everything VARIES
The question isnrsquot IF units vary
Itrsquos how much when and why
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
XX
XXX
XXXXX
XXXXXXX
50
The ldquonormal bell curverdquo
Widths heights depths thicknesses weights speeds strengths
and many other types of measurements when charted as a
histogram often form the shape of a bell
A ldquoperfect bellrdquo like a ldquoperfect circlerdquo doesnrsquot occur in nature but
many processes are close enough to make the bell curve useful
(A number of common industrial measurements such as flatness and straightness do NOT tend to distribute in a bell shape their proper statistical analysis is performed using models other than the bell curve)
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
51
What is a ldquostandard deviationrdquo
If we measure the DISTANCE from the CENTER of the bell
to each individual measurement that makes up the bell curve
we can find a TYPICAL DISTANCE
The most commonly used statistic to estimate this distance is the
Standard Deviation (also called ldquoSigmardquo)
Because of the natural shape of the bell curve the area of +1 to ndash1
standard deviations includes about 68 of the curve
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
Typical distance
from the center +1
standard deviation
Typical distance
from the center -1
standard deviation
52
How much of the curve is included in how many standard
deviations
From ndash1 to +1 is about 68 of the bell curve
From ndash2 to +2 is about 95
From ndash3 to +3 is about 9973
From ndash4 to +4 is about 9999
(NOTE We usually show the bell from ndash3 to +3 to make it easier to draw but in concept the ldquotailsrdquo of the bell get very thin and go on forever)
-6 -5 -4 -3 -2 -1 +1 +2 +3 +4 +5 +6 0
53
A
B
What is Cpk It is a measure of how well a process is within a specification
Cpk = A divided by B
A = Distance from process mean to closest spec limit
B = 3 Standard Deviations (also called ldquo3 Sigmardquo)
A bigger Cpk is better because fewer units will be beyond spec
(A bigger ldquoArdquo and a smaller ldquoBrdquo are better)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
54
A
B
ldquoProcess Capabilityrdquo is the ability of a process
to fit its output within the tolerances
hellipa LARGER ldquoArdquo
hellipand a SMALLER ldquoBrdquo
hellipmeans BETTER ldquoProcess Capabilityrdquo
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
55
A
B
An Analogy
Analogy
The bell curve is your automobile
The spec limits are the edges of your garage door
If A = B you are hitting the frame of your garage door with your car
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
56
A
B
How can we make Cpk (A divided by B) better
1 Design the product so a wider tolerance is functional (ldquorobust designrdquo)
2 Choose equipment and methods for a good safety margin (ldquoprocess capabilityrdquo)
3 Correctly adjust but only when needed (ldquocontrolrdquo)
4 Discover ways to narrow the natural variation (ldquoimprovementrdquo)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
57
A
B
What does a very good Cpk do for us
This process is producing good units with a good safety margin
Note that when Cpk = 2 our process mean is 6 standard deviations from
the nearest spec so we say it has ldquo6 Sigma Capabilityrdquo
Specification
Limit
Specification
Limit
This Cpk is
about 2
Very good
Mean
58
A
B
What does a problem Cpk look like
This process is in danger of producing some defects
It is too close to the specification limits
(Remember the bell curve tail goes further than Bhellip hellipwe only show the bell to 3-sigma to make it easier to draw)
Specification
Limit
Specification
Limit
This Cpk is just
slightly greater
than 1 Not good
59
A
B
What does a very bad Cpk look like
A significant part of the ldquotailrdquo is hanging out beyond the spec limits
This process is producing scrap rework and customer rejects
Notice that if distance ldquoArdquo approaches zerohellip
hellipthe Cpk would approach zero andhellip
hellipthe process would become 50 defective
Specification
Limit
Specification
Limit
This Cpk is less
than 1 We desire
a minimum of 133
and ultimately we
want 2 or more
60
-
Q amp A
61
MEASUREMENT SYSTEM ANALYSIS (MSA)
An MSA is a statistical tool used to determine if a measurement system is capable of precise measurement
What is It
Objective or Purpose
bull To determine how much error is in the measurement due to the measurement process itself
bull Quantifies the variability added by the measurement system
bull Applicable to attribute data and variable data
When to Use It
bull On the critical inputs and outputs prior to collecting data for analysis
bull For any new or modified process in order to ensure the quality of the data
Measurement System Analysis is an analysis of the measurement process not an analysis of the people
IMPORTANT
Who Should be Involved
Everyone that measures and makes decisions about these measurements should be involved in the MSA
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The observed variation in process output measurements is not simply the variation in the process itself it is the variation in the process plus the variation in measurement that results from an inadequate measurement system
Conducting an MSA reduces the likelihood of passing a bad part or rejecting a good part
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The output of the process measured by bull Cycle time bull Dimensional data bull Number of defects and others
Observed Variation
Process Variation
Measurement System
Variation
Reproducibility
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Accuracy (Central Location)
OBSERVED VARIATION
Calibration addresses accuracy
Measurement System Analysis (MSA)
MEASUREMENT SYSTEM ERRORS
Accuracy difference between the observed measurement and the actual measurement
Precision variation that occurs when measuring the same part with the same instrument
MEASUREMENT SYSTEM ERROR
Precise but not
accurate
Accurate but not
precise
Not accurate or
precise
Accurate and
precise
ACCURACY OF MEASUREMENT
Broken down into three components
aStability
The consistency of measurements over time
bBias
A measure of the amount of partiality in the system
cLinearity
A measure of the bias values through the expected
range of measurements
OBSERVED VARIATION
Observed Variation
Process Variation
Measurement System
Variation
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Reproducibility
Accuracy (Central Location)
Calibration Addresses Accuracy
Letrsquos take a closer look at Precision
Measurement System Analysis (MSA)
Measurement System Analysis (MSA)
Error in Resolution The inability to detect small changes
Possible Cause
Wrong measurement device selected - divisions on scale not fine enough to detect changes
Resolution
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Repeatability The inability to get the same answer from repeated measurements made of the same item under absolutely identical conditions
Possible Cause
Lack of standard operating procedures (SOP) lack of training measuring system variablilty
Repeatability
Equipment Variation
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Reproducibility The inability to get the same answer from repeated measurements made under various conditions from different inspectors
Possible Cause
Lack of SOP lack of training
Reproducibility
Appraiser Variation
VARIABLE MSA ndash GAGE RampR STUDY
bull Gage RampR is the combined estimate of
measurement system Repeatability and
Reproducibility
bull Typically a 3-person study is performed Each person randomly measures 10 marked parts per trial
Each person can perform up to 3 trials
bull There are 3 key indicators EV or Equipment Variation
AV or Appraiser Variation
Overall GRR
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
PARETO CHART - EXAMPLE
Lets assume we are listing all the rejected products that are removed from a candy manufacturing line in one week
First we put the rejects in specific categories
No wrapper - 10
No center - 37
Wrong shape - 53
Short shot - 6
Wrapper open - 132
Underweight - 4
Overweight ndash 17
Get the total rejects - 259
20
Develop a percentage for each category
No wrapper ndash 10259 = 39
No center ndash 37259 = 143
Wrong shape ndash 53259 = 205
Short shot ndash 6259 = 23
Wrapper open ndash 132259 = 51
Underweight ndash 4259 = 15
Overweight ndash 17259 = 66
PARETO CHART - EXAMPLE
21
Now place the counts in a histogram largest to smallest
0
10
20
30
40
50
60
Wrapper
Open
No Center No Wrapper Underweight
70
80
90
100
51
205
143
66 39
23 15
22
Finally add up each and plot as a line diagram
0
10
20
30
40
50
60
Wrapper
Open
No Center No Wrapper Underweight
70
80
90
100
715
51
205
143
858
66
924
39
963
23
986
15
1001
23
0
10
20
30
40
50
60
Wrapper
Open
No Center No Wrapper Underweight
70
80
90
100
715
51
205
143
858
66
924
39
963
23
986
15
1001
24
CONTROL CHARTS
Control charts are one of the most commonly used methods of Statistical Process Control (SPC) which
monitors the stability of a process
The main features of a control chart include the data points a centreline (mean value) and upper and
lower limits (bounds to indicate where a process output is considered out of control)They visually
display the fluctuations of a particular process variable that easily determine whether these variations
fall within the specified process limits
Control charts
a graphical method for detecting if the underlying distribution of variation of some measurable
characteristic of the product seems to have undergone a shift
monitor a process in real time
Map the output of a production process over time
A control chart always has a central line for the average an upper line for the upper control limit and a
lower line for the lower control limit These lines are determined from historical data
By comparing current data to these lines you can draw conclusions about whether the process
variation is consistent (in control) or is unpredictable
25
CONTROL CHART - PURPOSE
The main purpose of using a control chart is to monitor control and improve
process performance over time by studying variation and its source There are
several functions of a control chart
It centres attention on detecting and monitoring process variation over time
It provides a tool for on-going control of a process
It differentiates special from common causes of variation in order to be a guide for
local or management action
It helps improve a process to perform consistently and predictably to achieve higher
quality lower cost and higher effective capacity
It serves as a common language for discussing process performance
26
TYPES OF CONTROL CHARTS
The basic tool used in SPC is the control chart
There are various types of control charts
Variable Control Chart
Averages and range chart (X-Bar and R Bar Chart)
X bar and s chart
Moving Range Chart
Moving AveragendashMoving Range chart (also called MAndashMR chart)
p chart (also called proportion chart)
c chart (also called count chart)
np chart
u chart
27
POPULARITY OF CONTROL CHARTS
Control charts are a proven technique for improving productivity
Control charts are effective in defect prevention
Control charts prevent unnecessary process
adjustment
Control charts provide diagnostic information
Control charts provide information about process
capability
28
PROCEDURE FOR X ndashBAR AND R BAR CHART
1 Randomly sample ldquonrdquo units throughout the day (can be every 5
minutes every 30 minutes etc - whatever is appropriate for your
case)
2 For each sample calculate ldquoX-BARrdquo to estimate the mean and ldquoR
(range)rdquo to estimate variability NOTE THE RANGE CAN BE USED TO
ESTIMATE THE STANDARD DEVIATION
3 After collecting the 20-25 samples calculate X-BAR-BAR (the
average of all the X-BARs) and R-BAR (the average of all the ranges)
4 Using X-BAR-BAR and R-BAR calculate the control limits for your X-
BAR and R Control Charts
29
X-BAR CONTROL LIMITS
Upper Control Limit (UCL) = (X-BAR-BAR) + A2 (R-BAR)
Lower Control Limit(LCL) = (X-BAR-BAR) - A2 (R-BAR)
R CONTROL LIMITS
Upper Control Limit - D3 (R-BAR)
Lower Control Limit - D4 (R-BAR)
PROCEDURE FOR X ndashBAR AND R BAR CHART
30
CONTROL CHART CONSTANTS
sample size constant constant constant constant constant constant constant
n d2 A2 A3 B3 B4 D3 D4
2 1128 188 2659 0 3267 0 3267
3 1693 1023 1954 0 2568 0 2574
4 2059 0729 1628 0 2266 0 2282
5 2326 0577 1427 0 2089 0 2114
6 2534 0483 1287 003 197 0 2004
7 2704 0419 1182 0118 1882 0076 1924
8 2847 0373 1099 0185 1815 0136 1864
9 297 0337 1032 0239 1761 0184 1816
10 3078 0308 0975 0284 1716 0223 1777
31
5 For the R Control Chart plot all R values on the R Control Chart
to see if all the Ranges are ldquobetween the control limitsrdquo If they are
then your process is considered to be in a state of statistical control
(as far as the variability of the process is concerned)
6 For the X-BAR Control Chart plot all the X-BARs on the X-BAR
control chart to see if all the X-BARs are ldquobetween the control
limitsrdquo If they are then your process is considered in a state of
statistical control (as far as the average of the process is
concerned)
PROCEDURE FOR X ndashBAR AND R BAR CHART
32
SAMPLE DATA FOR X BAR ndashR CHART
Sub Group 1 2 3 4 5 X -Bar Range reg
1 1195 1191 1211 1203 1198 1200 02
2 1201 1198 1198 1197 12 1199 004
3 1193 1206 1198 1196 1202 1199 013
4 1205 1198 1205 1206 1198 1202 008
5 1198 1203 1206 1201 1199 1201 008
6 1202 1205 1196 1201 1195 1200 01
7 1199 1206 1201 1204 1201 1202 007
8 1201 1197 1198 1204 1198 1200 007
9 1198 1204 1198 1204 1204 1202 006
10 1205 1195 1198 1204 1196 1200 01
` X Bar-Bar 1200 009
X Bar Chart
UCL = X BAR-BAR + A2 R Bar
1200 +(0577009) 1205
LCL= X BAR-BAR - A2 R Bar
1200 - (0577009) 1195
R Chart
UCL = D4R Bar 211 009 021
LCL = D3 R Bar 0009 0
33
PLOT DATA ON CONTROL CHARTS
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1 2 3 4 5 6 7 8 9 10
Ave
rage
(X
ba
r)
X Bar Chart
UCL
LCL
X Bar
34
PLOT DATA ON CONTROL CHARTS
001
003
005
007
009
011
013
015
017
019
021
023
025
1 2 3 4 5 6 7 8 9 10
R Chart
UCL
LCL
35
PROCEDURE TO DETERMINE IF PROCESS IS IN A STATE OF
STATISTICAL CONTROL
7 If process is determined to be ldquoNOT STABLErdquo then stop and find out what
an assignable cause might be fix and then repeat the complete process of
collecting new data
8 If the process is determined to be ldquoSTABLErdquo then you may use the
control charts you developed to monitor future production to ensure that the
process REMAINS stable
More Samples for Control charts
36
READING OF CONTROL CHART
Control charts can determine whether a process is behaving in an unusual way The quality of the individual points of a subset is determined unstable if any of the
following occurs
Rule 1 Any point falls beyond 3σ from the centreline(this is represented by the upper and
lower control limits)
Rule 2 Two out of three consecutive points fall beyond 2σ on the same side of the
centreline
Rule 3 Four out of five consecutive points fall beyond 1σ on the same side of the
centreline
Rule 4 Nine or more consecutive points fall on the same side of the centreline
(Ref Next page for sample)
37
READING THE CONTROL CHART
38
CONTROL CHARTS FOR ATTRIBUTES ndashP-CHARTS amp C-CHARTS
Attributes are discrete events yesno or passfail
Use P-Charts for quality characteristics that are discrete and involve yesno or goodbad decisions
Eg
Number of leaking caulking tubes in a box of 48
Number of broken eggs in a carton
Use C-Charts for discrete defects when there can be more than one defect per unit
Eg
Number of stains in a carpet sample cut from a production run
Number of complaints per customer at a hotel
39
P-CHART EXAMPLE A PRODUCTION MANAGER FOR A TIRE COMPANY HAS INSPECTED THE NUMBER OF
DEFECTIVE TIRES IN FIVE RANDOM SAMPLES WITH 20 TIRES IN EACH SAMPLE THE TABLE BELOW SHOWS THE
NUMBER OF DEFECTIVE TIRES IN EACH SAMPLE OF 20 TIRES CALCULATE THE CONTROL LIMITS
Sample Number of
Defective Tires
Number of Tires in each
Sample
Proportion Defective
1 3 20 15
2 2 20 10
3 1 20 05
4 2 20 10
5 2 20 05
Total 9 100 09
01023(064)09σzpLCL
2823(064)09σzpUCL
06420
(09)(91)
n
)p(1pσ
09100
9
Inspected Total
DefectivespCL
p
p
p
Solution
40
P- CONTROL CHART
41
C-CHART EXAMPLE THE NUMBER OF WEEKLY CUSTOMER COMPLAINTS ARE MONITORED IN A LARGE HOTEL USING A C-CHART DEVELOP THREE SIGMA CONTROL LIMITS USING THE DATA TABLE BELOW
Week Number of Complaints
1 3
2 2
3 3
4 1
5 3
6 3
7 2
8 1
9 3
10 1
Total 22
022522322ccLCL
66522322ccUCL
2210
22
samples of
complaintsc
c
c
z
z
Solution
42
C- CONTROL CHART
43
The ability of a process to meet product designtechnical specifications
Assessing capability involves evaluating process variability relative to preset product or service specifications
Process Capability ndash Cp and Cpk
Cp assumes that the process is centered in the specification range
Cpk helps to address a possible lack of centering of the process
PROCESS CAPABILITY
6σ
LSLUSL
width process
width ionspecificatCp
3σ
LSLμ
3σ
μUSLminCpk
44
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
45
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
46
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
47
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
--and an individual part is measured at 520rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
48
GRAPHING THE TOLERANCE AND MEASUREMENTS
Suppose we made and measured several more
units and they were all EXACTLY the same
We wouldnrsquot have very many part problems
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
X
X
X
49
GRAPHING THE TOLERANCE AND MEASUREMENTS
In the real world units are NOT EXACTLY the same
Everything VARIES
The question isnrsquot IF units vary
Itrsquos how much when and why
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
XX
XXX
XXXXX
XXXXXXX
50
The ldquonormal bell curverdquo
Widths heights depths thicknesses weights speeds strengths
and many other types of measurements when charted as a
histogram often form the shape of a bell
A ldquoperfect bellrdquo like a ldquoperfect circlerdquo doesnrsquot occur in nature but
many processes are close enough to make the bell curve useful
(A number of common industrial measurements such as flatness and straightness do NOT tend to distribute in a bell shape their proper statistical analysis is performed using models other than the bell curve)
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
51
What is a ldquostandard deviationrdquo
If we measure the DISTANCE from the CENTER of the bell
to each individual measurement that makes up the bell curve
we can find a TYPICAL DISTANCE
The most commonly used statistic to estimate this distance is the
Standard Deviation (also called ldquoSigmardquo)
Because of the natural shape of the bell curve the area of +1 to ndash1
standard deviations includes about 68 of the curve
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
Typical distance
from the center +1
standard deviation
Typical distance
from the center -1
standard deviation
52
How much of the curve is included in how many standard
deviations
From ndash1 to +1 is about 68 of the bell curve
From ndash2 to +2 is about 95
From ndash3 to +3 is about 9973
From ndash4 to +4 is about 9999
(NOTE We usually show the bell from ndash3 to +3 to make it easier to draw but in concept the ldquotailsrdquo of the bell get very thin and go on forever)
-6 -5 -4 -3 -2 -1 +1 +2 +3 +4 +5 +6 0
53
A
B
What is Cpk It is a measure of how well a process is within a specification
Cpk = A divided by B
A = Distance from process mean to closest spec limit
B = 3 Standard Deviations (also called ldquo3 Sigmardquo)
A bigger Cpk is better because fewer units will be beyond spec
(A bigger ldquoArdquo and a smaller ldquoBrdquo are better)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
54
A
B
ldquoProcess Capabilityrdquo is the ability of a process
to fit its output within the tolerances
hellipa LARGER ldquoArdquo
hellipand a SMALLER ldquoBrdquo
hellipmeans BETTER ldquoProcess Capabilityrdquo
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
55
A
B
An Analogy
Analogy
The bell curve is your automobile
The spec limits are the edges of your garage door
If A = B you are hitting the frame of your garage door with your car
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
56
A
B
How can we make Cpk (A divided by B) better
1 Design the product so a wider tolerance is functional (ldquorobust designrdquo)
2 Choose equipment and methods for a good safety margin (ldquoprocess capabilityrdquo)
3 Correctly adjust but only when needed (ldquocontrolrdquo)
4 Discover ways to narrow the natural variation (ldquoimprovementrdquo)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
57
A
B
What does a very good Cpk do for us
This process is producing good units with a good safety margin
Note that when Cpk = 2 our process mean is 6 standard deviations from
the nearest spec so we say it has ldquo6 Sigma Capabilityrdquo
Specification
Limit
Specification
Limit
This Cpk is
about 2
Very good
Mean
58
A
B
What does a problem Cpk look like
This process is in danger of producing some defects
It is too close to the specification limits
(Remember the bell curve tail goes further than Bhellip hellipwe only show the bell to 3-sigma to make it easier to draw)
Specification
Limit
Specification
Limit
This Cpk is just
slightly greater
than 1 Not good
59
A
B
What does a very bad Cpk look like
A significant part of the ldquotailrdquo is hanging out beyond the spec limits
This process is producing scrap rework and customer rejects
Notice that if distance ldquoArdquo approaches zerohellip
hellipthe Cpk would approach zero andhellip
hellipthe process would become 50 defective
Specification
Limit
Specification
Limit
This Cpk is less
than 1 We desire
a minimum of 133
and ultimately we
want 2 or more
60
-
Q amp A
61
MEASUREMENT SYSTEM ANALYSIS (MSA)
An MSA is a statistical tool used to determine if a measurement system is capable of precise measurement
What is It
Objective or Purpose
bull To determine how much error is in the measurement due to the measurement process itself
bull Quantifies the variability added by the measurement system
bull Applicable to attribute data and variable data
When to Use It
bull On the critical inputs and outputs prior to collecting data for analysis
bull For any new or modified process in order to ensure the quality of the data
Measurement System Analysis is an analysis of the measurement process not an analysis of the people
IMPORTANT
Who Should be Involved
Everyone that measures and makes decisions about these measurements should be involved in the MSA
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The observed variation in process output measurements is not simply the variation in the process itself it is the variation in the process plus the variation in measurement that results from an inadequate measurement system
Conducting an MSA reduces the likelihood of passing a bad part or rejecting a good part
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The output of the process measured by bull Cycle time bull Dimensional data bull Number of defects and others
Observed Variation
Process Variation
Measurement System
Variation
Reproducibility
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Accuracy (Central Location)
OBSERVED VARIATION
Calibration addresses accuracy
Measurement System Analysis (MSA)
MEASUREMENT SYSTEM ERRORS
Accuracy difference between the observed measurement and the actual measurement
Precision variation that occurs when measuring the same part with the same instrument
MEASUREMENT SYSTEM ERROR
Precise but not
accurate
Accurate but not
precise
Not accurate or
precise
Accurate and
precise
ACCURACY OF MEASUREMENT
Broken down into three components
aStability
The consistency of measurements over time
bBias
A measure of the amount of partiality in the system
cLinearity
A measure of the bias values through the expected
range of measurements
OBSERVED VARIATION
Observed Variation
Process Variation
Measurement System
Variation
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Reproducibility
Accuracy (Central Location)
Calibration Addresses Accuracy
Letrsquos take a closer look at Precision
Measurement System Analysis (MSA)
Measurement System Analysis (MSA)
Error in Resolution The inability to detect small changes
Possible Cause
Wrong measurement device selected - divisions on scale not fine enough to detect changes
Resolution
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Repeatability The inability to get the same answer from repeated measurements made of the same item under absolutely identical conditions
Possible Cause
Lack of standard operating procedures (SOP) lack of training measuring system variablilty
Repeatability
Equipment Variation
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Reproducibility The inability to get the same answer from repeated measurements made under various conditions from different inspectors
Possible Cause
Lack of SOP lack of training
Reproducibility
Appraiser Variation
VARIABLE MSA ndash GAGE RampR STUDY
bull Gage RampR is the combined estimate of
measurement system Repeatability and
Reproducibility
bull Typically a 3-person study is performed Each person randomly measures 10 marked parts per trial
Each person can perform up to 3 trials
bull There are 3 key indicators EV or Equipment Variation
AV or Appraiser Variation
Overall GRR
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
Develop a percentage for each category
No wrapper ndash 10259 = 39
No center ndash 37259 = 143
Wrong shape ndash 53259 = 205
Short shot ndash 6259 = 23
Wrapper open ndash 132259 = 51
Underweight ndash 4259 = 15
Overweight ndash 17259 = 66
PARETO CHART - EXAMPLE
21
Now place the counts in a histogram largest to smallest
0
10
20
30
40
50
60
Wrapper
Open
No Center No Wrapper Underweight
70
80
90
100
51
205
143
66 39
23 15
22
Finally add up each and plot as a line diagram
0
10
20
30
40
50
60
Wrapper
Open
No Center No Wrapper Underweight
70
80
90
100
715
51
205
143
858
66
924
39
963
23
986
15
1001
23
0
10
20
30
40
50
60
Wrapper
Open
No Center No Wrapper Underweight
70
80
90
100
715
51
205
143
858
66
924
39
963
23
986
15
1001
24
CONTROL CHARTS
Control charts are one of the most commonly used methods of Statistical Process Control (SPC) which
monitors the stability of a process
The main features of a control chart include the data points a centreline (mean value) and upper and
lower limits (bounds to indicate where a process output is considered out of control)They visually
display the fluctuations of a particular process variable that easily determine whether these variations
fall within the specified process limits
Control charts
a graphical method for detecting if the underlying distribution of variation of some measurable
characteristic of the product seems to have undergone a shift
monitor a process in real time
Map the output of a production process over time
A control chart always has a central line for the average an upper line for the upper control limit and a
lower line for the lower control limit These lines are determined from historical data
By comparing current data to these lines you can draw conclusions about whether the process
variation is consistent (in control) or is unpredictable
25
CONTROL CHART - PURPOSE
The main purpose of using a control chart is to monitor control and improve
process performance over time by studying variation and its source There are
several functions of a control chart
It centres attention on detecting and monitoring process variation over time
It provides a tool for on-going control of a process
It differentiates special from common causes of variation in order to be a guide for
local or management action
It helps improve a process to perform consistently and predictably to achieve higher
quality lower cost and higher effective capacity
It serves as a common language for discussing process performance
26
TYPES OF CONTROL CHARTS
The basic tool used in SPC is the control chart
There are various types of control charts
Variable Control Chart
Averages and range chart (X-Bar and R Bar Chart)
X bar and s chart
Moving Range Chart
Moving AveragendashMoving Range chart (also called MAndashMR chart)
p chart (also called proportion chart)
c chart (also called count chart)
np chart
u chart
27
POPULARITY OF CONTROL CHARTS
Control charts are a proven technique for improving productivity
Control charts are effective in defect prevention
Control charts prevent unnecessary process
adjustment
Control charts provide diagnostic information
Control charts provide information about process
capability
28
PROCEDURE FOR X ndashBAR AND R BAR CHART
1 Randomly sample ldquonrdquo units throughout the day (can be every 5
minutes every 30 minutes etc - whatever is appropriate for your
case)
2 For each sample calculate ldquoX-BARrdquo to estimate the mean and ldquoR
(range)rdquo to estimate variability NOTE THE RANGE CAN BE USED TO
ESTIMATE THE STANDARD DEVIATION
3 After collecting the 20-25 samples calculate X-BAR-BAR (the
average of all the X-BARs) and R-BAR (the average of all the ranges)
4 Using X-BAR-BAR and R-BAR calculate the control limits for your X-
BAR and R Control Charts
29
X-BAR CONTROL LIMITS
Upper Control Limit (UCL) = (X-BAR-BAR) + A2 (R-BAR)
Lower Control Limit(LCL) = (X-BAR-BAR) - A2 (R-BAR)
R CONTROL LIMITS
Upper Control Limit - D3 (R-BAR)
Lower Control Limit - D4 (R-BAR)
PROCEDURE FOR X ndashBAR AND R BAR CHART
30
CONTROL CHART CONSTANTS
sample size constant constant constant constant constant constant constant
n d2 A2 A3 B3 B4 D3 D4
2 1128 188 2659 0 3267 0 3267
3 1693 1023 1954 0 2568 0 2574
4 2059 0729 1628 0 2266 0 2282
5 2326 0577 1427 0 2089 0 2114
6 2534 0483 1287 003 197 0 2004
7 2704 0419 1182 0118 1882 0076 1924
8 2847 0373 1099 0185 1815 0136 1864
9 297 0337 1032 0239 1761 0184 1816
10 3078 0308 0975 0284 1716 0223 1777
31
5 For the R Control Chart plot all R values on the R Control Chart
to see if all the Ranges are ldquobetween the control limitsrdquo If they are
then your process is considered to be in a state of statistical control
(as far as the variability of the process is concerned)
6 For the X-BAR Control Chart plot all the X-BARs on the X-BAR
control chart to see if all the X-BARs are ldquobetween the control
limitsrdquo If they are then your process is considered in a state of
statistical control (as far as the average of the process is
concerned)
PROCEDURE FOR X ndashBAR AND R BAR CHART
32
SAMPLE DATA FOR X BAR ndashR CHART
Sub Group 1 2 3 4 5 X -Bar Range reg
1 1195 1191 1211 1203 1198 1200 02
2 1201 1198 1198 1197 12 1199 004
3 1193 1206 1198 1196 1202 1199 013
4 1205 1198 1205 1206 1198 1202 008
5 1198 1203 1206 1201 1199 1201 008
6 1202 1205 1196 1201 1195 1200 01
7 1199 1206 1201 1204 1201 1202 007
8 1201 1197 1198 1204 1198 1200 007
9 1198 1204 1198 1204 1204 1202 006
10 1205 1195 1198 1204 1196 1200 01
` X Bar-Bar 1200 009
X Bar Chart
UCL = X BAR-BAR + A2 R Bar
1200 +(0577009) 1205
LCL= X BAR-BAR - A2 R Bar
1200 - (0577009) 1195
R Chart
UCL = D4R Bar 211 009 021
LCL = D3 R Bar 0009 0
33
PLOT DATA ON CONTROL CHARTS
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1 2 3 4 5 6 7 8 9 10
Ave
rage
(X
ba
r)
X Bar Chart
UCL
LCL
X Bar
34
PLOT DATA ON CONTROL CHARTS
001
003
005
007
009
011
013
015
017
019
021
023
025
1 2 3 4 5 6 7 8 9 10
R Chart
UCL
LCL
35
PROCEDURE TO DETERMINE IF PROCESS IS IN A STATE OF
STATISTICAL CONTROL
7 If process is determined to be ldquoNOT STABLErdquo then stop and find out what
an assignable cause might be fix and then repeat the complete process of
collecting new data
8 If the process is determined to be ldquoSTABLErdquo then you may use the
control charts you developed to monitor future production to ensure that the
process REMAINS stable
More Samples for Control charts
36
READING OF CONTROL CHART
Control charts can determine whether a process is behaving in an unusual way The quality of the individual points of a subset is determined unstable if any of the
following occurs
Rule 1 Any point falls beyond 3σ from the centreline(this is represented by the upper and
lower control limits)
Rule 2 Two out of three consecutive points fall beyond 2σ on the same side of the
centreline
Rule 3 Four out of five consecutive points fall beyond 1σ on the same side of the
centreline
Rule 4 Nine or more consecutive points fall on the same side of the centreline
(Ref Next page for sample)
37
READING THE CONTROL CHART
38
CONTROL CHARTS FOR ATTRIBUTES ndashP-CHARTS amp C-CHARTS
Attributes are discrete events yesno or passfail
Use P-Charts for quality characteristics that are discrete and involve yesno or goodbad decisions
Eg
Number of leaking caulking tubes in a box of 48
Number of broken eggs in a carton
Use C-Charts for discrete defects when there can be more than one defect per unit
Eg
Number of stains in a carpet sample cut from a production run
Number of complaints per customer at a hotel
39
P-CHART EXAMPLE A PRODUCTION MANAGER FOR A TIRE COMPANY HAS INSPECTED THE NUMBER OF
DEFECTIVE TIRES IN FIVE RANDOM SAMPLES WITH 20 TIRES IN EACH SAMPLE THE TABLE BELOW SHOWS THE
NUMBER OF DEFECTIVE TIRES IN EACH SAMPLE OF 20 TIRES CALCULATE THE CONTROL LIMITS
Sample Number of
Defective Tires
Number of Tires in each
Sample
Proportion Defective
1 3 20 15
2 2 20 10
3 1 20 05
4 2 20 10
5 2 20 05
Total 9 100 09
01023(064)09σzpLCL
2823(064)09σzpUCL
06420
(09)(91)
n
)p(1pσ
09100
9
Inspected Total
DefectivespCL
p
p
p
Solution
40
P- CONTROL CHART
41
C-CHART EXAMPLE THE NUMBER OF WEEKLY CUSTOMER COMPLAINTS ARE MONITORED IN A LARGE HOTEL USING A C-CHART DEVELOP THREE SIGMA CONTROL LIMITS USING THE DATA TABLE BELOW
Week Number of Complaints
1 3
2 2
3 3
4 1
5 3
6 3
7 2
8 1
9 3
10 1
Total 22
022522322ccLCL
66522322ccUCL
2210
22
samples of
complaintsc
c
c
z
z
Solution
42
C- CONTROL CHART
43
The ability of a process to meet product designtechnical specifications
Assessing capability involves evaluating process variability relative to preset product or service specifications
Process Capability ndash Cp and Cpk
Cp assumes that the process is centered in the specification range
Cpk helps to address a possible lack of centering of the process
PROCESS CAPABILITY
6σ
LSLUSL
width process
width ionspecificatCp
3σ
LSLμ
3σ
μUSLminCpk
44
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
45
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
46
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
47
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
--and an individual part is measured at 520rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
48
GRAPHING THE TOLERANCE AND MEASUREMENTS
Suppose we made and measured several more
units and they were all EXACTLY the same
We wouldnrsquot have very many part problems
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
X
X
X
49
GRAPHING THE TOLERANCE AND MEASUREMENTS
In the real world units are NOT EXACTLY the same
Everything VARIES
The question isnrsquot IF units vary
Itrsquos how much when and why
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
XX
XXX
XXXXX
XXXXXXX
50
The ldquonormal bell curverdquo
Widths heights depths thicknesses weights speeds strengths
and many other types of measurements when charted as a
histogram often form the shape of a bell
A ldquoperfect bellrdquo like a ldquoperfect circlerdquo doesnrsquot occur in nature but
many processes are close enough to make the bell curve useful
(A number of common industrial measurements such as flatness and straightness do NOT tend to distribute in a bell shape their proper statistical analysis is performed using models other than the bell curve)
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
51
What is a ldquostandard deviationrdquo
If we measure the DISTANCE from the CENTER of the bell
to each individual measurement that makes up the bell curve
we can find a TYPICAL DISTANCE
The most commonly used statistic to estimate this distance is the
Standard Deviation (also called ldquoSigmardquo)
Because of the natural shape of the bell curve the area of +1 to ndash1
standard deviations includes about 68 of the curve
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
Typical distance
from the center +1
standard deviation
Typical distance
from the center -1
standard deviation
52
How much of the curve is included in how many standard
deviations
From ndash1 to +1 is about 68 of the bell curve
From ndash2 to +2 is about 95
From ndash3 to +3 is about 9973
From ndash4 to +4 is about 9999
(NOTE We usually show the bell from ndash3 to +3 to make it easier to draw but in concept the ldquotailsrdquo of the bell get very thin and go on forever)
-6 -5 -4 -3 -2 -1 +1 +2 +3 +4 +5 +6 0
53
A
B
What is Cpk It is a measure of how well a process is within a specification
Cpk = A divided by B
A = Distance from process mean to closest spec limit
B = 3 Standard Deviations (also called ldquo3 Sigmardquo)
A bigger Cpk is better because fewer units will be beyond spec
(A bigger ldquoArdquo and a smaller ldquoBrdquo are better)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
54
A
B
ldquoProcess Capabilityrdquo is the ability of a process
to fit its output within the tolerances
hellipa LARGER ldquoArdquo
hellipand a SMALLER ldquoBrdquo
hellipmeans BETTER ldquoProcess Capabilityrdquo
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
55
A
B
An Analogy
Analogy
The bell curve is your automobile
The spec limits are the edges of your garage door
If A = B you are hitting the frame of your garage door with your car
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
56
A
B
How can we make Cpk (A divided by B) better
1 Design the product so a wider tolerance is functional (ldquorobust designrdquo)
2 Choose equipment and methods for a good safety margin (ldquoprocess capabilityrdquo)
3 Correctly adjust but only when needed (ldquocontrolrdquo)
4 Discover ways to narrow the natural variation (ldquoimprovementrdquo)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
57
A
B
What does a very good Cpk do for us
This process is producing good units with a good safety margin
Note that when Cpk = 2 our process mean is 6 standard deviations from
the nearest spec so we say it has ldquo6 Sigma Capabilityrdquo
Specification
Limit
Specification
Limit
This Cpk is
about 2
Very good
Mean
58
A
B
What does a problem Cpk look like
This process is in danger of producing some defects
It is too close to the specification limits
(Remember the bell curve tail goes further than Bhellip hellipwe only show the bell to 3-sigma to make it easier to draw)
Specification
Limit
Specification
Limit
This Cpk is just
slightly greater
than 1 Not good
59
A
B
What does a very bad Cpk look like
A significant part of the ldquotailrdquo is hanging out beyond the spec limits
This process is producing scrap rework and customer rejects
Notice that if distance ldquoArdquo approaches zerohellip
hellipthe Cpk would approach zero andhellip
hellipthe process would become 50 defective
Specification
Limit
Specification
Limit
This Cpk is less
than 1 We desire
a minimum of 133
and ultimately we
want 2 or more
60
-
Q amp A
61
MEASUREMENT SYSTEM ANALYSIS (MSA)
An MSA is a statistical tool used to determine if a measurement system is capable of precise measurement
What is It
Objective or Purpose
bull To determine how much error is in the measurement due to the measurement process itself
bull Quantifies the variability added by the measurement system
bull Applicable to attribute data and variable data
When to Use It
bull On the critical inputs and outputs prior to collecting data for analysis
bull For any new or modified process in order to ensure the quality of the data
Measurement System Analysis is an analysis of the measurement process not an analysis of the people
IMPORTANT
Who Should be Involved
Everyone that measures and makes decisions about these measurements should be involved in the MSA
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The observed variation in process output measurements is not simply the variation in the process itself it is the variation in the process plus the variation in measurement that results from an inadequate measurement system
Conducting an MSA reduces the likelihood of passing a bad part or rejecting a good part
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The output of the process measured by bull Cycle time bull Dimensional data bull Number of defects and others
Observed Variation
Process Variation
Measurement System
Variation
Reproducibility
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Accuracy (Central Location)
OBSERVED VARIATION
Calibration addresses accuracy
Measurement System Analysis (MSA)
MEASUREMENT SYSTEM ERRORS
Accuracy difference between the observed measurement and the actual measurement
Precision variation that occurs when measuring the same part with the same instrument
MEASUREMENT SYSTEM ERROR
Precise but not
accurate
Accurate but not
precise
Not accurate or
precise
Accurate and
precise
ACCURACY OF MEASUREMENT
Broken down into three components
aStability
The consistency of measurements over time
bBias
A measure of the amount of partiality in the system
cLinearity
A measure of the bias values through the expected
range of measurements
OBSERVED VARIATION
Observed Variation
Process Variation
Measurement System
Variation
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Reproducibility
Accuracy (Central Location)
Calibration Addresses Accuracy
Letrsquos take a closer look at Precision
Measurement System Analysis (MSA)
Measurement System Analysis (MSA)
Error in Resolution The inability to detect small changes
Possible Cause
Wrong measurement device selected - divisions on scale not fine enough to detect changes
Resolution
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Repeatability The inability to get the same answer from repeated measurements made of the same item under absolutely identical conditions
Possible Cause
Lack of standard operating procedures (SOP) lack of training measuring system variablilty
Repeatability
Equipment Variation
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Reproducibility The inability to get the same answer from repeated measurements made under various conditions from different inspectors
Possible Cause
Lack of SOP lack of training
Reproducibility
Appraiser Variation
VARIABLE MSA ndash GAGE RampR STUDY
bull Gage RampR is the combined estimate of
measurement system Repeatability and
Reproducibility
bull Typically a 3-person study is performed Each person randomly measures 10 marked parts per trial
Each person can perform up to 3 trials
bull There are 3 key indicators EV or Equipment Variation
AV or Appraiser Variation
Overall GRR
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
Now place the counts in a histogram largest to smallest
0
10
20
30
40
50
60
Wrapper
Open
No Center No Wrapper Underweight
70
80
90
100
51
205
143
66 39
23 15
22
Finally add up each and plot as a line diagram
0
10
20
30
40
50
60
Wrapper
Open
No Center No Wrapper Underweight
70
80
90
100
715
51
205
143
858
66
924
39
963
23
986
15
1001
23
0
10
20
30
40
50
60
Wrapper
Open
No Center No Wrapper Underweight
70
80
90
100
715
51
205
143
858
66
924
39
963
23
986
15
1001
24
CONTROL CHARTS
Control charts are one of the most commonly used methods of Statistical Process Control (SPC) which
monitors the stability of a process
The main features of a control chart include the data points a centreline (mean value) and upper and
lower limits (bounds to indicate where a process output is considered out of control)They visually
display the fluctuations of a particular process variable that easily determine whether these variations
fall within the specified process limits
Control charts
a graphical method for detecting if the underlying distribution of variation of some measurable
characteristic of the product seems to have undergone a shift
monitor a process in real time
Map the output of a production process over time
A control chart always has a central line for the average an upper line for the upper control limit and a
lower line for the lower control limit These lines are determined from historical data
By comparing current data to these lines you can draw conclusions about whether the process
variation is consistent (in control) or is unpredictable
25
CONTROL CHART - PURPOSE
The main purpose of using a control chart is to monitor control and improve
process performance over time by studying variation and its source There are
several functions of a control chart
It centres attention on detecting and monitoring process variation over time
It provides a tool for on-going control of a process
It differentiates special from common causes of variation in order to be a guide for
local or management action
It helps improve a process to perform consistently and predictably to achieve higher
quality lower cost and higher effective capacity
It serves as a common language for discussing process performance
26
TYPES OF CONTROL CHARTS
The basic tool used in SPC is the control chart
There are various types of control charts
Variable Control Chart
Averages and range chart (X-Bar and R Bar Chart)
X bar and s chart
Moving Range Chart
Moving AveragendashMoving Range chart (also called MAndashMR chart)
p chart (also called proportion chart)
c chart (also called count chart)
np chart
u chart
27
POPULARITY OF CONTROL CHARTS
Control charts are a proven technique for improving productivity
Control charts are effective in defect prevention
Control charts prevent unnecessary process
adjustment
Control charts provide diagnostic information
Control charts provide information about process
capability
28
PROCEDURE FOR X ndashBAR AND R BAR CHART
1 Randomly sample ldquonrdquo units throughout the day (can be every 5
minutes every 30 minutes etc - whatever is appropriate for your
case)
2 For each sample calculate ldquoX-BARrdquo to estimate the mean and ldquoR
(range)rdquo to estimate variability NOTE THE RANGE CAN BE USED TO
ESTIMATE THE STANDARD DEVIATION
3 After collecting the 20-25 samples calculate X-BAR-BAR (the
average of all the X-BARs) and R-BAR (the average of all the ranges)
4 Using X-BAR-BAR and R-BAR calculate the control limits for your X-
BAR and R Control Charts
29
X-BAR CONTROL LIMITS
Upper Control Limit (UCL) = (X-BAR-BAR) + A2 (R-BAR)
Lower Control Limit(LCL) = (X-BAR-BAR) - A2 (R-BAR)
R CONTROL LIMITS
Upper Control Limit - D3 (R-BAR)
Lower Control Limit - D4 (R-BAR)
PROCEDURE FOR X ndashBAR AND R BAR CHART
30
CONTROL CHART CONSTANTS
sample size constant constant constant constant constant constant constant
n d2 A2 A3 B3 B4 D3 D4
2 1128 188 2659 0 3267 0 3267
3 1693 1023 1954 0 2568 0 2574
4 2059 0729 1628 0 2266 0 2282
5 2326 0577 1427 0 2089 0 2114
6 2534 0483 1287 003 197 0 2004
7 2704 0419 1182 0118 1882 0076 1924
8 2847 0373 1099 0185 1815 0136 1864
9 297 0337 1032 0239 1761 0184 1816
10 3078 0308 0975 0284 1716 0223 1777
31
5 For the R Control Chart plot all R values on the R Control Chart
to see if all the Ranges are ldquobetween the control limitsrdquo If they are
then your process is considered to be in a state of statistical control
(as far as the variability of the process is concerned)
6 For the X-BAR Control Chart plot all the X-BARs on the X-BAR
control chart to see if all the X-BARs are ldquobetween the control
limitsrdquo If they are then your process is considered in a state of
statistical control (as far as the average of the process is
concerned)
PROCEDURE FOR X ndashBAR AND R BAR CHART
32
SAMPLE DATA FOR X BAR ndashR CHART
Sub Group 1 2 3 4 5 X -Bar Range reg
1 1195 1191 1211 1203 1198 1200 02
2 1201 1198 1198 1197 12 1199 004
3 1193 1206 1198 1196 1202 1199 013
4 1205 1198 1205 1206 1198 1202 008
5 1198 1203 1206 1201 1199 1201 008
6 1202 1205 1196 1201 1195 1200 01
7 1199 1206 1201 1204 1201 1202 007
8 1201 1197 1198 1204 1198 1200 007
9 1198 1204 1198 1204 1204 1202 006
10 1205 1195 1198 1204 1196 1200 01
` X Bar-Bar 1200 009
X Bar Chart
UCL = X BAR-BAR + A2 R Bar
1200 +(0577009) 1205
LCL= X BAR-BAR - A2 R Bar
1200 - (0577009) 1195
R Chart
UCL = D4R Bar 211 009 021
LCL = D3 R Bar 0009 0
33
PLOT DATA ON CONTROL CHARTS
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1 2 3 4 5 6 7 8 9 10
Ave
rage
(X
ba
r)
X Bar Chart
UCL
LCL
X Bar
34
PLOT DATA ON CONTROL CHARTS
001
003
005
007
009
011
013
015
017
019
021
023
025
1 2 3 4 5 6 7 8 9 10
R Chart
UCL
LCL
35
PROCEDURE TO DETERMINE IF PROCESS IS IN A STATE OF
STATISTICAL CONTROL
7 If process is determined to be ldquoNOT STABLErdquo then stop and find out what
an assignable cause might be fix and then repeat the complete process of
collecting new data
8 If the process is determined to be ldquoSTABLErdquo then you may use the
control charts you developed to monitor future production to ensure that the
process REMAINS stable
More Samples for Control charts
36
READING OF CONTROL CHART
Control charts can determine whether a process is behaving in an unusual way The quality of the individual points of a subset is determined unstable if any of the
following occurs
Rule 1 Any point falls beyond 3σ from the centreline(this is represented by the upper and
lower control limits)
Rule 2 Two out of three consecutive points fall beyond 2σ on the same side of the
centreline
Rule 3 Four out of five consecutive points fall beyond 1σ on the same side of the
centreline
Rule 4 Nine or more consecutive points fall on the same side of the centreline
(Ref Next page for sample)
37
READING THE CONTROL CHART
38
CONTROL CHARTS FOR ATTRIBUTES ndashP-CHARTS amp C-CHARTS
Attributes are discrete events yesno or passfail
Use P-Charts for quality characteristics that are discrete and involve yesno or goodbad decisions
Eg
Number of leaking caulking tubes in a box of 48
Number of broken eggs in a carton
Use C-Charts for discrete defects when there can be more than one defect per unit
Eg
Number of stains in a carpet sample cut from a production run
Number of complaints per customer at a hotel
39
P-CHART EXAMPLE A PRODUCTION MANAGER FOR A TIRE COMPANY HAS INSPECTED THE NUMBER OF
DEFECTIVE TIRES IN FIVE RANDOM SAMPLES WITH 20 TIRES IN EACH SAMPLE THE TABLE BELOW SHOWS THE
NUMBER OF DEFECTIVE TIRES IN EACH SAMPLE OF 20 TIRES CALCULATE THE CONTROL LIMITS
Sample Number of
Defective Tires
Number of Tires in each
Sample
Proportion Defective
1 3 20 15
2 2 20 10
3 1 20 05
4 2 20 10
5 2 20 05
Total 9 100 09
01023(064)09σzpLCL
2823(064)09σzpUCL
06420
(09)(91)
n
)p(1pσ
09100
9
Inspected Total
DefectivespCL
p
p
p
Solution
40
P- CONTROL CHART
41
C-CHART EXAMPLE THE NUMBER OF WEEKLY CUSTOMER COMPLAINTS ARE MONITORED IN A LARGE HOTEL USING A C-CHART DEVELOP THREE SIGMA CONTROL LIMITS USING THE DATA TABLE BELOW
Week Number of Complaints
1 3
2 2
3 3
4 1
5 3
6 3
7 2
8 1
9 3
10 1
Total 22
022522322ccLCL
66522322ccUCL
2210
22
samples of
complaintsc
c
c
z
z
Solution
42
C- CONTROL CHART
43
The ability of a process to meet product designtechnical specifications
Assessing capability involves evaluating process variability relative to preset product or service specifications
Process Capability ndash Cp and Cpk
Cp assumes that the process is centered in the specification range
Cpk helps to address a possible lack of centering of the process
PROCESS CAPABILITY
6σ
LSLUSL
width process
width ionspecificatCp
3σ
LSLμ
3σ
μUSLminCpk
44
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
45
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
46
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
47
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
--and an individual part is measured at 520rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
48
GRAPHING THE TOLERANCE AND MEASUREMENTS
Suppose we made and measured several more
units and they were all EXACTLY the same
We wouldnrsquot have very many part problems
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
X
X
X
49
GRAPHING THE TOLERANCE AND MEASUREMENTS
In the real world units are NOT EXACTLY the same
Everything VARIES
The question isnrsquot IF units vary
Itrsquos how much when and why
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
XX
XXX
XXXXX
XXXXXXX
50
The ldquonormal bell curverdquo
Widths heights depths thicknesses weights speeds strengths
and many other types of measurements when charted as a
histogram often form the shape of a bell
A ldquoperfect bellrdquo like a ldquoperfect circlerdquo doesnrsquot occur in nature but
many processes are close enough to make the bell curve useful
(A number of common industrial measurements such as flatness and straightness do NOT tend to distribute in a bell shape their proper statistical analysis is performed using models other than the bell curve)
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
51
What is a ldquostandard deviationrdquo
If we measure the DISTANCE from the CENTER of the bell
to each individual measurement that makes up the bell curve
we can find a TYPICAL DISTANCE
The most commonly used statistic to estimate this distance is the
Standard Deviation (also called ldquoSigmardquo)
Because of the natural shape of the bell curve the area of +1 to ndash1
standard deviations includes about 68 of the curve
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
Typical distance
from the center +1
standard deviation
Typical distance
from the center -1
standard deviation
52
How much of the curve is included in how many standard
deviations
From ndash1 to +1 is about 68 of the bell curve
From ndash2 to +2 is about 95
From ndash3 to +3 is about 9973
From ndash4 to +4 is about 9999
(NOTE We usually show the bell from ndash3 to +3 to make it easier to draw but in concept the ldquotailsrdquo of the bell get very thin and go on forever)
-6 -5 -4 -3 -2 -1 +1 +2 +3 +4 +5 +6 0
53
A
B
What is Cpk It is a measure of how well a process is within a specification
Cpk = A divided by B
A = Distance from process mean to closest spec limit
B = 3 Standard Deviations (also called ldquo3 Sigmardquo)
A bigger Cpk is better because fewer units will be beyond spec
(A bigger ldquoArdquo and a smaller ldquoBrdquo are better)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
54
A
B
ldquoProcess Capabilityrdquo is the ability of a process
to fit its output within the tolerances
hellipa LARGER ldquoArdquo
hellipand a SMALLER ldquoBrdquo
hellipmeans BETTER ldquoProcess Capabilityrdquo
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
55
A
B
An Analogy
Analogy
The bell curve is your automobile
The spec limits are the edges of your garage door
If A = B you are hitting the frame of your garage door with your car
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
56
A
B
How can we make Cpk (A divided by B) better
1 Design the product so a wider tolerance is functional (ldquorobust designrdquo)
2 Choose equipment and methods for a good safety margin (ldquoprocess capabilityrdquo)
3 Correctly adjust but only when needed (ldquocontrolrdquo)
4 Discover ways to narrow the natural variation (ldquoimprovementrdquo)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
57
A
B
What does a very good Cpk do for us
This process is producing good units with a good safety margin
Note that when Cpk = 2 our process mean is 6 standard deviations from
the nearest spec so we say it has ldquo6 Sigma Capabilityrdquo
Specification
Limit
Specification
Limit
This Cpk is
about 2
Very good
Mean
58
A
B
What does a problem Cpk look like
This process is in danger of producing some defects
It is too close to the specification limits
(Remember the bell curve tail goes further than Bhellip hellipwe only show the bell to 3-sigma to make it easier to draw)
Specification
Limit
Specification
Limit
This Cpk is just
slightly greater
than 1 Not good
59
A
B
What does a very bad Cpk look like
A significant part of the ldquotailrdquo is hanging out beyond the spec limits
This process is producing scrap rework and customer rejects
Notice that if distance ldquoArdquo approaches zerohellip
hellipthe Cpk would approach zero andhellip
hellipthe process would become 50 defective
Specification
Limit
Specification
Limit
This Cpk is less
than 1 We desire
a minimum of 133
and ultimately we
want 2 or more
60
-
Q amp A
61
MEASUREMENT SYSTEM ANALYSIS (MSA)
An MSA is a statistical tool used to determine if a measurement system is capable of precise measurement
What is It
Objective or Purpose
bull To determine how much error is in the measurement due to the measurement process itself
bull Quantifies the variability added by the measurement system
bull Applicable to attribute data and variable data
When to Use It
bull On the critical inputs and outputs prior to collecting data for analysis
bull For any new or modified process in order to ensure the quality of the data
Measurement System Analysis is an analysis of the measurement process not an analysis of the people
IMPORTANT
Who Should be Involved
Everyone that measures and makes decisions about these measurements should be involved in the MSA
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The observed variation in process output measurements is not simply the variation in the process itself it is the variation in the process plus the variation in measurement that results from an inadequate measurement system
Conducting an MSA reduces the likelihood of passing a bad part or rejecting a good part
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The output of the process measured by bull Cycle time bull Dimensional data bull Number of defects and others
Observed Variation
Process Variation
Measurement System
Variation
Reproducibility
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Accuracy (Central Location)
OBSERVED VARIATION
Calibration addresses accuracy
Measurement System Analysis (MSA)
MEASUREMENT SYSTEM ERRORS
Accuracy difference between the observed measurement and the actual measurement
Precision variation that occurs when measuring the same part with the same instrument
MEASUREMENT SYSTEM ERROR
Precise but not
accurate
Accurate but not
precise
Not accurate or
precise
Accurate and
precise
ACCURACY OF MEASUREMENT
Broken down into three components
aStability
The consistency of measurements over time
bBias
A measure of the amount of partiality in the system
cLinearity
A measure of the bias values through the expected
range of measurements
OBSERVED VARIATION
Observed Variation
Process Variation
Measurement System
Variation
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Reproducibility
Accuracy (Central Location)
Calibration Addresses Accuracy
Letrsquos take a closer look at Precision
Measurement System Analysis (MSA)
Measurement System Analysis (MSA)
Error in Resolution The inability to detect small changes
Possible Cause
Wrong measurement device selected - divisions on scale not fine enough to detect changes
Resolution
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Repeatability The inability to get the same answer from repeated measurements made of the same item under absolutely identical conditions
Possible Cause
Lack of standard operating procedures (SOP) lack of training measuring system variablilty
Repeatability
Equipment Variation
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Reproducibility The inability to get the same answer from repeated measurements made under various conditions from different inspectors
Possible Cause
Lack of SOP lack of training
Reproducibility
Appraiser Variation
VARIABLE MSA ndash GAGE RampR STUDY
bull Gage RampR is the combined estimate of
measurement system Repeatability and
Reproducibility
bull Typically a 3-person study is performed Each person randomly measures 10 marked parts per trial
Each person can perform up to 3 trials
bull There are 3 key indicators EV or Equipment Variation
AV or Appraiser Variation
Overall GRR
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
Finally add up each and plot as a line diagram
0
10
20
30
40
50
60
Wrapper
Open
No Center No Wrapper Underweight
70
80
90
100
715
51
205
143
858
66
924
39
963
23
986
15
1001
23
0
10
20
30
40
50
60
Wrapper
Open
No Center No Wrapper Underweight
70
80
90
100
715
51
205
143
858
66
924
39
963
23
986
15
1001
24
CONTROL CHARTS
Control charts are one of the most commonly used methods of Statistical Process Control (SPC) which
monitors the stability of a process
The main features of a control chart include the data points a centreline (mean value) and upper and
lower limits (bounds to indicate where a process output is considered out of control)They visually
display the fluctuations of a particular process variable that easily determine whether these variations
fall within the specified process limits
Control charts
a graphical method for detecting if the underlying distribution of variation of some measurable
characteristic of the product seems to have undergone a shift
monitor a process in real time
Map the output of a production process over time
A control chart always has a central line for the average an upper line for the upper control limit and a
lower line for the lower control limit These lines are determined from historical data
By comparing current data to these lines you can draw conclusions about whether the process
variation is consistent (in control) or is unpredictable
25
CONTROL CHART - PURPOSE
The main purpose of using a control chart is to monitor control and improve
process performance over time by studying variation and its source There are
several functions of a control chart
It centres attention on detecting and monitoring process variation over time
It provides a tool for on-going control of a process
It differentiates special from common causes of variation in order to be a guide for
local or management action
It helps improve a process to perform consistently and predictably to achieve higher
quality lower cost and higher effective capacity
It serves as a common language for discussing process performance
26
TYPES OF CONTROL CHARTS
The basic tool used in SPC is the control chart
There are various types of control charts
Variable Control Chart
Averages and range chart (X-Bar and R Bar Chart)
X bar and s chart
Moving Range Chart
Moving AveragendashMoving Range chart (also called MAndashMR chart)
p chart (also called proportion chart)
c chart (also called count chart)
np chart
u chart
27
POPULARITY OF CONTROL CHARTS
Control charts are a proven technique for improving productivity
Control charts are effective in defect prevention
Control charts prevent unnecessary process
adjustment
Control charts provide diagnostic information
Control charts provide information about process
capability
28
PROCEDURE FOR X ndashBAR AND R BAR CHART
1 Randomly sample ldquonrdquo units throughout the day (can be every 5
minutes every 30 minutes etc - whatever is appropriate for your
case)
2 For each sample calculate ldquoX-BARrdquo to estimate the mean and ldquoR
(range)rdquo to estimate variability NOTE THE RANGE CAN BE USED TO
ESTIMATE THE STANDARD DEVIATION
3 After collecting the 20-25 samples calculate X-BAR-BAR (the
average of all the X-BARs) and R-BAR (the average of all the ranges)
4 Using X-BAR-BAR and R-BAR calculate the control limits for your X-
BAR and R Control Charts
29
X-BAR CONTROL LIMITS
Upper Control Limit (UCL) = (X-BAR-BAR) + A2 (R-BAR)
Lower Control Limit(LCL) = (X-BAR-BAR) - A2 (R-BAR)
R CONTROL LIMITS
Upper Control Limit - D3 (R-BAR)
Lower Control Limit - D4 (R-BAR)
PROCEDURE FOR X ndashBAR AND R BAR CHART
30
CONTROL CHART CONSTANTS
sample size constant constant constant constant constant constant constant
n d2 A2 A3 B3 B4 D3 D4
2 1128 188 2659 0 3267 0 3267
3 1693 1023 1954 0 2568 0 2574
4 2059 0729 1628 0 2266 0 2282
5 2326 0577 1427 0 2089 0 2114
6 2534 0483 1287 003 197 0 2004
7 2704 0419 1182 0118 1882 0076 1924
8 2847 0373 1099 0185 1815 0136 1864
9 297 0337 1032 0239 1761 0184 1816
10 3078 0308 0975 0284 1716 0223 1777
31
5 For the R Control Chart plot all R values on the R Control Chart
to see if all the Ranges are ldquobetween the control limitsrdquo If they are
then your process is considered to be in a state of statistical control
(as far as the variability of the process is concerned)
6 For the X-BAR Control Chart plot all the X-BARs on the X-BAR
control chart to see if all the X-BARs are ldquobetween the control
limitsrdquo If they are then your process is considered in a state of
statistical control (as far as the average of the process is
concerned)
PROCEDURE FOR X ndashBAR AND R BAR CHART
32
SAMPLE DATA FOR X BAR ndashR CHART
Sub Group 1 2 3 4 5 X -Bar Range reg
1 1195 1191 1211 1203 1198 1200 02
2 1201 1198 1198 1197 12 1199 004
3 1193 1206 1198 1196 1202 1199 013
4 1205 1198 1205 1206 1198 1202 008
5 1198 1203 1206 1201 1199 1201 008
6 1202 1205 1196 1201 1195 1200 01
7 1199 1206 1201 1204 1201 1202 007
8 1201 1197 1198 1204 1198 1200 007
9 1198 1204 1198 1204 1204 1202 006
10 1205 1195 1198 1204 1196 1200 01
` X Bar-Bar 1200 009
X Bar Chart
UCL = X BAR-BAR + A2 R Bar
1200 +(0577009) 1205
LCL= X BAR-BAR - A2 R Bar
1200 - (0577009) 1195
R Chart
UCL = D4R Bar 211 009 021
LCL = D3 R Bar 0009 0
33
PLOT DATA ON CONTROL CHARTS
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1 2 3 4 5 6 7 8 9 10
Ave
rage
(X
ba
r)
X Bar Chart
UCL
LCL
X Bar
34
PLOT DATA ON CONTROL CHARTS
001
003
005
007
009
011
013
015
017
019
021
023
025
1 2 3 4 5 6 7 8 9 10
R Chart
UCL
LCL
35
PROCEDURE TO DETERMINE IF PROCESS IS IN A STATE OF
STATISTICAL CONTROL
7 If process is determined to be ldquoNOT STABLErdquo then stop and find out what
an assignable cause might be fix and then repeat the complete process of
collecting new data
8 If the process is determined to be ldquoSTABLErdquo then you may use the
control charts you developed to monitor future production to ensure that the
process REMAINS stable
More Samples for Control charts
36
READING OF CONTROL CHART
Control charts can determine whether a process is behaving in an unusual way The quality of the individual points of a subset is determined unstable if any of the
following occurs
Rule 1 Any point falls beyond 3σ from the centreline(this is represented by the upper and
lower control limits)
Rule 2 Two out of three consecutive points fall beyond 2σ on the same side of the
centreline
Rule 3 Four out of five consecutive points fall beyond 1σ on the same side of the
centreline
Rule 4 Nine or more consecutive points fall on the same side of the centreline
(Ref Next page for sample)
37
READING THE CONTROL CHART
38
CONTROL CHARTS FOR ATTRIBUTES ndashP-CHARTS amp C-CHARTS
Attributes are discrete events yesno or passfail
Use P-Charts for quality characteristics that are discrete and involve yesno or goodbad decisions
Eg
Number of leaking caulking tubes in a box of 48
Number of broken eggs in a carton
Use C-Charts for discrete defects when there can be more than one defect per unit
Eg
Number of stains in a carpet sample cut from a production run
Number of complaints per customer at a hotel
39
P-CHART EXAMPLE A PRODUCTION MANAGER FOR A TIRE COMPANY HAS INSPECTED THE NUMBER OF
DEFECTIVE TIRES IN FIVE RANDOM SAMPLES WITH 20 TIRES IN EACH SAMPLE THE TABLE BELOW SHOWS THE
NUMBER OF DEFECTIVE TIRES IN EACH SAMPLE OF 20 TIRES CALCULATE THE CONTROL LIMITS
Sample Number of
Defective Tires
Number of Tires in each
Sample
Proportion Defective
1 3 20 15
2 2 20 10
3 1 20 05
4 2 20 10
5 2 20 05
Total 9 100 09
01023(064)09σzpLCL
2823(064)09σzpUCL
06420
(09)(91)
n
)p(1pσ
09100
9
Inspected Total
DefectivespCL
p
p
p
Solution
40
P- CONTROL CHART
41
C-CHART EXAMPLE THE NUMBER OF WEEKLY CUSTOMER COMPLAINTS ARE MONITORED IN A LARGE HOTEL USING A C-CHART DEVELOP THREE SIGMA CONTROL LIMITS USING THE DATA TABLE BELOW
Week Number of Complaints
1 3
2 2
3 3
4 1
5 3
6 3
7 2
8 1
9 3
10 1
Total 22
022522322ccLCL
66522322ccUCL
2210
22
samples of
complaintsc
c
c
z
z
Solution
42
C- CONTROL CHART
43
The ability of a process to meet product designtechnical specifications
Assessing capability involves evaluating process variability relative to preset product or service specifications
Process Capability ndash Cp and Cpk
Cp assumes that the process is centered in the specification range
Cpk helps to address a possible lack of centering of the process
PROCESS CAPABILITY
6σ
LSLUSL
width process
width ionspecificatCp
3σ
LSLμ
3σ
μUSLminCpk
44
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
45
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
46
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
47
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
--and an individual part is measured at 520rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
48
GRAPHING THE TOLERANCE AND MEASUREMENTS
Suppose we made and measured several more
units and they were all EXACTLY the same
We wouldnrsquot have very many part problems
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
X
X
X
49
GRAPHING THE TOLERANCE AND MEASUREMENTS
In the real world units are NOT EXACTLY the same
Everything VARIES
The question isnrsquot IF units vary
Itrsquos how much when and why
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
XX
XXX
XXXXX
XXXXXXX
50
The ldquonormal bell curverdquo
Widths heights depths thicknesses weights speeds strengths
and many other types of measurements when charted as a
histogram often form the shape of a bell
A ldquoperfect bellrdquo like a ldquoperfect circlerdquo doesnrsquot occur in nature but
many processes are close enough to make the bell curve useful
(A number of common industrial measurements such as flatness and straightness do NOT tend to distribute in a bell shape their proper statistical analysis is performed using models other than the bell curve)
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
51
What is a ldquostandard deviationrdquo
If we measure the DISTANCE from the CENTER of the bell
to each individual measurement that makes up the bell curve
we can find a TYPICAL DISTANCE
The most commonly used statistic to estimate this distance is the
Standard Deviation (also called ldquoSigmardquo)
Because of the natural shape of the bell curve the area of +1 to ndash1
standard deviations includes about 68 of the curve
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
Typical distance
from the center +1
standard deviation
Typical distance
from the center -1
standard deviation
52
How much of the curve is included in how many standard
deviations
From ndash1 to +1 is about 68 of the bell curve
From ndash2 to +2 is about 95
From ndash3 to +3 is about 9973
From ndash4 to +4 is about 9999
(NOTE We usually show the bell from ndash3 to +3 to make it easier to draw but in concept the ldquotailsrdquo of the bell get very thin and go on forever)
-6 -5 -4 -3 -2 -1 +1 +2 +3 +4 +5 +6 0
53
A
B
What is Cpk It is a measure of how well a process is within a specification
Cpk = A divided by B
A = Distance from process mean to closest spec limit
B = 3 Standard Deviations (also called ldquo3 Sigmardquo)
A bigger Cpk is better because fewer units will be beyond spec
(A bigger ldquoArdquo and a smaller ldquoBrdquo are better)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
54
A
B
ldquoProcess Capabilityrdquo is the ability of a process
to fit its output within the tolerances
hellipa LARGER ldquoArdquo
hellipand a SMALLER ldquoBrdquo
hellipmeans BETTER ldquoProcess Capabilityrdquo
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
55
A
B
An Analogy
Analogy
The bell curve is your automobile
The spec limits are the edges of your garage door
If A = B you are hitting the frame of your garage door with your car
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
56
A
B
How can we make Cpk (A divided by B) better
1 Design the product so a wider tolerance is functional (ldquorobust designrdquo)
2 Choose equipment and methods for a good safety margin (ldquoprocess capabilityrdquo)
3 Correctly adjust but only when needed (ldquocontrolrdquo)
4 Discover ways to narrow the natural variation (ldquoimprovementrdquo)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
57
A
B
What does a very good Cpk do for us
This process is producing good units with a good safety margin
Note that when Cpk = 2 our process mean is 6 standard deviations from
the nearest spec so we say it has ldquo6 Sigma Capabilityrdquo
Specification
Limit
Specification
Limit
This Cpk is
about 2
Very good
Mean
58
A
B
What does a problem Cpk look like
This process is in danger of producing some defects
It is too close to the specification limits
(Remember the bell curve tail goes further than Bhellip hellipwe only show the bell to 3-sigma to make it easier to draw)
Specification
Limit
Specification
Limit
This Cpk is just
slightly greater
than 1 Not good
59
A
B
What does a very bad Cpk look like
A significant part of the ldquotailrdquo is hanging out beyond the spec limits
This process is producing scrap rework and customer rejects
Notice that if distance ldquoArdquo approaches zerohellip
hellipthe Cpk would approach zero andhellip
hellipthe process would become 50 defective
Specification
Limit
Specification
Limit
This Cpk is less
than 1 We desire
a minimum of 133
and ultimately we
want 2 or more
60
-
Q amp A
61
MEASUREMENT SYSTEM ANALYSIS (MSA)
An MSA is a statistical tool used to determine if a measurement system is capable of precise measurement
What is It
Objective or Purpose
bull To determine how much error is in the measurement due to the measurement process itself
bull Quantifies the variability added by the measurement system
bull Applicable to attribute data and variable data
When to Use It
bull On the critical inputs and outputs prior to collecting data for analysis
bull For any new or modified process in order to ensure the quality of the data
Measurement System Analysis is an analysis of the measurement process not an analysis of the people
IMPORTANT
Who Should be Involved
Everyone that measures and makes decisions about these measurements should be involved in the MSA
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The observed variation in process output measurements is not simply the variation in the process itself it is the variation in the process plus the variation in measurement that results from an inadequate measurement system
Conducting an MSA reduces the likelihood of passing a bad part or rejecting a good part
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The output of the process measured by bull Cycle time bull Dimensional data bull Number of defects and others
Observed Variation
Process Variation
Measurement System
Variation
Reproducibility
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Accuracy (Central Location)
OBSERVED VARIATION
Calibration addresses accuracy
Measurement System Analysis (MSA)
MEASUREMENT SYSTEM ERRORS
Accuracy difference between the observed measurement and the actual measurement
Precision variation that occurs when measuring the same part with the same instrument
MEASUREMENT SYSTEM ERROR
Precise but not
accurate
Accurate but not
precise
Not accurate or
precise
Accurate and
precise
ACCURACY OF MEASUREMENT
Broken down into three components
aStability
The consistency of measurements over time
bBias
A measure of the amount of partiality in the system
cLinearity
A measure of the bias values through the expected
range of measurements
OBSERVED VARIATION
Observed Variation
Process Variation
Measurement System
Variation
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Reproducibility
Accuracy (Central Location)
Calibration Addresses Accuracy
Letrsquos take a closer look at Precision
Measurement System Analysis (MSA)
Measurement System Analysis (MSA)
Error in Resolution The inability to detect small changes
Possible Cause
Wrong measurement device selected - divisions on scale not fine enough to detect changes
Resolution
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Repeatability The inability to get the same answer from repeated measurements made of the same item under absolutely identical conditions
Possible Cause
Lack of standard operating procedures (SOP) lack of training measuring system variablilty
Repeatability
Equipment Variation
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Reproducibility The inability to get the same answer from repeated measurements made under various conditions from different inspectors
Possible Cause
Lack of SOP lack of training
Reproducibility
Appraiser Variation
VARIABLE MSA ndash GAGE RampR STUDY
bull Gage RampR is the combined estimate of
measurement system Repeatability and
Reproducibility
bull Typically a 3-person study is performed Each person randomly measures 10 marked parts per trial
Each person can perform up to 3 trials
bull There are 3 key indicators EV or Equipment Variation
AV or Appraiser Variation
Overall GRR
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
0
10
20
30
40
50
60
Wrapper
Open
No Center No Wrapper Underweight
70
80
90
100
715
51
205
143
858
66
924
39
963
23
986
15
1001
24
CONTROL CHARTS
Control charts are one of the most commonly used methods of Statistical Process Control (SPC) which
monitors the stability of a process
The main features of a control chart include the data points a centreline (mean value) and upper and
lower limits (bounds to indicate where a process output is considered out of control)They visually
display the fluctuations of a particular process variable that easily determine whether these variations
fall within the specified process limits
Control charts
a graphical method for detecting if the underlying distribution of variation of some measurable
characteristic of the product seems to have undergone a shift
monitor a process in real time
Map the output of a production process over time
A control chart always has a central line for the average an upper line for the upper control limit and a
lower line for the lower control limit These lines are determined from historical data
By comparing current data to these lines you can draw conclusions about whether the process
variation is consistent (in control) or is unpredictable
25
CONTROL CHART - PURPOSE
The main purpose of using a control chart is to monitor control and improve
process performance over time by studying variation and its source There are
several functions of a control chart
It centres attention on detecting and monitoring process variation over time
It provides a tool for on-going control of a process
It differentiates special from common causes of variation in order to be a guide for
local or management action
It helps improve a process to perform consistently and predictably to achieve higher
quality lower cost and higher effective capacity
It serves as a common language for discussing process performance
26
TYPES OF CONTROL CHARTS
The basic tool used in SPC is the control chart
There are various types of control charts
Variable Control Chart
Averages and range chart (X-Bar and R Bar Chart)
X bar and s chart
Moving Range Chart
Moving AveragendashMoving Range chart (also called MAndashMR chart)
p chart (also called proportion chart)
c chart (also called count chart)
np chart
u chart
27
POPULARITY OF CONTROL CHARTS
Control charts are a proven technique for improving productivity
Control charts are effective in defect prevention
Control charts prevent unnecessary process
adjustment
Control charts provide diagnostic information
Control charts provide information about process
capability
28
PROCEDURE FOR X ndashBAR AND R BAR CHART
1 Randomly sample ldquonrdquo units throughout the day (can be every 5
minutes every 30 minutes etc - whatever is appropriate for your
case)
2 For each sample calculate ldquoX-BARrdquo to estimate the mean and ldquoR
(range)rdquo to estimate variability NOTE THE RANGE CAN BE USED TO
ESTIMATE THE STANDARD DEVIATION
3 After collecting the 20-25 samples calculate X-BAR-BAR (the
average of all the X-BARs) and R-BAR (the average of all the ranges)
4 Using X-BAR-BAR and R-BAR calculate the control limits for your X-
BAR and R Control Charts
29
X-BAR CONTROL LIMITS
Upper Control Limit (UCL) = (X-BAR-BAR) + A2 (R-BAR)
Lower Control Limit(LCL) = (X-BAR-BAR) - A2 (R-BAR)
R CONTROL LIMITS
Upper Control Limit - D3 (R-BAR)
Lower Control Limit - D4 (R-BAR)
PROCEDURE FOR X ndashBAR AND R BAR CHART
30
CONTROL CHART CONSTANTS
sample size constant constant constant constant constant constant constant
n d2 A2 A3 B3 B4 D3 D4
2 1128 188 2659 0 3267 0 3267
3 1693 1023 1954 0 2568 0 2574
4 2059 0729 1628 0 2266 0 2282
5 2326 0577 1427 0 2089 0 2114
6 2534 0483 1287 003 197 0 2004
7 2704 0419 1182 0118 1882 0076 1924
8 2847 0373 1099 0185 1815 0136 1864
9 297 0337 1032 0239 1761 0184 1816
10 3078 0308 0975 0284 1716 0223 1777
31
5 For the R Control Chart plot all R values on the R Control Chart
to see if all the Ranges are ldquobetween the control limitsrdquo If they are
then your process is considered to be in a state of statistical control
(as far as the variability of the process is concerned)
6 For the X-BAR Control Chart plot all the X-BARs on the X-BAR
control chart to see if all the X-BARs are ldquobetween the control
limitsrdquo If they are then your process is considered in a state of
statistical control (as far as the average of the process is
concerned)
PROCEDURE FOR X ndashBAR AND R BAR CHART
32
SAMPLE DATA FOR X BAR ndashR CHART
Sub Group 1 2 3 4 5 X -Bar Range reg
1 1195 1191 1211 1203 1198 1200 02
2 1201 1198 1198 1197 12 1199 004
3 1193 1206 1198 1196 1202 1199 013
4 1205 1198 1205 1206 1198 1202 008
5 1198 1203 1206 1201 1199 1201 008
6 1202 1205 1196 1201 1195 1200 01
7 1199 1206 1201 1204 1201 1202 007
8 1201 1197 1198 1204 1198 1200 007
9 1198 1204 1198 1204 1204 1202 006
10 1205 1195 1198 1204 1196 1200 01
` X Bar-Bar 1200 009
X Bar Chart
UCL = X BAR-BAR + A2 R Bar
1200 +(0577009) 1205
LCL= X BAR-BAR - A2 R Bar
1200 - (0577009) 1195
R Chart
UCL = D4R Bar 211 009 021
LCL = D3 R Bar 0009 0
33
PLOT DATA ON CONTROL CHARTS
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1 2 3 4 5 6 7 8 9 10
Ave
rage
(X
ba
r)
X Bar Chart
UCL
LCL
X Bar
34
PLOT DATA ON CONTROL CHARTS
001
003
005
007
009
011
013
015
017
019
021
023
025
1 2 3 4 5 6 7 8 9 10
R Chart
UCL
LCL
35
PROCEDURE TO DETERMINE IF PROCESS IS IN A STATE OF
STATISTICAL CONTROL
7 If process is determined to be ldquoNOT STABLErdquo then stop and find out what
an assignable cause might be fix and then repeat the complete process of
collecting new data
8 If the process is determined to be ldquoSTABLErdquo then you may use the
control charts you developed to monitor future production to ensure that the
process REMAINS stable
More Samples for Control charts
36
READING OF CONTROL CHART
Control charts can determine whether a process is behaving in an unusual way The quality of the individual points of a subset is determined unstable if any of the
following occurs
Rule 1 Any point falls beyond 3σ from the centreline(this is represented by the upper and
lower control limits)
Rule 2 Two out of three consecutive points fall beyond 2σ on the same side of the
centreline
Rule 3 Four out of five consecutive points fall beyond 1σ on the same side of the
centreline
Rule 4 Nine or more consecutive points fall on the same side of the centreline
(Ref Next page for sample)
37
READING THE CONTROL CHART
38
CONTROL CHARTS FOR ATTRIBUTES ndashP-CHARTS amp C-CHARTS
Attributes are discrete events yesno or passfail
Use P-Charts for quality characteristics that are discrete and involve yesno or goodbad decisions
Eg
Number of leaking caulking tubes in a box of 48
Number of broken eggs in a carton
Use C-Charts for discrete defects when there can be more than one defect per unit
Eg
Number of stains in a carpet sample cut from a production run
Number of complaints per customer at a hotel
39
P-CHART EXAMPLE A PRODUCTION MANAGER FOR A TIRE COMPANY HAS INSPECTED THE NUMBER OF
DEFECTIVE TIRES IN FIVE RANDOM SAMPLES WITH 20 TIRES IN EACH SAMPLE THE TABLE BELOW SHOWS THE
NUMBER OF DEFECTIVE TIRES IN EACH SAMPLE OF 20 TIRES CALCULATE THE CONTROL LIMITS
Sample Number of
Defective Tires
Number of Tires in each
Sample
Proportion Defective
1 3 20 15
2 2 20 10
3 1 20 05
4 2 20 10
5 2 20 05
Total 9 100 09
01023(064)09σzpLCL
2823(064)09σzpUCL
06420
(09)(91)
n
)p(1pσ
09100
9
Inspected Total
DefectivespCL
p
p
p
Solution
40
P- CONTROL CHART
41
C-CHART EXAMPLE THE NUMBER OF WEEKLY CUSTOMER COMPLAINTS ARE MONITORED IN A LARGE HOTEL USING A C-CHART DEVELOP THREE SIGMA CONTROL LIMITS USING THE DATA TABLE BELOW
Week Number of Complaints
1 3
2 2
3 3
4 1
5 3
6 3
7 2
8 1
9 3
10 1
Total 22
022522322ccLCL
66522322ccUCL
2210
22
samples of
complaintsc
c
c
z
z
Solution
42
C- CONTROL CHART
43
The ability of a process to meet product designtechnical specifications
Assessing capability involves evaluating process variability relative to preset product or service specifications
Process Capability ndash Cp and Cpk
Cp assumes that the process is centered in the specification range
Cpk helps to address a possible lack of centering of the process
PROCESS CAPABILITY
6σ
LSLUSL
width process
width ionspecificatCp
3σ
LSLμ
3σ
μUSLminCpk
44
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
45
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
46
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
47
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
--and an individual part is measured at 520rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
48
GRAPHING THE TOLERANCE AND MEASUREMENTS
Suppose we made and measured several more
units and they were all EXACTLY the same
We wouldnrsquot have very many part problems
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
X
X
X
49
GRAPHING THE TOLERANCE AND MEASUREMENTS
In the real world units are NOT EXACTLY the same
Everything VARIES
The question isnrsquot IF units vary
Itrsquos how much when and why
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
XX
XXX
XXXXX
XXXXXXX
50
The ldquonormal bell curverdquo
Widths heights depths thicknesses weights speeds strengths
and many other types of measurements when charted as a
histogram often form the shape of a bell
A ldquoperfect bellrdquo like a ldquoperfect circlerdquo doesnrsquot occur in nature but
many processes are close enough to make the bell curve useful
(A number of common industrial measurements such as flatness and straightness do NOT tend to distribute in a bell shape their proper statistical analysis is performed using models other than the bell curve)
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
51
What is a ldquostandard deviationrdquo
If we measure the DISTANCE from the CENTER of the bell
to each individual measurement that makes up the bell curve
we can find a TYPICAL DISTANCE
The most commonly used statistic to estimate this distance is the
Standard Deviation (also called ldquoSigmardquo)
Because of the natural shape of the bell curve the area of +1 to ndash1
standard deviations includes about 68 of the curve
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
Typical distance
from the center +1
standard deviation
Typical distance
from the center -1
standard deviation
52
How much of the curve is included in how many standard
deviations
From ndash1 to +1 is about 68 of the bell curve
From ndash2 to +2 is about 95
From ndash3 to +3 is about 9973
From ndash4 to +4 is about 9999
(NOTE We usually show the bell from ndash3 to +3 to make it easier to draw but in concept the ldquotailsrdquo of the bell get very thin and go on forever)
-6 -5 -4 -3 -2 -1 +1 +2 +3 +4 +5 +6 0
53
A
B
What is Cpk It is a measure of how well a process is within a specification
Cpk = A divided by B
A = Distance from process mean to closest spec limit
B = 3 Standard Deviations (also called ldquo3 Sigmardquo)
A bigger Cpk is better because fewer units will be beyond spec
(A bigger ldquoArdquo and a smaller ldquoBrdquo are better)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
54
A
B
ldquoProcess Capabilityrdquo is the ability of a process
to fit its output within the tolerances
hellipa LARGER ldquoArdquo
hellipand a SMALLER ldquoBrdquo
hellipmeans BETTER ldquoProcess Capabilityrdquo
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
55
A
B
An Analogy
Analogy
The bell curve is your automobile
The spec limits are the edges of your garage door
If A = B you are hitting the frame of your garage door with your car
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
56
A
B
How can we make Cpk (A divided by B) better
1 Design the product so a wider tolerance is functional (ldquorobust designrdquo)
2 Choose equipment and methods for a good safety margin (ldquoprocess capabilityrdquo)
3 Correctly adjust but only when needed (ldquocontrolrdquo)
4 Discover ways to narrow the natural variation (ldquoimprovementrdquo)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
57
A
B
What does a very good Cpk do for us
This process is producing good units with a good safety margin
Note that when Cpk = 2 our process mean is 6 standard deviations from
the nearest spec so we say it has ldquo6 Sigma Capabilityrdquo
Specification
Limit
Specification
Limit
This Cpk is
about 2
Very good
Mean
58
A
B
What does a problem Cpk look like
This process is in danger of producing some defects
It is too close to the specification limits
(Remember the bell curve tail goes further than Bhellip hellipwe only show the bell to 3-sigma to make it easier to draw)
Specification
Limit
Specification
Limit
This Cpk is just
slightly greater
than 1 Not good
59
A
B
What does a very bad Cpk look like
A significant part of the ldquotailrdquo is hanging out beyond the spec limits
This process is producing scrap rework and customer rejects
Notice that if distance ldquoArdquo approaches zerohellip
hellipthe Cpk would approach zero andhellip
hellipthe process would become 50 defective
Specification
Limit
Specification
Limit
This Cpk is less
than 1 We desire
a minimum of 133
and ultimately we
want 2 or more
60
-
Q amp A
61
MEASUREMENT SYSTEM ANALYSIS (MSA)
An MSA is a statistical tool used to determine if a measurement system is capable of precise measurement
What is It
Objective or Purpose
bull To determine how much error is in the measurement due to the measurement process itself
bull Quantifies the variability added by the measurement system
bull Applicable to attribute data and variable data
When to Use It
bull On the critical inputs and outputs prior to collecting data for analysis
bull For any new or modified process in order to ensure the quality of the data
Measurement System Analysis is an analysis of the measurement process not an analysis of the people
IMPORTANT
Who Should be Involved
Everyone that measures and makes decisions about these measurements should be involved in the MSA
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The observed variation in process output measurements is not simply the variation in the process itself it is the variation in the process plus the variation in measurement that results from an inadequate measurement system
Conducting an MSA reduces the likelihood of passing a bad part or rejecting a good part
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The output of the process measured by bull Cycle time bull Dimensional data bull Number of defects and others
Observed Variation
Process Variation
Measurement System
Variation
Reproducibility
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Accuracy (Central Location)
OBSERVED VARIATION
Calibration addresses accuracy
Measurement System Analysis (MSA)
MEASUREMENT SYSTEM ERRORS
Accuracy difference between the observed measurement and the actual measurement
Precision variation that occurs when measuring the same part with the same instrument
MEASUREMENT SYSTEM ERROR
Precise but not
accurate
Accurate but not
precise
Not accurate or
precise
Accurate and
precise
ACCURACY OF MEASUREMENT
Broken down into three components
aStability
The consistency of measurements over time
bBias
A measure of the amount of partiality in the system
cLinearity
A measure of the bias values through the expected
range of measurements
OBSERVED VARIATION
Observed Variation
Process Variation
Measurement System
Variation
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Reproducibility
Accuracy (Central Location)
Calibration Addresses Accuracy
Letrsquos take a closer look at Precision
Measurement System Analysis (MSA)
Measurement System Analysis (MSA)
Error in Resolution The inability to detect small changes
Possible Cause
Wrong measurement device selected - divisions on scale not fine enough to detect changes
Resolution
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Repeatability The inability to get the same answer from repeated measurements made of the same item under absolutely identical conditions
Possible Cause
Lack of standard operating procedures (SOP) lack of training measuring system variablilty
Repeatability
Equipment Variation
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Reproducibility The inability to get the same answer from repeated measurements made under various conditions from different inspectors
Possible Cause
Lack of SOP lack of training
Reproducibility
Appraiser Variation
VARIABLE MSA ndash GAGE RampR STUDY
bull Gage RampR is the combined estimate of
measurement system Repeatability and
Reproducibility
bull Typically a 3-person study is performed Each person randomly measures 10 marked parts per trial
Each person can perform up to 3 trials
bull There are 3 key indicators EV or Equipment Variation
AV or Appraiser Variation
Overall GRR
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
CONTROL CHARTS
Control charts are one of the most commonly used methods of Statistical Process Control (SPC) which
monitors the stability of a process
The main features of a control chart include the data points a centreline (mean value) and upper and
lower limits (bounds to indicate where a process output is considered out of control)They visually
display the fluctuations of a particular process variable that easily determine whether these variations
fall within the specified process limits
Control charts
a graphical method for detecting if the underlying distribution of variation of some measurable
characteristic of the product seems to have undergone a shift
monitor a process in real time
Map the output of a production process over time
A control chart always has a central line for the average an upper line for the upper control limit and a
lower line for the lower control limit These lines are determined from historical data
By comparing current data to these lines you can draw conclusions about whether the process
variation is consistent (in control) or is unpredictable
25
CONTROL CHART - PURPOSE
The main purpose of using a control chart is to monitor control and improve
process performance over time by studying variation and its source There are
several functions of a control chart
It centres attention on detecting and monitoring process variation over time
It provides a tool for on-going control of a process
It differentiates special from common causes of variation in order to be a guide for
local or management action
It helps improve a process to perform consistently and predictably to achieve higher
quality lower cost and higher effective capacity
It serves as a common language for discussing process performance
26
TYPES OF CONTROL CHARTS
The basic tool used in SPC is the control chart
There are various types of control charts
Variable Control Chart
Averages and range chart (X-Bar and R Bar Chart)
X bar and s chart
Moving Range Chart
Moving AveragendashMoving Range chart (also called MAndashMR chart)
p chart (also called proportion chart)
c chart (also called count chart)
np chart
u chart
27
POPULARITY OF CONTROL CHARTS
Control charts are a proven technique for improving productivity
Control charts are effective in defect prevention
Control charts prevent unnecessary process
adjustment
Control charts provide diagnostic information
Control charts provide information about process
capability
28
PROCEDURE FOR X ndashBAR AND R BAR CHART
1 Randomly sample ldquonrdquo units throughout the day (can be every 5
minutes every 30 minutes etc - whatever is appropriate for your
case)
2 For each sample calculate ldquoX-BARrdquo to estimate the mean and ldquoR
(range)rdquo to estimate variability NOTE THE RANGE CAN BE USED TO
ESTIMATE THE STANDARD DEVIATION
3 After collecting the 20-25 samples calculate X-BAR-BAR (the
average of all the X-BARs) and R-BAR (the average of all the ranges)
4 Using X-BAR-BAR and R-BAR calculate the control limits for your X-
BAR and R Control Charts
29
X-BAR CONTROL LIMITS
Upper Control Limit (UCL) = (X-BAR-BAR) + A2 (R-BAR)
Lower Control Limit(LCL) = (X-BAR-BAR) - A2 (R-BAR)
R CONTROL LIMITS
Upper Control Limit - D3 (R-BAR)
Lower Control Limit - D4 (R-BAR)
PROCEDURE FOR X ndashBAR AND R BAR CHART
30
CONTROL CHART CONSTANTS
sample size constant constant constant constant constant constant constant
n d2 A2 A3 B3 B4 D3 D4
2 1128 188 2659 0 3267 0 3267
3 1693 1023 1954 0 2568 0 2574
4 2059 0729 1628 0 2266 0 2282
5 2326 0577 1427 0 2089 0 2114
6 2534 0483 1287 003 197 0 2004
7 2704 0419 1182 0118 1882 0076 1924
8 2847 0373 1099 0185 1815 0136 1864
9 297 0337 1032 0239 1761 0184 1816
10 3078 0308 0975 0284 1716 0223 1777
31
5 For the R Control Chart plot all R values on the R Control Chart
to see if all the Ranges are ldquobetween the control limitsrdquo If they are
then your process is considered to be in a state of statistical control
(as far as the variability of the process is concerned)
6 For the X-BAR Control Chart plot all the X-BARs on the X-BAR
control chart to see if all the X-BARs are ldquobetween the control
limitsrdquo If they are then your process is considered in a state of
statistical control (as far as the average of the process is
concerned)
PROCEDURE FOR X ndashBAR AND R BAR CHART
32
SAMPLE DATA FOR X BAR ndashR CHART
Sub Group 1 2 3 4 5 X -Bar Range reg
1 1195 1191 1211 1203 1198 1200 02
2 1201 1198 1198 1197 12 1199 004
3 1193 1206 1198 1196 1202 1199 013
4 1205 1198 1205 1206 1198 1202 008
5 1198 1203 1206 1201 1199 1201 008
6 1202 1205 1196 1201 1195 1200 01
7 1199 1206 1201 1204 1201 1202 007
8 1201 1197 1198 1204 1198 1200 007
9 1198 1204 1198 1204 1204 1202 006
10 1205 1195 1198 1204 1196 1200 01
` X Bar-Bar 1200 009
X Bar Chart
UCL = X BAR-BAR + A2 R Bar
1200 +(0577009) 1205
LCL= X BAR-BAR - A2 R Bar
1200 - (0577009) 1195
R Chart
UCL = D4R Bar 211 009 021
LCL = D3 R Bar 0009 0
33
PLOT DATA ON CONTROL CHARTS
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1 2 3 4 5 6 7 8 9 10
Ave
rage
(X
ba
r)
X Bar Chart
UCL
LCL
X Bar
34
PLOT DATA ON CONTROL CHARTS
001
003
005
007
009
011
013
015
017
019
021
023
025
1 2 3 4 5 6 7 8 9 10
R Chart
UCL
LCL
35
PROCEDURE TO DETERMINE IF PROCESS IS IN A STATE OF
STATISTICAL CONTROL
7 If process is determined to be ldquoNOT STABLErdquo then stop and find out what
an assignable cause might be fix and then repeat the complete process of
collecting new data
8 If the process is determined to be ldquoSTABLErdquo then you may use the
control charts you developed to monitor future production to ensure that the
process REMAINS stable
More Samples for Control charts
36
READING OF CONTROL CHART
Control charts can determine whether a process is behaving in an unusual way The quality of the individual points of a subset is determined unstable if any of the
following occurs
Rule 1 Any point falls beyond 3σ from the centreline(this is represented by the upper and
lower control limits)
Rule 2 Two out of three consecutive points fall beyond 2σ on the same side of the
centreline
Rule 3 Four out of five consecutive points fall beyond 1σ on the same side of the
centreline
Rule 4 Nine or more consecutive points fall on the same side of the centreline
(Ref Next page for sample)
37
READING THE CONTROL CHART
38
CONTROL CHARTS FOR ATTRIBUTES ndashP-CHARTS amp C-CHARTS
Attributes are discrete events yesno or passfail
Use P-Charts for quality characteristics that are discrete and involve yesno or goodbad decisions
Eg
Number of leaking caulking tubes in a box of 48
Number of broken eggs in a carton
Use C-Charts for discrete defects when there can be more than one defect per unit
Eg
Number of stains in a carpet sample cut from a production run
Number of complaints per customer at a hotel
39
P-CHART EXAMPLE A PRODUCTION MANAGER FOR A TIRE COMPANY HAS INSPECTED THE NUMBER OF
DEFECTIVE TIRES IN FIVE RANDOM SAMPLES WITH 20 TIRES IN EACH SAMPLE THE TABLE BELOW SHOWS THE
NUMBER OF DEFECTIVE TIRES IN EACH SAMPLE OF 20 TIRES CALCULATE THE CONTROL LIMITS
Sample Number of
Defective Tires
Number of Tires in each
Sample
Proportion Defective
1 3 20 15
2 2 20 10
3 1 20 05
4 2 20 10
5 2 20 05
Total 9 100 09
01023(064)09σzpLCL
2823(064)09σzpUCL
06420
(09)(91)
n
)p(1pσ
09100
9
Inspected Total
DefectivespCL
p
p
p
Solution
40
P- CONTROL CHART
41
C-CHART EXAMPLE THE NUMBER OF WEEKLY CUSTOMER COMPLAINTS ARE MONITORED IN A LARGE HOTEL USING A C-CHART DEVELOP THREE SIGMA CONTROL LIMITS USING THE DATA TABLE BELOW
Week Number of Complaints
1 3
2 2
3 3
4 1
5 3
6 3
7 2
8 1
9 3
10 1
Total 22
022522322ccLCL
66522322ccUCL
2210
22
samples of
complaintsc
c
c
z
z
Solution
42
C- CONTROL CHART
43
The ability of a process to meet product designtechnical specifications
Assessing capability involves evaluating process variability relative to preset product or service specifications
Process Capability ndash Cp and Cpk
Cp assumes that the process is centered in the specification range
Cpk helps to address a possible lack of centering of the process
PROCESS CAPABILITY
6σ
LSLUSL
width process
width ionspecificatCp
3σ
LSLμ
3σ
μUSLminCpk
44
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
45
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
46
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
47
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
--and an individual part is measured at 520rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
48
GRAPHING THE TOLERANCE AND MEASUREMENTS
Suppose we made and measured several more
units and they were all EXACTLY the same
We wouldnrsquot have very many part problems
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
X
X
X
49
GRAPHING THE TOLERANCE AND MEASUREMENTS
In the real world units are NOT EXACTLY the same
Everything VARIES
The question isnrsquot IF units vary
Itrsquos how much when and why
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
XX
XXX
XXXXX
XXXXXXX
50
The ldquonormal bell curverdquo
Widths heights depths thicknesses weights speeds strengths
and many other types of measurements when charted as a
histogram often form the shape of a bell
A ldquoperfect bellrdquo like a ldquoperfect circlerdquo doesnrsquot occur in nature but
many processes are close enough to make the bell curve useful
(A number of common industrial measurements such as flatness and straightness do NOT tend to distribute in a bell shape their proper statistical analysis is performed using models other than the bell curve)
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
51
What is a ldquostandard deviationrdquo
If we measure the DISTANCE from the CENTER of the bell
to each individual measurement that makes up the bell curve
we can find a TYPICAL DISTANCE
The most commonly used statistic to estimate this distance is the
Standard Deviation (also called ldquoSigmardquo)
Because of the natural shape of the bell curve the area of +1 to ndash1
standard deviations includes about 68 of the curve
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
Typical distance
from the center +1
standard deviation
Typical distance
from the center -1
standard deviation
52
How much of the curve is included in how many standard
deviations
From ndash1 to +1 is about 68 of the bell curve
From ndash2 to +2 is about 95
From ndash3 to +3 is about 9973
From ndash4 to +4 is about 9999
(NOTE We usually show the bell from ndash3 to +3 to make it easier to draw but in concept the ldquotailsrdquo of the bell get very thin and go on forever)
-6 -5 -4 -3 -2 -1 +1 +2 +3 +4 +5 +6 0
53
A
B
What is Cpk It is a measure of how well a process is within a specification
Cpk = A divided by B
A = Distance from process mean to closest spec limit
B = 3 Standard Deviations (also called ldquo3 Sigmardquo)
A bigger Cpk is better because fewer units will be beyond spec
(A bigger ldquoArdquo and a smaller ldquoBrdquo are better)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
54
A
B
ldquoProcess Capabilityrdquo is the ability of a process
to fit its output within the tolerances
hellipa LARGER ldquoArdquo
hellipand a SMALLER ldquoBrdquo
hellipmeans BETTER ldquoProcess Capabilityrdquo
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
55
A
B
An Analogy
Analogy
The bell curve is your automobile
The spec limits are the edges of your garage door
If A = B you are hitting the frame of your garage door with your car
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
56
A
B
How can we make Cpk (A divided by B) better
1 Design the product so a wider tolerance is functional (ldquorobust designrdquo)
2 Choose equipment and methods for a good safety margin (ldquoprocess capabilityrdquo)
3 Correctly adjust but only when needed (ldquocontrolrdquo)
4 Discover ways to narrow the natural variation (ldquoimprovementrdquo)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
57
A
B
What does a very good Cpk do for us
This process is producing good units with a good safety margin
Note that when Cpk = 2 our process mean is 6 standard deviations from
the nearest spec so we say it has ldquo6 Sigma Capabilityrdquo
Specification
Limit
Specification
Limit
This Cpk is
about 2
Very good
Mean
58
A
B
What does a problem Cpk look like
This process is in danger of producing some defects
It is too close to the specification limits
(Remember the bell curve tail goes further than Bhellip hellipwe only show the bell to 3-sigma to make it easier to draw)
Specification
Limit
Specification
Limit
This Cpk is just
slightly greater
than 1 Not good
59
A
B
What does a very bad Cpk look like
A significant part of the ldquotailrdquo is hanging out beyond the spec limits
This process is producing scrap rework and customer rejects
Notice that if distance ldquoArdquo approaches zerohellip
hellipthe Cpk would approach zero andhellip
hellipthe process would become 50 defective
Specification
Limit
Specification
Limit
This Cpk is less
than 1 We desire
a minimum of 133
and ultimately we
want 2 or more
60
-
Q amp A
61
MEASUREMENT SYSTEM ANALYSIS (MSA)
An MSA is a statistical tool used to determine if a measurement system is capable of precise measurement
What is It
Objective or Purpose
bull To determine how much error is in the measurement due to the measurement process itself
bull Quantifies the variability added by the measurement system
bull Applicable to attribute data and variable data
When to Use It
bull On the critical inputs and outputs prior to collecting data for analysis
bull For any new or modified process in order to ensure the quality of the data
Measurement System Analysis is an analysis of the measurement process not an analysis of the people
IMPORTANT
Who Should be Involved
Everyone that measures and makes decisions about these measurements should be involved in the MSA
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The observed variation in process output measurements is not simply the variation in the process itself it is the variation in the process plus the variation in measurement that results from an inadequate measurement system
Conducting an MSA reduces the likelihood of passing a bad part or rejecting a good part
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The output of the process measured by bull Cycle time bull Dimensional data bull Number of defects and others
Observed Variation
Process Variation
Measurement System
Variation
Reproducibility
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Accuracy (Central Location)
OBSERVED VARIATION
Calibration addresses accuracy
Measurement System Analysis (MSA)
MEASUREMENT SYSTEM ERRORS
Accuracy difference between the observed measurement and the actual measurement
Precision variation that occurs when measuring the same part with the same instrument
MEASUREMENT SYSTEM ERROR
Precise but not
accurate
Accurate but not
precise
Not accurate or
precise
Accurate and
precise
ACCURACY OF MEASUREMENT
Broken down into three components
aStability
The consistency of measurements over time
bBias
A measure of the amount of partiality in the system
cLinearity
A measure of the bias values through the expected
range of measurements
OBSERVED VARIATION
Observed Variation
Process Variation
Measurement System
Variation
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Reproducibility
Accuracy (Central Location)
Calibration Addresses Accuracy
Letrsquos take a closer look at Precision
Measurement System Analysis (MSA)
Measurement System Analysis (MSA)
Error in Resolution The inability to detect small changes
Possible Cause
Wrong measurement device selected - divisions on scale not fine enough to detect changes
Resolution
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Repeatability The inability to get the same answer from repeated measurements made of the same item under absolutely identical conditions
Possible Cause
Lack of standard operating procedures (SOP) lack of training measuring system variablilty
Repeatability
Equipment Variation
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Reproducibility The inability to get the same answer from repeated measurements made under various conditions from different inspectors
Possible Cause
Lack of SOP lack of training
Reproducibility
Appraiser Variation
VARIABLE MSA ndash GAGE RampR STUDY
bull Gage RampR is the combined estimate of
measurement system Repeatability and
Reproducibility
bull Typically a 3-person study is performed Each person randomly measures 10 marked parts per trial
Each person can perform up to 3 trials
bull There are 3 key indicators EV or Equipment Variation
AV or Appraiser Variation
Overall GRR
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
CONTROL CHART - PURPOSE
The main purpose of using a control chart is to monitor control and improve
process performance over time by studying variation and its source There are
several functions of a control chart
It centres attention on detecting and monitoring process variation over time
It provides a tool for on-going control of a process
It differentiates special from common causes of variation in order to be a guide for
local or management action
It helps improve a process to perform consistently and predictably to achieve higher
quality lower cost and higher effective capacity
It serves as a common language for discussing process performance
26
TYPES OF CONTROL CHARTS
The basic tool used in SPC is the control chart
There are various types of control charts
Variable Control Chart
Averages and range chart (X-Bar and R Bar Chart)
X bar and s chart
Moving Range Chart
Moving AveragendashMoving Range chart (also called MAndashMR chart)
p chart (also called proportion chart)
c chart (also called count chart)
np chart
u chart
27
POPULARITY OF CONTROL CHARTS
Control charts are a proven technique for improving productivity
Control charts are effective in defect prevention
Control charts prevent unnecessary process
adjustment
Control charts provide diagnostic information
Control charts provide information about process
capability
28
PROCEDURE FOR X ndashBAR AND R BAR CHART
1 Randomly sample ldquonrdquo units throughout the day (can be every 5
minutes every 30 minutes etc - whatever is appropriate for your
case)
2 For each sample calculate ldquoX-BARrdquo to estimate the mean and ldquoR
(range)rdquo to estimate variability NOTE THE RANGE CAN BE USED TO
ESTIMATE THE STANDARD DEVIATION
3 After collecting the 20-25 samples calculate X-BAR-BAR (the
average of all the X-BARs) and R-BAR (the average of all the ranges)
4 Using X-BAR-BAR and R-BAR calculate the control limits for your X-
BAR and R Control Charts
29
X-BAR CONTROL LIMITS
Upper Control Limit (UCL) = (X-BAR-BAR) + A2 (R-BAR)
Lower Control Limit(LCL) = (X-BAR-BAR) - A2 (R-BAR)
R CONTROL LIMITS
Upper Control Limit - D3 (R-BAR)
Lower Control Limit - D4 (R-BAR)
PROCEDURE FOR X ndashBAR AND R BAR CHART
30
CONTROL CHART CONSTANTS
sample size constant constant constant constant constant constant constant
n d2 A2 A3 B3 B4 D3 D4
2 1128 188 2659 0 3267 0 3267
3 1693 1023 1954 0 2568 0 2574
4 2059 0729 1628 0 2266 0 2282
5 2326 0577 1427 0 2089 0 2114
6 2534 0483 1287 003 197 0 2004
7 2704 0419 1182 0118 1882 0076 1924
8 2847 0373 1099 0185 1815 0136 1864
9 297 0337 1032 0239 1761 0184 1816
10 3078 0308 0975 0284 1716 0223 1777
31
5 For the R Control Chart plot all R values on the R Control Chart
to see if all the Ranges are ldquobetween the control limitsrdquo If they are
then your process is considered to be in a state of statistical control
(as far as the variability of the process is concerned)
6 For the X-BAR Control Chart plot all the X-BARs on the X-BAR
control chart to see if all the X-BARs are ldquobetween the control
limitsrdquo If they are then your process is considered in a state of
statistical control (as far as the average of the process is
concerned)
PROCEDURE FOR X ndashBAR AND R BAR CHART
32
SAMPLE DATA FOR X BAR ndashR CHART
Sub Group 1 2 3 4 5 X -Bar Range reg
1 1195 1191 1211 1203 1198 1200 02
2 1201 1198 1198 1197 12 1199 004
3 1193 1206 1198 1196 1202 1199 013
4 1205 1198 1205 1206 1198 1202 008
5 1198 1203 1206 1201 1199 1201 008
6 1202 1205 1196 1201 1195 1200 01
7 1199 1206 1201 1204 1201 1202 007
8 1201 1197 1198 1204 1198 1200 007
9 1198 1204 1198 1204 1204 1202 006
10 1205 1195 1198 1204 1196 1200 01
` X Bar-Bar 1200 009
X Bar Chart
UCL = X BAR-BAR + A2 R Bar
1200 +(0577009) 1205
LCL= X BAR-BAR - A2 R Bar
1200 - (0577009) 1195
R Chart
UCL = D4R Bar 211 009 021
LCL = D3 R Bar 0009 0
33
PLOT DATA ON CONTROL CHARTS
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1 2 3 4 5 6 7 8 9 10
Ave
rage
(X
ba
r)
X Bar Chart
UCL
LCL
X Bar
34
PLOT DATA ON CONTROL CHARTS
001
003
005
007
009
011
013
015
017
019
021
023
025
1 2 3 4 5 6 7 8 9 10
R Chart
UCL
LCL
35
PROCEDURE TO DETERMINE IF PROCESS IS IN A STATE OF
STATISTICAL CONTROL
7 If process is determined to be ldquoNOT STABLErdquo then stop and find out what
an assignable cause might be fix and then repeat the complete process of
collecting new data
8 If the process is determined to be ldquoSTABLErdquo then you may use the
control charts you developed to monitor future production to ensure that the
process REMAINS stable
More Samples for Control charts
36
READING OF CONTROL CHART
Control charts can determine whether a process is behaving in an unusual way The quality of the individual points of a subset is determined unstable if any of the
following occurs
Rule 1 Any point falls beyond 3σ from the centreline(this is represented by the upper and
lower control limits)
Rule 2 Two out of three consecutive points fall beyond 2σ on the same side of the
centreline
Rule 3 Four out of five consecutive points fall beyond 1σ on the same side of the
centreline
Rule 4 Nine or more consecutive points fall on the same side of the centreline
(Ref Next page for sample)
37
READING THE CONTROL CHART
38
CONTROL CHARTS FOR ATTRIBUTES ndashP-CHARTS amp C-CHARTS
Attributes are discrete events yesno or passfail
Use P-Charts for quality characteristics that are discrete and involve yesno or goodbad decisions
Eg
Number of leaking caulking tubes in a box of 48
Number of broken eggs in a carton
Use C-Charts for discrete defects when there can be more than one defect per unit
Eg
Number of stains in a carpet sample cut from a production run
Number of complaints per customer at a hotel
39
P-CHART EXAMPLE A PRODUCTION MANAGER FOR A TIRE COMPANY HAS INSPECTED THE NUMBER OF
DEFECTIVE TIRES IN FIVE RANDOM SAMPLES WITH 20 TIRES IN EACH SAMPLE THE TABLE BELOW SHOWS THE
NUMBER OF DEFECTIVE TIRES IN EACH SAMPLE OF 20 TIRES CALCULATE THE CONTROL LIMITS
Sample Number of
Defective Tires
Number of Tires in each
Sample
Proportion Defective
1 3 20 15
2 2 20 10
3 1 20 05
4 2 20 10
5 2 20 05
Total 9 100 09
01023(064)09σzpLCL
2823(064)09σzpUCL
06420
(09)(91)
n
)p(1pσ
09100
9
Inspected Total
DefectivespCL
p
p
p
Solution
40
P- CONTROL CHART
41
C-CHART EXAMPLE THE NUMBER OF WEEKLY CUSTOMER COMPLAINTS ARE MONITORED IN A LARGE HOTEL USING A C-CHART DEVELOP THREE SIGMA CONTROL LIMITS USING THE DATA TABLE BELOW
Week Number of Complaints
1 3
2 2
3 3
4 1
5 3
6 3
7 2
8 1
9 3
10 1
Total 22
022522322ccLCL
66522322ccUCL
2210
22
samples of
complaintsc
c
c
z
z
Solution
42
C- CONTROL CHART
43
The ability of a process to meet product designtechnical specifications
Assessing capability involves evaluating process variability relative to preset product or service specifications
Process Capability ndash Cp and Cpk
Cp assumes that the process is centered in the specification range
Cpk helps to address a possible lack of centering of the process
PROCESS CAPABILITY
6σ
LSLUSL
width process
width ionspecificatCp
3σ
LSLμ
3σ
μUSLminCpk
44
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
45
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
46
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
47
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
--and an individual part is measured at 520rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
48
GRAPHING THE TOLERANCE AND MEASUREMENTS
Suppose we made and measured several more
units and they were all EXACTLY the same
We wouldnrsquot have very many part problems
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
X
X
X
49
GRAPHING THE TOLERANCE AND MEASUREMENTS
In the real world units are NOT EXACTLY the same
Everything VARIES
The question isnrsquot IF units vary
Itrsquos how much when and why
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
XX
XXX
XXXXX
XXXXXXX
50
The ldquonormal bell curverdquo
Widths heights depths thicknesses weights speeds strengths
and many other types of measurements when charted as a
histogram often form the shape of a bell
A ldquoperfect bellrdquo like a ldquoperfect circlerdquo doesnrsquot occur in nature but
many processes are close enough to make the bell curve useful
(A number of common industrial measurements such as flatness and straightness do NOT tend to distribute in a bell shape their proper statistical analysis is performed using models other than the bell curve)
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
51
What is a ldquostandard deviationrdquo
If we measure the DISTANCE from the CENTER of the bell
to each individual measurement that makes up the bell curve
we can find a TYPICAL DISTANCE
The most commonly used statistic to estimate this distance is the
Standard Deviation (also called ldquoSigmardquo)
Because of the natural shape of the bell curve the area of +1 to ndash1
standard deviations includes about 68 of the curve
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
Typical distance
from the center +1
standard deviation
Typical distance
from the center -1
standard deviation
52
How much of the curve is included in how many standard
deviations
From ndash1 to +1 is about 68 of the bell curve
From ndash2 to +2 is about 95
From ndash3 to +3 is about 9973
From ndash4 to +4 is about 9999
(NOTE We usually show the bell from ndash3 to +3 to make it easier to draw but in concept the ldquotailsrdquo of the bell get very thin and go on forever)
-6 -5 -4 -3 -2 -1 +1 +2 +3 +4 +5 +6 0
53
A
B
What is Cpk It is a measure of how well a process is within a specification
Cpk = A divided by B
A = Distance from process mean to closest spec limit
B = 3 Standard Deviations (also called ldquo3 Sigmardquo)
A bigger Cpk is better because fewer units will be beyond spec
(A bigger ldquoArdquo and a smaller ldquoBrdquo are better)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
54
A
B
ldquoProcess Capabilityrdquo is the ability of a process
to fit its output within the tolerances
hellipa LARGER ldquoArdquo
hellipand a SMALLER ldquoBrdquo
hellipmeans BETTER ldquoProcess Capabilityrdquo
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
55
A
B
An Analogy
Analogy
The bell curve is your automobile
The spec limits are the edges of your garage door
If A = B you are hitting the frame of your garage door with your car
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
56
A
B
How can we make Cpk (A divided by B) better
1 Design the product so a wider tolerance is functional (ldquorobust designrdquo)
2 Choose equipment and methods for a good safety margin (ldquoprocess capabilityrdquo)
3 Correctly adjust but only when needed (ldquocontrolrdquo)
4 Discover ways to narrow the natural variation (ldquoimprovementrdquo)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
57
A
B
What does a very good Cpk do for us
This process is producing good units with a good safety margin
Note that when Cpk = 2 our process mean is 6 standard deviations from
the nearest spec so we say it has ldquo6 Sigma Capabilityrdquo
Specification
Limit
Specification
Limit
This Cpk is
about 2
Very good
Mean
58
A
B
What does a problem Cpk look like
This process is in danger of producing some defects
It is too close to the specification limits
(Remember the bell curve tail goes further than Bhellip hellipwe only show the bell to 3-sigma to make it easier to draw)
Specification
Limit
Specification
Limit
This Cpk is just
slightly greater
than 1 Not good
59
A
B
What does a very bad Cpk look like
A significant part of the ldquotailrdquo is hanging out beyond the spec limits
This process is producing scrap rework and customer rejects
Notice that if distance ldquoArdquo approaches zerohellip
hellipthe Cpk would approach zero andhellip
hellipthe process would become 50 defective
Specification
Limit
Specification
Limit
This Cpk is less
than 1 We desire
a minimum of 133
and ultimately we
want 2 or more
60
-
Q amp A
61
MEASUREMENT SYSTEM ANALYSIS (MSA)
An MSA is a statistical tool used to determine if a measurement system is capable of precise measurement
What is It
Objective or Purpose
bull To determine how much error is in the measurement due to the measurement process itself
bull Quantifies the variability added by the measurement system
bull Applicable to attribute data and variable data
When to Use It
bull On the critical inputs and outputs prior to collecting data for analysis
bull For any new or modified process in order to ensure the quality of the data
Measurement System Analysis is an analysis of the measurement process not an analysis of the people
IMPORTANT
Who Should be Involved
Everyone that measures and makes decisions about these measurements should be involved in the MSA
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The observed variation in process output measurements is not simply the variation in the process itself it is the variation in the process plus the variation in measurement that results from an inadequate measurement system
Conducting an MSA reduces the likelihood of passing a bad part or rejecting a good part
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The output of the process measured by bull Cycle time bull Dimensional data bull Number of defects and others
Observed Variation
Process Variation
Measurement System
Variation
Reproducibility
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Accuracy (Central Location)
OBSERVED VARIATION
Calibration addresses accuracy
Measurement System Analysis (MSA)
MEASUREMENT SYSTEM ERRORS
Accuracy difference between the observed measurement and the actual measurement
Precision variation that occurs when measuring the same part with the same instrument
MEASUREMENT SYSTEM ERROR
Precise but not
accurate
Accurate but not
precise
Not accurate or
precise
Accurate and
precise
ACCURACY OF MEASUREMENT
Broken down into three components
aStability
The consistency of measurements over time
bBias
A measure of the amount of partiality in the system
cLinearity
A measure of the bias values through the expected
range of measurements
OBSERVED VARIATION
Observed Variation
Process Variation
Measurement System
Variation
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Reproducibility
Accuracy (Central Location)
Calibration Addresses Accuracy
Letrsquos take a closer look at Precision
Measurement System Analysis (MSA)
Measurement System Analysis (MSA)
Error in Resolution The inability to detect small changes
Possible Cause
Wrong measurement device selected - divisions on scale not fine enough to detect changes
Resolution
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Repeatability The inability to get the same answer from repeated measurements made of the same item under absolutely identical conditions
Possible Cause
Lack of standard operating procedures (SOP) lack of training measuring system variablilty
Repeatability
Equipment Variation
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Reproducibility The inability to get the same answer from repeated measurements made under various conditions from different inspectors
Possible Cause
Lack of SOP lack of training
Reproducibility
Appraiser Variation
VARIABLE MSA ndash GAGE RampR STUDY
bull Gage RampR is the combined estimate of
measurement system Repeatability and
Reproducibility
bull Typically a 3-person study is performed Each person randomly measures 10 marked parts per trial
Each person can perform up to 3 trials
bull There are 3 key indicators EV or Equipment Variation
AV or Appraiser Variation
Overall GRR
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
TYPES OF CONTROL CHARTS
The basic tool used in SPC is the control chart
There are various types of control charts
Variable Control Chart
Averages and range chart (X-Bar and R Bar Chart)
X bar and s chart
Moving Range Chart
Moving AveragendashMoving Range chart (also called MAndashMR chart)
p chart (also called proportion chart)
c chart (also called count chart)
np chart
u chart
27
POPULARITY OF CONTROL CHARTS
Control charts are a proven technique for improving productivity
Control charts are effective in defect prevention
Control charts prevent unnecessary process
adjustment
Control charts provide diagnostic information
Control charts provide information about process
capability
28
PROCEDURE FOR X ndashBAR AND R BAR CHART
1 Randomly sample ldquonrdquo units throughout the day (can be every 5
minutes every 30 minutes etc - whatever is appropriate for your
case)
2 For each sample calculate ldquoX-BARrdquo to estimate the mean and ldquoR
(range)rdquo to estimate variability NOTE THE RANGE CAN BE USED TO
ESTIMATE THE STANDARD DEVIATION
3 After collecting the 20-25 samples calculate X-BAR-BAR (the
average of all the X-BARs) and R-BAR (the average of all the ranges)
4 Using X-BAR-BAR and R-BAR calculate the control limits for your X-
BAR and R Control Charts
29
X-BAR CONTROL LIMITS
Upper Control Limit (UCL) = (X-BAR-BAR) + A2 (R-BAR)
Lower Control Limit(LCL) = (X-BAR-BAR) - A2 (R-BAR)
R CONTROL LIMITS
Upper Control Limit - D3 (R-BAR)
Lower Control Limit - D4 (R-BAR)
PROCEDURE FOR X ndashBAR AND R BAR CHART
30
CONTROL CHART CONSTANTS
sample size constant constant constant constant constant constant constant
n d2 A2 A3 B3 B4 D3 D4
2 1128 188 2659 0 3267 0 3267
3 1693 1023 1954 0 2568 0 2574
4 2059 0729 1628 0 2266 0 2282
5 2326 0577 1427 0 2089 0 2114
6 2534 0483 1287 003 197 0 2004
7 2704 0419 1182 0118 1882 0076 1924
8 2847 0373 1099 0185 1815 0136 1864
9 297 0337 1032 0239 1761 0184 1816
10 3078 0308 0975 0284 1716 0223 1777
31
5 For the R Control Chart plot all R values on the R Control Chart
to see if all the Ranges are ldquobetween the control limitsrdquo If they are
then your process is considered to be in a state of statistical control
(as far as the variability of the process is concerned)
6 For the X-BAR Control Chart plot all the X-BARs on the X-BAR
control chart to see if all the X-BARs are ldquobetween the control
limitsrdquo If they are then your process is considered in a state of
statistical control (as far as the average of the process is
concerned)
PROCEDURE FOR X ndashBAR AND R BAR CHART
32
SAMPLE DATA FOR X BAR ndashR CHART
Sub Group 1 2 3 4 5 X -Bar Range reg
1 1195 1191 1211 1203 1198 1200 02
2 1201 1198 1198 1197 12 1199 004
3 1193 1206 1198 1196 1202 1199 013
4 1205 1198 1205 1206 1198 1202 008
5 1198 1203 1206 1201 1199 1201 008
6 1202 1205 1196 1201 1195 1200 01
7 1199 1206 1201 1204 1201 1202 007
8 1201 1197 1198 1204 1198 1200 007
9 1198 1204 1198 1204 1204 1202 006
10 1205 1195 1198 1204 1196 1200 01
` X Bar-Bar 1200 009
X Bar Chart
UCL = X BAR-BAR + A2 R Bar
1200 +(0577009) 1205
LCL= X BAR-BAR - A2 R Bar
1200 - (0577009) 1195
R Chart
UCL = D4R Bar 211 009 021
LCL = D3 R Bar 0009 0
33
PLOT DATA ON CONTROL CHARTS
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1 2 3 4 5 6 7 8 9 10
Ave
rage
(X
ba
r)
X Bar Chart
UCL
LCL
X Bar
34
PLOT DATA ON CONTROL CHARTS
001
003
005
007
009
011
013
015
017
019
021
023
025
1 2 3 4 5 6 7 8 9 10
R Chart
UCL
LCL
35
PROCEDURE TO DETERMINE IF PROCESS IS IN A STATE OF
STATISTICAL CONTROL
7 If process is determined to be ldquoNOT STABLErdquo then stop and find out what
an assignable cause might be fix and then repeat the complete process of
collecting new data
8 If the process is determined to be ldquoSTABLErdquo then you may use the
control charts you developed to monitor future production to ensure that the
process REMAINS stable
More Samples for Control charts
36
READING OF CONTROL CHART
Control charts can determine whether a process is behaving in an unusual way The quality of the individual points of a subset is determined unstable if any of the
following occurs
Rule 1 Any point falls beyond 3σ from the centreline(this is represented by the upper and
lower control limits)
Rule 2 Two out of three consecutive points fall beyond 2σ on the same side of the
centreline
Rule 3 Four out of five consecutive points fall beyond 1σ on the same side of the
centreline
Rule 4 Nine or more consecutive points fall on the same side of the centreline
(Ref Next page for sample)
37
READING THE CONTROL CHART
38
CONTROL CHARTS FOR ATTRIBUTES ndashP-CHARTS amp C-CHARTS
Attributes are discrete events yesno or passfail
Use P-Charts for quality characteristics that are discrete and involve yesno or goodbad decisions
Eg
Number of leaking caulking tubes in a box of 48
Number of broken eggs in a carton
Use C-Charts for discrete defects when there can be more than one defect per unit
Eg
Number of stains in a carpet sample cut from a production run
Number of complaints per customer at a hotel
39
P-CHART EXAMPLE A PRODUCTION MANAGER FOR A TIRE COMPANY HAS INSPECTED THE NUMBER OF
DEFECTIVE TIRES IN FIVE RANDOM SAMPLES WITH 20 TIRES IN EACH SAMPLE THE TABLE BELOW SHOWS THE
NUMBER OF DEFECTIVE TIRES IN EACH SAMPLE OF 20 TIRES CALCULATE THE CONTROL LIMITS
Sample Number of
Defective Tires
Number of Tires in each
Sample
Proportion Defective
1 3 20 15
2 2 20 10
3 1 20 05
4 2 20 10
5 2 20 05
Total 9 100 09
01023(064)09σzpLCL
2823(064)09σzpUCL
06420
(09)(91)
n
)p(1pσ
09100
9
Inspected Total
DefectivespCL
p
p
p
Solution
40
P- CONTROL CHART
41
C-CHART EXAMPLE THE NUMBER OF WEEKLY CUSTOMER COMPLAINTS ARE MONITORED IN A LARGE HOTEL USING A C-CHART DEVELOP THREE SIGMA CONTROL LIMITS USING THE DATA TABLE BELOW
Week Number of Complaints
1 3
2 2
3 3
4 1
5 3
6 3
7 2
8 1
9 3
10 1
Total 22
022522322ccLCL
66522322ccUCL
2210
22
samples of
complaintsc
c
c
z
z
Solution
42
C- CONTROL CHART
43
The ability of a process to meet product designtechnical specifications
Assessing capability involves evaluating process variability relative to preset product or service specifications
Process Capability ndash Cp and Cpk
Cp assumes that the process is centered in the specification range
Cpk helps to address a possible lack of centering of the process
PROCESS CAPABILITY
6σ
LSLUSL
width process
width ionspecificatCp
3σ
LSLμ
3σ
μUSLminCpk
44
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
45
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
46
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
47
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
--and an individual part is measured at 520rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
48
GRAPHING THE TOLERANCE AND MEASUREMENTS
Suppose we made and measured several more
units and they were all EXACTLY the same
We wouldnrsquot have very many part problems
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
X
X
X
49
GRAPHING THE TOLERANCE AND MEASUREMENTS
In the real world units are NOT EXACTLY the same
Everything VARIES
The question isnrsquot IF units vary
Itrsquos how much when and why
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
XX
XXX
XXXXX
XXXXXXX
50
The ldquonormal bell curverdquo
Widths heights depths thicknesses weights speeds strengths
and many other types of measurements when charted as a
histogram often form the shape of a bell
A ldquoperfect bellrdquo like a ldquoperfect circlerdquo doesnrsquot occur in nature but
many processes are close enough to make the bell curve useful
(A number of common industrial measurements such as flatness and straightness do NOT tend to distribute in a bell shape their proper statistical analysis is performed using models other than the bell curve)
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
51
What is a ldquostandard deviationrdquo
If we measure the DISTANCE from the CENTER of the bell
to each individual measurement that makes up the bell curve
we can find a TYPICAL DISTANCE
The most commonly used statistic to estimate this distance is the
Standard Deviation (also called ldquoSigmardquo)
Because of the natural shape of the bell curve the area of +1 to ndash1
standard deviations includes about 68 of the curve
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
Typical distance
from the center +1
standard deviation
Typical distance
from the center -1
standard deviation
52
How much of the curve is included in how many standard
deviations
From ndash1 to +1 is about 68 of the bell curve
From ndash2 to +2 is about 95
From ndash3 to +3 is about 9973
From ndash4 to +4 is about 9999
(NOTE We usually show the bell from ndash3 to +3 to make it easier to draw but in concept the ldquotailsrdquo of the bell get very thin and go on forever)
-6 -5 -4 -3 -2 -1 +1 +2 +3 +4 +5 +6 0
53
A
B
What is Cpk It is a measure of how well a process is within a specification
Cpk = A divided by B
A = Distance from process mean to closest spec limit
B = 3 Standard Deviations (also called ldquo3 Sigmardquo)
A bigger Cpk is better because fewer units will be beyond spec
(A bigger ldquoArdquo and a smaller ldquoBrdquo are better)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
54
A
B
ldquoProcess Capabilityrdquo is the ability of a process
to fit its output within the tolerances
hellipa LARGER ldquoArdquo
hellipand a SMALLER ldquoBrdquo
hellipmeans BETTER ldquoProcess Capabilityrdquo
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
55
A
B
An Analogy
Analogy
The bell curve is your automobile
The spec limits are the edges of your garage door
If A = B you are hitting the frame of your garage door with your car
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
56
A
B
How can we make Cpk (A divided by B) better
1 Design the product so a wider tolerance is functional (ldquorobust designrdquo)
2 Choose equipment and methods for a good safety margin (ldquoprocess capabilityrdquo)
3 Correctly adjust but only when needed (ldquocontrolrdquo)
4 Discover ways to narrow the natural variation (ldquoimprovementrdquo)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
57
A
B
What does a very good Cpk do for us
This process is producing good units with a good safety margin
Note that when Cpk = 2 our process mean is 6 standard deviations from
the nearest spec so we say it has ldquo6 Sigma Capabilityrdquo
Specification
Limit
Specification
Limit
This Cpk is
about 2
Very good
Mean
58
A
B
What does a problem Cpk look like
This process is in danger of producing some defects
It is too close to the specification limits
(Remember the bell curve tail goes further than Bhellip hellipwe only show the bell to 3-sigma to make it easier to draw)
Specification
Limit
Specification
Limit
This Cpk is just
slightly greater
than 1 Not good
59
A
B
What does a very bad Cpk look like
A significant part of the ldquotailrdquo is hanging out beyond the spec limits
This process is producing scrap rework and customer rejects
Notice that if distance ldquoArdquo approaches zerohellip
hellipthe Cpk would approach zero andhellip
hellipthe process would become 50 defective
Specification
Limit
Specification
Limit
This Cpk is less
than 1 We desire
a minimum of 133
and ultimately we
want 2 or more
60
-
Q amp A
61
MEASUREMENT SYSTEM ANALYSIS (MSA)
An MSA is a statistical tool used to determine if a measurement system is capable of precise measurement
What is It
Objective or Purpose
bull To determine how much error is in the measurement due to the measurement process itself
bull Quantifies the variability added by the measurement system
bull Applicable to attribute data and variable data
When to Use It
bull On the critical inputs and outputs prior to collecting data for analysis
bull For any new or modified process in order to ensure the quality of the data
Measurement System Analysis is an analysis of the measurement process not an analysis of the people
IMPORTANT
Who Should be Involved
Everyone that measures and makes decisions about these measurements should be involved in the MSA
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The observed variation in process output measurements is not simply the variation in the process itself it is the variation in the process plus the variation in measurement that results from an inadequate measurement system
Conducting an MSA reduces the likelihood of passing a bad part or rejecting a good part
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The output of the process measured by bull Cycle time bull Dimensional data bull Number of defects and others
Observed Variation
Process Variation
Measurement System
Variation
Reproducibility
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Accuracy (Central Location)
OBSERVED VARIATION
Calibration addresses accuracy
Measurement System Analysis (MSA)
MEASUREMENT SYSTEM ERRORS
Accuracy difference between the observed measurement and the actual measurement
Precision variation that occurs when measuring the same part with the same instrument
MEASUREMENT SYSTEM ERROR
Precise but not
accurate
Accurate but not
precise
Not accurate or
precise
Accurate and
precise
ACCURACY OF MEASUREMENT
Broken down into three components
aStability
The consistency of measurements over time
bBias
A measure of the amount of partiality in the system
cLinearity
A measure of the bias values through the expected
range of measurements
OBSERVED VARIATION
Observed Variation
Process Variation
Measurement System
Variation
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Reproducibility
Accuracy (Central Location)
Calibration Addresses Accuracy
Letrsquos take a closer look at Precision
Measurement System Analysis (MSA)
Measurement System Analysis (MSA)
Error in Resolution The inability to detect small changes
Possible Cause
Wrong measurement device selected - divisions on scale not fine enough to detect changes
Resolution
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Repeatability The inability to get the same answer from repeated measurements made of the same item under absolutely identical conditions
Possible Cause
Lack of standard operating procedures (SOP) lack of training measuring system variablilty
Repeatability
Equipment Variation
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Reproducibility The inability to get the same answer from repeated measurements made under various conditions from different inspectors
Possible Cause
Lack of SOP lack of training
Reproducibility
Appraiser Variation
VARIABLE MSA ndash GAGE RampR STUDY
bull Gage RampR is the combined estimate of
measurement system Repeatability and
Reproducibility
bull Typically a 3-person study is performed Each person randomly measures 10 marked parts per trial
Each person can perform up to 3 trials
bull There are 3 key indicators EV or Equipment Variation
AV or Appraiser Variation
Overall GRR
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
POPULARITY OF CONTROL CHARTS
Control charts are a proven technique for improving productivity
Control charts are effective in defect prevention
Control charts prevent unnecessary process
adjustment
Control charts provide diagnostic information
Control charts provide information about process
capability
28
PROCEDURE FOR X ndashBAR AND R BAR CHART
1 Randomly sample ldquonrdquo units throughout the day (can be every 5
minutes every 30 minutes etc - whatever is appropriate for your
case)
2 For each sample calculate ldquoX-BARrdquo to estimate the mean and ldquoR
(range)rdquo to estimate variability NOTE THE RANGE CAN BE USED TO
ESTIMATE THE STANDARD DEVIATION
3 After collecting the 20-25 samples calculate X-BAR-BAR (the
average of all the X-BARs) and R-BAR (the average of all the ranges)
4 Using X-BAR-BAR and R-BAR calculate the control limits for your X-
BAR and R Control Charts
29
X-BAR CONTROL LIMITS
Upper Control Limit (UCL) = (X-BAR-BAR) + A2 (R-BAR)
Lower Control Limit(LCL) = (X-BAR-BAR) - A2 (R-BAR)
R CONTROL LIMITS
Upper Control Limit - D3 (R-BAR)
Lower Control Limit - D4 (R-BAR)
PROCEDURE FOR X ndashBAR AND R BAR CHART
30
CONTROL CHART CONSTANTS
sample size constant constant constant constant constant constant constant
n d2 A2 A3 B3 B4 D3 D4
2 1128 188 2659 0 3267 0 3267
3 1693 1023 1954 0 2568 0 2574
4 2059 0729 1628 0 2266 0 2282
5 2326 0577 1427 0 2089 0 2114
6 2534 0483 1287 003 197 0 2004
7 2704 0419 1182 0118 1882 0076 1924
8 2847 0373 1099 0185 1815 0136 1864
9 297 0337 1032 0239 1761 0184 1816
10 3078 0308 0975 0284 1716 0223 1777
31
5 For the R Control Chart plot all R values on the R Control Chart
to see if all the Ranges are ldquobetween the control limitsrdquo If they are
then your process is considered to be in a state of statistical control
(as far as the variability of the process is concerned)
6 For the X-BAR Control Chart plot all the X-BARs on the X-BAR
control chart to see if all the X-BARs are ldquobetween the control
limitsrdquo If they are then your process is considered in a state of
statistical control (as far as the average of the process is
concerned)
PROCEDURE FOR X ndashBAR AND R BAR CHART
32
SAMPLE DATA FOR X BAR ndashR CHART
Sub Group 1 2 3 4 5 X -Bar Range reg
1 1195 1191 1211 1203 1198 1200 02
2 1201 1198 1198 1197 12 1199 004
3 1193 1206 1198 1196 1202 1199 013
4 1205 1198 1205 1206 1198 1202 008
5 1198 1203 1206 1201 1199 1201 008
6 1202 1205 1196 1201 1195 1200 01
7 1199 1206 1201 1204 1201 1202 007
8 1201 1197 1198 1204 1198 1200 007
9 1198 1204 1198 1204 1204 1202 006
10 1205 1195 1198 1204 1196 1200 01
` X Bar-Bar 1200 009
X Bar Chart
UCL = X BAR-BAR + A2 R Bar
1200 +(0577009) 1205
LCL= X BAR-BAR - A2 R Bar
1200 - (0577009) 1195
R Chart
UCL = D4R Bar 211 009 021
LCL = D3 R Bar 0009 0
33
PLOT DATA ON CONTROL CHARTS
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1 2 3 4 5 6 7 8 9 10
Ave
rage
(X
ba
r)
X Bar Chart
UCL
LCL
X Bar
34
PLOT DATA ON CONTROL CHARTS
001
003
005
007
009
011
013
015
017
019
021
023
025
1 2 3 4 5 6 7 8 9 10
R Chart
UCL
LCL
35
PROCEDURE TO DETERMINE IF PROCESS IS IN A STATE OF
STATISTICAL CONTROL
7 If process is determined to be ldquoNOT STABLErdquo then stop and find out what
an assignable cause might be fix and then repeat the complete process of
collecting new data
8 If the process is determined to be ldquoSTABLErdquo then you may use the
control charts you developed to monitor future production to ensure that the
process REMAINS stable
More Samples for Control charts
36
READING OF CONTROL CHART
Control charts can determine whether a process is behaving in an unusual way The quality of the individual points of a subset is determined unstable if any of the
following occurs
Rule 1 Any point falls beyond 3σ from the centreline(this is represented by the upper and
lower control limits)
Rule 2 Two out of three consecutive points fall beyond 2σ on the same side of the
centreline
Rule 3 Four out of five consecutive points fall beyond 1σ on the same side of the
centreline
Rule 4 Nine or more consecutive points fall on the same side of the centreline
(Ref Next page for sample)
37
READING THE CONTROL CHART
38
CONTROL CHARTS FOR ATTRIBUTES ndashP-CHARTS amp C-CHARTS
Attributes are discrete events yesno or passfail
Use P-Charts for quality characteristics that are discrete and involve yesno or goodbad decisions
Eg
Number of leaking caulking tubes in a box of 48
Number of broken eggs in a carton
Use C-Charts for discrete defects when there can be more than one defect per unit
Eg
Number of stains in a carpet sample cut from a production run
Number of complaints per customer at a hotel
39
P-CHART EXAMPLE A PRODUCTION MANAGER FOR A TIRE COMPANY HAS INSPECTED THE NUMBER OF
DEFECTIVE TIRES IN FIVE RANDOM SAMPLES WITH 20 TIRES IN EACH SAMPLE THE TABLE BELOW SHOWS THE
NUMBER OF DEFECTIVE TIRES IN EACH SAMPLE OF 20 TIRES CALCULATE THE CONTROL LIMITS
Sample Number of
Defective Tires
Number of Tires in each
Sample
Proportion Defective
1 3 20 15
2 2 20 10
3 1 20 05
4 2 20 10
5 2 20 05
Total 9 100 09
01023(064)09σzpLCL
2823(064)09σzpUCL
06420
(09)(91)
n
)p(1pσ
09100
9
Inspected Total
DefectivespCL
p
p
p
Solution
40
P- CONTROL CHART
41
C-CHART EXAMPLE THE NUMBER OF WEEKLY CUSTOMER COMPLAINTS ARE MONITORED IN A LARGE HOTEL USING A C-CHART DEVELOP THREE SIGMA CONTROL LIMITS USING THE DATA TABLE BELOW
Week Number of Complaints
1 3
2 2
3 3
4 1
5 3
6 3
7 2
8 1
9 3
10 1
Total 22
022522322ccLCL
66522322ccUCL
2210
22
samples of
complaintsc
c
c
z
z
Solution
42
C- CONTROL CHART
43
The ability of a process to meet product designtechnical specifications
Assessing capability involves evaluating process variability relative to preset product or service specifications
Process Capability ndash Cp and Cpk
Cp assumes that the process is centered in the specification range
Cpk helps to address a possible lack of centering of the process
PROCESS CAPABILITY
6σ
LSLUSL
width process
width ionspecificatCp
3σ
LSLμ
3σ
μUSLminCpk
44
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
45
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
46
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
47
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
--and an individual part is measured at 520rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
48
GRAPHING THE TOLERANCE AND MEASUREMENTS
Suppose we made and measured several more
units and they were all EXACTLY the same
We wouldnrsquot have very many part problems
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
X
X
X
49
GRAPHING THE TOLERANCE AND MEASUREMENTS
In the real world units are NOT EXACTLY the same
Everything VARIES
The question isnrsquot IF units vary
Itrsquos how much when and why
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
XX
XXX
XXXXX
XXXXXXX
50
The ldquonormal bell curverdquo
Widths heights depths thicknesses weights speeds strengths
and many other types of measurements when charted as a
histogram often form the shape of a bell
A ldquoperfect bellrdquo like a ldquoperfect circlerdquo doesnrsquot occur in nature but
many processes are close enough to make the bell curve useful
(A number of common industrial measurements such as flatness and straightness do NOT tend to distribute in a bell shape their proper statistical analysis is performed using models other than the bell curve)
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
51
What is a ldquostandard deviationrdquo
If we measure the DISTANCE from the CENTER of the bell
to each individual measurement that makes up the bell curve
we can find a TYPICAL DISTANCE
The most commonly used statistic to estimate this distance is the
Standard Deviation (also called ldquoSigmardquo)
Because of the natural shape of the bell curve the area of +1 to ndash1
standard deviations includes about 68 of the curve
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
Typical distance
from the center +1
standard deviation
Typical distance
from the center -1
standard deviation
52
How much of the curve is included in how many standard
deviations
From ndash1 to +1 is about 68 of the bell curve
From ndash2 to +2 is about 95
From ndash3 to +3 is about 9973
From ndash4 to +4 is about 9999
(NOTE We usually show the bell from ndash3 to +3 to make it easier to draw but in concept the ldquotailsrdquo of the bell get very thin and go on forever)
-6 -5 -4 -3 -2 -1 +1 +2 +3 +4 +5 +6 0
53
A
B
What is Cpk It is a measure of how well a process is within a specification
Cpk = A divided by B
A = Distance from process mean to closest spec limit
B = 3 Standard Deviations (also called ldquo3 Sigmardquo)
A bigger Cpk is better because fewer units will be beyond spec
(A bigger ldquoArdquo and a smaller ldquoBrdquo are better)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
54
A
B
ldquoProcess Capabilityrdquo is the ability of a process
to fit its output within the tolerances
hellipa LARGER ldquoArdquo
hellipand a SMALLER ldquoBrdquo
hellipmeans BETTER ldquoProcess Capabilityrdquo
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
55
A
B
An Analogy
Analogy
The bell curve is your automobile
The spec limits are the edges of your garage door
If A = B you are hitting the frame of your garage door with your car
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
56
A
B
How can we make Cpk (A divided by B) better
1 Design the product so a wider tolerance is functional (ldquorobust designrdquo)
2 Choose equipment and methods for a good safety margin (ldquoprocess capabilityrdquo)
3 Correctly adjust but only when needed (ldquocontrolrdquo)
4 Discover ways to narrow the natural variation (ldquoimprovementrdquo)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
57
A
B
What does a very good Cpk do for us
This process is producing good units with a good safety margin
Note that when Cpk = 2 our process mean is 6 standard deviations from
the nearest spec so we say it has ldquo6 Sigma Capabilityrdquo
Specification
Limit
Specification
Limit
This Cpk is
about 2
Very good
Mean
58
A
B
What does a problem Cpk look like
This process is in danger of producing some defects
It is too close to the specification limits
(Remember the bell curve tail goes further than Bhellip hellipwe only show the bell to 3-sigma to make it easier to draw)
Specification
Limit
Specification
Limit
This Cpk is just
slightly greater
than 1 Not good
59
A
B
What does a very bad Cpk look like
A significant part of the ldquotailrdquo is hanging out beyond the spec limits
This process is producing scrap rework and customer rejects
Notice that if distance ldquoArdquo approaches zerohellip
hellipthe Cpk would approach zero andhellip
hellipthe process would become 50 defective
Specification
Limit
Specification
Limit
This Cpk is less
than 1 We desire
a minimum of 133
and ultimately we
want 2 or more
60
-
Q amp A
61
MEASUREMENT SYSTEM ANALYSIS (MSA)
An MSA is a statistical tool used to determine if a measurement system is capable of precise measurement
What is It
Objective or Purpose
bull To determine how much error is in the measurement due to the measurement process itself
bull Quantifies the variability added by the measurement system
bull Applicable to attribute data and variable data
When to Use It
bull On the critical inputs and outputs prior to collecting data for analysis
bull For any new or modified process in order to ensure the quality of the data
Measurement System Analysis is an analysis of the measurement process not an analysis of the people
IMPORTANT
Who Should be Involved
Everyone that measures and makes decisions about these measurements should be involved in the MSA
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The observed variation in process output measurements is not simply the variation in the process itself it is the variation in the process plus the variation in measurement that results from an inadequate measurement system
Conducting an MSA reduces the likelihood of passing a bad part or rejecting a good part
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The output of the process measured by bull Cycle time bull Dimensional data bull Number of defects and others
Observed Variation
Process Variation
Measurement System
Variation
Reproducibility
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Accuracy (Central Location)
OBSERVED VARIATION
Calibration addresses accuracy
Measurement System Analysis (MSA)
MEASUREMENT SYSTEM ERRORS
Accuracy difference between the observed measurement and the actual measurement
Precision variation that occurs when measuring the same part with the same instrument
MEASUREMENT SYSTEM ERROR
Precise but not
accurate
Accurate but not
precise
Not accurate or
precise
Accurate and
precise
ACCURACY OF MEASUREMENT
Broken down into three components
aStability
The consistency of measurements over time
bBias
A measure of the amount of partiality in the system
cLinearity
A measure of the bias values through the expected
range of measurements
OBSERVED VARIATION
Observed Variation
Process Variation
Measurement System
Variation
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Reproducibility
Accuracy (Central Location)
Calibration Addresses Accuracy
Letrsquos take a closer look at Precision
Measurement System Analysis (MSA)
Measurement System Analysis (MSA)
Error in Resolution The inability to detect small changes
Possible Cause
Wrong measurement device selected - divisions on scale not fine enough to detect changes
Resolution
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Repeatability The inability to get the same answer from repeated measurements made of the same item under absolutely identical conditions
Possible Cause
Lack of standard operating procedures (SOP) lack of training measuring system variablilty
Repeatability
Equipment Variation
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Reproducibility The inability to get the same answer from repeated measurements made under various conditions from different inspectors
Possible Cause
Lack of SOP lack of training
Reproducibility
Appraiser Variation
VARIABLE MSA ndash GAGE RampR STUDY
bull Gage RampR is the combined estimate of
measurement system Repeatability and
Reproducibility
bull Typically a 3-person study is performed Each person randomly measures 10 marked parts per trial
Each person can perform up to 3 trials
bull There are 3 key indicators EV or Equipment Variation
AV or Appraiser Variation
Overall GRR
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
PROCEDURE FOR X ndashBAR AND R BAR CHART
1 Randomly sample ldquonrdquo units throughout the day (can be every 5
minutes every 30 minutes etc - whatever is appropriate for your
case)
2 For each sample calculate ldquoX-BARrdquo to estimate the mean and ldquoR
(range)rdquo to estimate variability NOTE THE RANGE CAN BE USED TO
ESTIMATE THE STANDARD DEVIATION
3 After collecting the 20-25 samples calculate X-BAR-BAR (the
average of all the X-BARs) and R-BAR (the average of all the ranges)
4 Using X-BAR-BAR and R-BAR calculate the control limits for your X-
BAR and R Control Charts
29
X-BAR CONTROL LIMITS
Upper Control Limit (UCL) = (X-BAR-BAR) + A2 (R-BAR)
Lower Control Limit(LCL) = (X-BAR-BAR) - A2 (R-BAR)
R CONTROL LIMITS
Upper Control Limit - D3 (R-BAR)
Lower Control Limit - D4 (R-BAR)
PROCEDURE FOR X ndashBAR AND R BAR CHART
30
CONTROL CHART CONSTANTS
sample size constant constant constant constant constant constant constant
n d2 A2 A3 B3 B4 D3 D4
2 1128 188 2659 0 3267 0 3267
3 1693 1023 1954 0 2568 0 2574
4 2059 0729 1628 0 2266 0 2282
5 2326 0577 1427 0 2089 0 2114
6 2534 0483 1287 003 197 0 2004
7 2704 0419 1182 0118 1882 0076 1924
8 2847 0373 1099 0185 1815 0136 1864
9 297 0337 1032 0239 1761 0184 1816
10 3078 0308 0975 0284 1716 0223 1777
31
5 For the R Control Chart plot all R values on the R Control Chart
to see if all the Ranges are ldquobetween the control limitsrdquo If they are
then your process is considered to be in a state of statistical control
(as far as the variability of the process is concerned)
6 For the X-BAR Control Chart plot all the X-BARs on the X-BAR
control chart to see if all the X-BARs are ldquobetween the control
limitsrdquo If they are then your process is considered in a state of
statistical control (as far as the average of the process is
concerned)
PROCEDURE FOR X ndashBAR AND R BAR CHART
32
SAMPLE DATA FOR X BAR ndashR CHART
Sub Group 1 2 3 4 5 X -Bar Range reg
1 1195 1191 1211 1203 1198 1200 02
2 1201 1198 1198 1197 12 1199 004
3 1193 1206 1198 1196 1202 1199 013
4 1205 1198 1205 1206 1198 1202 008
5 1198 1203 1206 1201 1199 1201 008
6 1202 1205 1196 1201 1195 1200 01
7 1199 1206 1201 1204 1201 1202 007
8 1201 1197 1198 1204 1198 1200 007
9 1198 1204 1198 1204 1204 1202 006
10 1205 1195 1198 1204 1196 1200 01
` X Bar-Bar 1200 009
X Bar Chart
UCL = X BAR-BAR + A2 R Bar
1200 +(0577009) 1205
LCL= X BAR-BAR - A2 R Bar
1200 - (0577009) 1195
R Chart
UCL = D4R Bar 211 009 021
LCL = D3 R Bar 0009 0
33
PLOT DATA ON CONTROL CHARTS
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1 2 3 4 5 6 7 8 9 10
Ave
rage
(X
ba
r)
X Bar Chart
UCL
LCL
X Bar
34
PLOT DATA ON CONTROL CHARTS
001
003
005
007
009
011
013
015
017
019
021
023
025
1 2 3 4 5 6 7 8 9 10
R Chart
UCL
LCL
35
PROCEDURE TO DETERMINE IF PROCESS IS IN A STATE OF
STATISTICAL CONTROL
7 If process is determined to be ldquoNOT STABLErdquo then stop and find out what
an assignable cause might be fix and then repeat the complete process of
collecting new data
8 If the process is determined to be ldquoSTABLErdquo then you may use the
control charts you developed to monitor future production to ensure that the
process REMAINS stable
More Samples for Control charts
36
READING OF CONTROL CHART
Control charts can determine whether a process is behaving in an unusual way The quality of the individual points of a subset is determined unstable if any of the
following occurs
Rule 1 Any point falls beyond 3σ from the centreline(this is represented by the upper and
lower control limits)
Rule 2 Two out of three consecutive points fall beyond 2σ on the same side of the
centreline
Rule 3 Four out of five consecutive points fall beyond 1σ on the same side of the
centreline
Rule 4 Nine or more consecutive points fall on the same side of the centreline
(Ref Next page for sample)
37
READING THE CONTROL CHART
38
CONTROL CHARTS FOR ATTRIBUTES ndashP-CHARTS amp C-CHARTS
Attributes are discrete events yesno or passfail
Use P-Charts for quality characteristics that are discrete and involve yesno or goodbad decisions
Eg
Number of leaking caulking tubes in a box of 48
Number of broken eggs in a carton
Use C-Charts for discrete defects when there can be more than one defect per unit
Eg
Number of stains in a carpet sample cut from a production run
Number of complaints per customer at a hotel
39
P-CHART EXAMPLE A PRODUCTION MANAGER FOR A TIRE COMPANY HAS INSPECTED THE NUMBER OF
DEFECTIVE TIRES IN FIVE RANDOM SAMPLES WITH 20 TIRES IN EACH SAMPLE THE TABLE BELOW SHOWS THE
NUMBER OF DEFECTIVE TIRES IN EACH SAMPLE OF 20 TIRES CALCULATE THE CONTROL LIMITS
Sample Number of
Defective Tires
Number of Tires in each
Sample
Proportion Defective
1 3 20 15
2 2 20 10
3 1 20 05
4 2 20 10
5 2 20 05
Total 9 100 09
01023(064)09σzpLCL
2823(064)09σzpUCL
06420
(09)(91)
n
)p(1pσ
09100
9
Inspected Total
DefectivespCL
p
p
p
Solution
40
P- CONTROL CHART
41
C-CHART EXAMPLE THE NUMBER OF WEEKLY CUSTOMER COMPLAINTS ARE MONITORED IN A LARGE HOTEL USING A C-CHART DEVELOP THREE SIGMA CONTROL LIMITS USING THE DATA TABLE BELOW
Week Number of Complaints
1 3
2 2
3 3
4 1
5 3
6 3
7 2
8 1
9 3
10 1
Total 22
022522322ccLCL
66522322ccUCL
2210
22
samples of
complaintsc
c
c
z
z
Solution
42
C- CONTROL CHART
43
The ability of a process to meet product designtechnical specifications
Assessing capability involves evaluating process variability relative to preset product or service specifications
Process Capability ndash Cp and Cpk
Cp assumes that the process is centered in the specification range
Cpk helps to address a possible lack of centering of the process
PROCESS CAPABILITY
6σ
LSLUSL
width process
width ionspecificatCp
3σ
LSLμ
3σ
μUSLminCpk
44
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
45
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
46
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
47
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
--and an individual part is measured at 520rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
48
GRAPHING THE TOLERANCE AND MEASUREMENTS
Suppose we made and measured several more
units and they were all EXACTLY the same
We wouldnrsquot have very many part problems
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
X
X
X
49
GRAPHING THE TOLERANCE AND MEASUREMENTS
In the real world units are NOT EXACTLY the same
Everything VARIES
The question isnrsquot IF units vary
Itrsquos how much when and why
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
XX
XXX
XXXXX
XXXXXXX
50
The ldquonormal bell curverdquo
Widths heights depths thicknesses weights speeds strengths
and many other types of measurements when charted as a
histogram often form the shape of a bell
A ldquoperfect bellrdquo like a ldquoperfect circlerdquo doesnrsquot occur in nature but
many processes are close enough to make the bell curve useful
(A number of common industrial measurements such as flatness and straightness do NOT tend to distribute in a bell shape their proper statistical analysis is performed using models other than the bell curve)
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
51
What is a ldquostandard deviationrdquo
If we measure the DISTANCE from the CENTER of the bell
to each individual measurement that makes up the bell curve
we can find a TYPICAL DISTANCE
The most commonly used statistic to estimate this distance is the
Standard Deviation (also called ldquoSigmardquo)
Because of the natural shape of the bell curve the area of +1 to ndash1
standard deviations includes about 68 of the curve
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
Typical distance
from the center +1
standard deviation
Typical distance
from the center -1
standard deviation
52
How much of the curve is included in how many standard
deviations
From ndash1 to +1 is about 68 of the bell curve
From ndash2 to +2 is about 95
From ndash3 to +3 is about 9973
From ndash4 to +4 is about 9999
(NOTE We usually show the bell from ndash3 to +3 to make it easier to draw but in concept the ldquotailsrdquo of the bell get very thin and go on forever)
-6 -5 -4 -3 -2 -1 +1 +2 +3 +4 +5 +6 0
53
A
B
What is Cpk It is a measure of how well a process is within a specification
Cpk = A divided by B
A = Distance from process mean to closest spec limit
B = 3 Standard Deviations (also called ldquo3 Sigmardquo)
A bigger Cpk is better because fewer units will be beyond spec
(A bigger ldquoArdquo and a smaller ldquoBrdquo are better)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
54
A
B
ldquoProcess Capabilityrdquo is the ability of a process
to fit its output within the tolerances
hellipa LARGER ldquoArdquo
hellipand a SMALLER ldquoBrdquo
hellipmeans BETTER ldquoProcess Capabilityrdquo
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
55
A
B
An Analogy
Analogy
The bell curve is your automobile
The spec limits are the edges of your garage door
If A = B you are hitting the frame of your garage door with your car
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
56
A
B
How can we make Cpk (A divided by B) better
1 Design the product so a wider tolerance is functional (ldquorobust designrdquo)
2 Choose equipment and methods for a good safety margin (ldquoprocess capabilityrdquo)
3 Correctly adjust but only when needed (ldquocontrolrdquo)
4 Discover ways to narrow the natural variation (ldquoimprovementrdquo)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
57
A
B
What does a very good Cpk do for us
This process is producing good units with a good safety margin
Note that when Cpk = 2 our process mean is 6 standard deviations from
the nearest spec so we say it has ldquo6 Sigma Capabilityrdquo
Specification
Limit
Specification
Limit
This Cpk is
about 2
Very good
Mean
58
A
B
What does a problem Cpk look like
This process is in danger of producing some defects
It is too close to the specification limits
(Remember the bell curve tail goes further than Bhellip hellipwe only show the bell to 3-sigma to make it easier to draw)
Specification
Limit
Specification
Limit
This Cpk is just
slightly greater
than 1 Not good
59
A
B
What does a very bad Cpk look like
A significant part of the ldquotailrdquo is hanging out beyond the spec limits
This process is producing scrap rework and customer rejects
Notice that if distance ldquoArdquo approaches zerohellip
hellipthe Cpk would approach zero andhellip
hellipthe process would become 50 defective
Specification
Limit
Specification
Limit
This Cpk is less
than 1 We desire
a minimum of 133
and ultimately we
want 2 or more
60
-
Q amp A
61
MEASUREMENT SYSTEM ANALYSIS (MSA)
An MSA is a statistical tool used to determine if a measurement system is capable of precise measurement
What is It
Objective or Purpose
bull To determine how much error is in the measurement due to the measurement process itself
bull Quantifies the variability added by the measurement system
bull Applicable to attribute data and variable data
When to Use It
bull On the critical inputs and outputs prior to collecting data for analysis
bull For any new or modified process in order to ensure the quality of the data
Measurement System Analysis is an analysis of the measurement process not an analysis of the people
IMPORTANT
Who Should be Involved
Everyone that measures and makes decisions about these measurements should be involved in the MSA
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The observed variation in process output measurements is not simply the variation in the process itself it is the variation in the process plus the variation in measurement that results from an inadequate measurement system
Conducting an MSA reduces the likelihood of passing a bad part or rejecting a good part
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The output of the process measured by bull Cycle time bull Dimensional data bull Number of defects and others
Observed Variation
Process Variation
Measurement System
Variation
Reproducibility
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Accuracy (Central Location)
OBSERVED VARIATION
Calibration addresses accuracy
Measurement System Analysis (MSA)
MEASUREMENT SYSTEM ERRORS
Accuracy difference between the observed measurement and the actual measurement
Precision variation that occurs when measuring the same part with the same instrument
MEASUREMENT SYSTEM ERROR
Precise but not
accurate
Accurate but not
precise
Not accurate or
precise
Accurate and
precise
ACCURACY OF MEASUREMENT
Broken down into three components
aStability
The consistency of measurements over time
bBias
A measure of the amount of partiality in the system
cLinearity
A measure of the bias values through the expected
range of measurements
OBSERVED VARIATION
Observed Variation
Process Variation
Measurement System
Variation
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Reproducibility
Accuracy (Central Location)
Calibration Addresses Accuracy
Letrsquos take a closer look at Precision
Measurement System Analysis (MSA)
Measurement System Analysis (MSA)
Error in Resolution The inability to detect small changes
Possible Cause
Wrong measurement device selected - divisions on scale not fine enough to detect changes
Resolution
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Repeatability The inability to get the same answer from repeated measurements made of the same item under absolutely identical conditions
Possible Cause
Lack of standard operating procedures (SOP) lack of training measuring system variablilty
Repeatability
Equipment Variation
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Reproducibility The inability to get the same answer from repeated measurements made under various conditions from different inspectors
Possible Cause
Lack of SOP lack of training
Reproducibility
Appraiser Variation
VARIABLE MSA ndash GAGE RampR STUDY
bull Gage RampR is the combined estimate of
measurement system Repeatability and
Reproducibility
bull Typically a 3-person study is performed Each person randomly measures 10 marked parts per trial
Each person can perform up to 3 trials
bull There are 3 key indicators EV or Equipment Variation
AV or Appraiser Variation
Overall GRR
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
X-BAR CONTROL LIMITS
Upper Control Limit (UCL) = (X-BAR-BAR) + A2 (R-BAR)
Lower Control Limit(LCL) = (X-BAR-BAR) - A2 (R-BAR)
R CONTROL LIMITS
Upper Control Limit - D3 (R-BAR)
Lower Control Limit - D4 (R-BAR)
PROCEDURE FOR X ndashBAR AND R BAR CHART
30
CONTROL CHART CONSTANTS
sample size constant constant constant constant constant constant constant
n d2 A2 A3 B3 B4 D3 D4
2 1128 188 2659 0 3267 0 3267
3 1693 1023 1954 0 2568 0 2574
4 2059 0729 1628 0 2266 0 2282
5 2326 0577 1427 0 2089 0 2114
6 2534 0483 1287 003 197 0 2004
7 2704 0419 1182 0118 1882 0076 1924
8 2847 0373 1099 0185 1815 0136 1864
9 297 0337 1032 0239 1761 0184 1816
10 3078 0308 0975 0284 1716 0223 1777
31
5 For the R Control Chart plot all R values on the R Control Chart
to see if all the Ranges are ldquobetween the control limitsrdquo If they are
then your process is considered to be in a state of statistical control
(as far as the variability of the process is concerned)
6 For the X-BAR Control Chart plot all the X-BARs on the X-BAR
control chart to see if all the X-BARs are ldquobetween the control
limitsrdquo If they are then your process is considered in a state of
statistical control (as far as the average of the process is
concerned)
PROCEDURE FOR X ndashBAR AND R BAR CHART
32
SAMPLE DATA FOR X BAR ndashR CHART
Sub Group 1 2 3 4 5 X -Bar Range reg
1 1195 1191 1211 1203 1198 1200 02
2 1201 1198 1198 1197 12 1199 004
3 1193 1206 1198 1196 1202 1199 013
4 1205 1198 1205 1206 1198 1202 008
5 1198 1203 1206 1201 1199 1201 008
6 1202 1205 1196 1201 1195 1200 01
7 1199 1206 1201 1204 1201 1202 007
8 1201 1197 1198 1204 1198 1200 007
9 1198 1204 1198 1204 1204 1202 006
10 1205 1195 1198 1204 1196 1200 01
` X Bar-Bar 1200 009
X Bar Chart
UCL = X BAR-BAR + A2 R Bar
1200 +(0577009) 1205
LCL= X BAR-BAR - A2 R Bar
1200 - (0577009) 1195
R Chart
UCL = D4R Bar 211 009 021
LCL = D3 R Bar 0009 0
33
PLOT DATA ON CONTROL CHARTS
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1 2 3 4 5 6 7 8 9 10
Ave
rage
(X
ba
r)
X Bar Chart
UCL
LCL
X Bar
34
PLOT DATA ON CONTROL CHARTS
001
003
005
007
009
011
013
015
017
019
021
023
025
1 2 3 4 5 6 7 8 9 10
R Chart
UCL
LCL
35
PROCEDURE TO DETERMINE IF PROCESS IS IN A STATE OF
STATISTICAL CONTROL
7 If process is determined to be ldquoNOT STABLErdquo then stop and find out what
an assignable cause might be fix and then repeat the complete process of
collecting new data
8 If the process is determined to be ldquoSTABLErdquo then you may use the
control charts you developed to monitor future production to ensure that the
process REMAINS stable
More Samples for Control charts
36
READING OF CONTROL CHART
Control charts can determine whether a process is behaving in an unusual way The quality of the individual points of a subset is determined unstable if any of the
following occurs
Rule 1 Any point falls beyond 3σ from the centreline(this is represented by the upper and
lower control limits)
Rule 2 Two out of three consecutive points fall beyond 2σ on the same side of the
centreline
Rule 3 Four out of five consecutive points fall beyond 1σ on the same side of the
centreline
Rule 4 Nine or more consecutive points fall on the same side of the centreline
(Ref Next page for sample)
37
READING THE CONTROL CHART
38
CONTROL CHARTS FOR ATTRIBUTES ndashP-CHARTS amp C-CHARTS
Attributes are discrete events yesno or passfail
Use P-Charts for quality characteristics that are discrete and involve yesno or goodbad decisions
Eg
Number of leaking caulking tubes in a box of 48
Number of broken eggs in a carton
Use C-Charts for discrete defects when there can be more than one defect per unit
Eg
Number of stains in a carpet sample cut from a production run
Number of complaints per customer at a hotel
39
P-CHART EXAMPLE A PRODUCTION MANAGER FOR A TIRE COMPANY HAS INSPECTED THE NUMBER OF
DEFECTIVE TIRES IN FIVE RANDOM SAMPLES WITH 20 TIRES IN EACH SAMPLE THE TABLE BELOW SHOWS THE
NUMBER OF DEFECTIVE TIRES IN EACH SAMPLE OF 20 TIRES CALCULATE THE CONTROL LIMITS
Sample Number of
Defective Tires
Number of Tires in each
Sample
Proportion Defective
1 3 20 15
2 2 20 10
3 1 20 05
4 2 20 10
5 2 20 05
Total 9 100 09
01023(064)09σzpLCL
2823(064)09σzpUCL
06420
(09)(91)
n
)p(1pσ
09100
9
Inspected Total
DefectivespCL
p
p
p
Solution
40
P- CONTROL CHART
41
C-CHART EXAMPLE THE NUMBER OF WEEKLY CUSTOMER COMPLAINTS ARE MONITORED IN A LARGE HOTEL USING A C-CHART DEVELOP THREE SIGMA CONTROL LIMITS USING THE DATA TABLE BELOW
Week Number of Complaints
1 3
2 2
3 3
4 1
5 3
6 3
7 2
8 1
9 3
10 1
Total 22
022522322ccLCL
66522322ccUCL
2210
22
samples of
complaintsc
c
c
z
z
Solution
42
C- CONTROL CHART
43
The ability of a process to meet product designtechnical specifications
Assessing capability involves evaluating process variability relative to preset product or service specifications
Process Capability ndash Cp and Cpk
Cp assumes that the process is centered in the specification range
Cpk helps to address a possible lack of centering of the process
PROCESS CAPABILITY
6σ
LSLUSL
width process
width ionspecificatCp
3σ
LSLμ
3σ
μUSLminCpk
44
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
45
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
46
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
47
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
--and an individual part is measured at 520rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
48
GRAPHING THE TOLERANCE AND MEASUREMENTS
Suppose we made and measured several more
units and they were all EXACTLY the same
We wouldnrsquot have very many part problems
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
X
X
X
49
GRAPHING THE TOLERANCE AND MEASUREMENTS
In the real world units are NOT EXACTLY the same
Everything VARIES
The question isnrsquot IF units vary
Itrsquos how much when and why
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
XX
XXX
XXXXX
XXXXXXX
50
The ldquonormal bell curverdquo
Widths heights depths thicknesses weights speeds strengths
and many other types of measurements when charted as a
histogram often form the shape of a bell
A ldquoperfect bellrdquo like a ldquoperfect circlerdquo doesnrsquot occur in nature but
many processes are close enough to make the bell curve useful
(A number of common industrial measurements such as flatness and straightness do NOT tend to distribute in a bell shape their proper statistical analysis is performed using models other than the bell curve)
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
51
What is a ldquostandard deviationrdquo
If we measure the DISTANCE from the CENTER of the bell
to each individual measurement that makes up the bell curve
we can find a TYPICAL DISTANCE
The most commonly used statistic to estimate this distance is the
Standard Deviation (also called ldquoSigmardquo)
Because of the natural shape of the bell curve the area of +1 to ndash1
standard deviations includes about 68 of the curve
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
Typical distance
from the center +1
standard deviation
Typical distance
from the center -1
standard deviation
52
How much of the curve is included in how many standard
deviations
From ndash1 to +1 is about 68 of the bell curve
From ndash2 to +2 is about 95
From ndash3 to +3 is about 9973
From ndash4 to +4 is about 9999
(NOTE We usually show the bell from ndash3 to +3 to make it easier to draw but in concept the ldquotailsrdquo of the bell get very thin and go on forever)
-6 -5 -4 -3 -2 -1 +1 +2 +3 +4 +5 +6 0
53
A
B
What is Cpk It is a measure of how well a process is within a specification
Cpk = A divided by B
A = Distance from process mean to closest spec limit
B = 3 Standard Deviations (also called ldquo3 Sigmardquo)
A bigger Cpk is better because fewer units will be beyond spec
(A bigger ldquoArdquo and a smaller ldquoBrdquo are better)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
54
A
B
ldquoProcess Capabilityrdquo is the ability of a process
to fit its output within the tolerances
hellipa LARGER ldquoArdquo
hellipand a SMALLER ldquoBrdquo
hellipmeans BETTER ldquoProcess Capabilityrdquo
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
55
A
B
An Analogy
Analogy
The bell curve is your automobile
The spec limits are the edges of your garage door
If A = B you are hitting the frame of your garage door with your car
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
56
A
B
How can we make Cpk (A divided by B) better
1 Design the product so a wider tolerance is functional (ldquorobust designrdquo)
2 Choose equipment and methods for a good safety margin (ldquoprocess capabilityrdquo)
3 Correctly adjust but only when needed (ldquocontrolrdquo)
4 Discover ways to narrow the natural variation (ldquoimprovementrdquo)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
57
A
B
What does a very good Cpk do for us
This process is producing good units with a good safety margin
Note that when Cpk = 2 our process mean is 6 standard deviations from
the nearest spec so we say it has ldquo6 Sigma Capabilityrdquo
Specification
Limit
Specification
Limit
This Cpk is
about 2
Very good
Mean
58
A
B
What does a problem Cpk look like
This process is in danger of producing some defects
It is too close to the specification limits
(Remember the bell curve tail goes further than Bhellip hellipwe only show the bell to 3-sigma to make it easier to draw)
Specification
Limit
Specification
Limit
This Cpk is just
slightly greater
than 1 Not good
59
A
B
What does a very bad Cpk look like
A significant part of the ldquotailrdquo is hanging out beyond the spec limits
This process is producing scrap rework and customer rejects
Notice that if distance ldquoArdquo approaches zerohellip
hellipthe Cpk would approach zero andhellip
hellipthe process would become 50 defective
Specification
Limit
Specification
Limit
This Cpk is less
than 1 We desire
a minimum of 133
and ultimately we
want 2 or more
60
-
Q amp A
61
MEASUREMENT SYSTEM ANALYSIS (MSA)
An MSA is a statistical tool used to determine if a measurement system is capable of precise measurement
What is It
Objective or Purpose
bull To determine how much error is in the measurement due to the measurement process itself
bull Quantifies the variability added by the measurement system
bull Applicable to attribute data and variable data
When to Use It
bull On the critical inputs and outputs prior to collecting data for analysis
bull For any new or modified process in order to ensure the quality of the data
Measurement System Analysis is an analysis of the measurement process not an analysis of the people
IMPORTANT
Who Should be Involved
Everyone that measures and makes decisions about these measurements should be involved in the MSA
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The observed variation in process output measurements is not simply the variation in the process itself it is the variation in the process plus the variation in measurement that results from an inadequate measurement system
Conducting an MSA reduces the likelihood of passing a bad part or rejecting a good part
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The output of the process measured by bull Cycle time bull Dimensional data bull Number of defects and others
Observed Variation
Process Variation
Measurement System
Variation
Reproducibility
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Accuracy (Central Location)
OBSERVED VARIATION
Calibration addresses accuracy
Measurement System Analysis (MSA)
MEASUREMENT SYSTEM ERRORS
Accuracy difference between the observed measurement and the actual measurement
Precision variation that occurs when measuring the same part with the same instrument
MEASUREMENT SYSTEM ERROR
Precise but not
accurate
Accurate but not
precise
Not accurate or
precise
Accurate and
precise
ACCURACY OF MEASUREMENT
Broken down into three components
aStability
The consistency of measurements over time
bBias
A measure of the amount of partiality in the system
cLinearity
A measure of the bias values through the expected
range of measurements
OBSERVED VARIATION
Observed Variation
Process Variation
Measurement System
Variation
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Reproducibility
Accuracy (Central Location)
Calibration Addresses Accuracy
Letrsquos take a closer look at Precision
Measurement System Analysis (MSA)
Measurement System Analysis (MSA)
Error in Resolution The inability to detect small changes
Possible Cause
Wrong measurement device selected - divisions on scale not fine enough to detect changes
Resolution
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Repeatability The inability to get the same answer from repeated measurements made of the same item under absolutely identical conditions
Possible Cause
Lack of standard operating procedures (SOP) lack of training measuring system variablilty
Repeatability
Equipment Variation
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Reproducibility The inability to get the same answer from repeated measurements made under various conditions from different inspectors
Possible Cause
Lack of SOP lack of training
Reproducibility
Appraiser Variation
VARIABLE MSA ndash GAGE RampR STUDY
bull Gage RampR is the combined estimate of
measurement system Repeatability and
Reproducibility
bull Typically a 3-person study is performed Each person randomly measures 10 marked parts per trial
Each person can perform up to 3 trials
bull There are 3 key indicators EV or Equipment Variation
AV or Appraiser Variation
Overall GRR
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
CONTROL CHART CONSTANTS
sample size constant constant constant constant constant constant constant
n d2 A2 A3 B3 B4 D3 D4
2 1128 188 2659 0 3267 0 3267
3 1693 1023 1954 0 2568 0 2574
4 2059 0729 1628 0 2266 0 2282
5 2326 0577 1427 0 2089 0 2114
6 2534 0483 1287 003 197 0 2004
7 2704 0419 1182 0118 1882 0076 1924
8 2847 0373 1099 0185 1815 0136 1864
9 297 0337 1032 0239 1761 0184 1816
10 3078 0308 0975 0284 1716 0223 1777
31
5 For the R Control Chart plot all R values on the R Control Chart
to see if all the Ranges are ldquobetween the control limitsrdquo If they are
then your process is considered to be in a state of statistical control
(as far as the variability of the process is concerned)
6 For the X-BAR Control Chart plot all the X-BARs on the X-BAR
control chart to see if all the X-BARs are ldquobetween the control
limitsrdquo If they are then your process is considered in a state of
statistical control (as far as the average of the process is
concerned)
PROCEDURE FOR X ndashBAR AND R BAR CHART
32
SAMPLE DATA FOR X BAR ndashR CHART
Sub Group 1 2 3 4 5 X -Bar Range reg
1 1195 1191 1211 1203 1198 1200 02
2 1201 1198 1198 1197 12 1199 004
3 1193 1206 1198 1196 1202 1199 013
4 1205 1198 1205 1206 1198 1202 008
5 1198 1203 1206 1201 1199 1201 008
6 1202 1205 1196 1201 1195 1200 01
7 1199 1206 1201 1204 1201 1202 007
8 1201 1197 1198 1204 1198 1200 007
9 1198 1204 1198 1204 1204 1202 006
10 1205 1195 1198 1204 1196 1200 01
` X Bar-Bar 1200 009
X Bar Chart
UCL = X BAR-BAR + A2 R Bar
1200 +(0577009) 1205
LCL= X BAR-BAR - A2 R Bar
1200 - (0577009) 1195
R Chart
UCL = D4R Bar 211 009 021
LCL = D3 R Bar 0009 0
33
PLOT DATA ON CONTROL CHARTS
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1 2 3 4 5 6 7 8 9 10
Ave
rage
(X
ba
r)
X Bar Chart
UCL
LCL
X Bar
34
PLOT DATA ON CONTROL CHARTS
001
003
005
007
009
011
013
015
017
019
021
023
025
1 2 3 4 5 6 7 8 9 10
R Chart
UCL
LCL
35
PROCEDURE TO DETERMINE IF PROCESS IS IN A STATE OF
STATISTICAL CONTROL
7 If process is determined to be ldquoNOT STABLErdquo then stop and find out what
an assignable cause might be fix and then repeat the complete process of
collecting new data
8 If the process is determined to be ldquoSTABLErdquo then you may use the
control charts you developed to monitor future production to ensure that the
process REMAINS stable
More Samples for Control charts
36
READING OF CONTROL CHART
Control charts can determine whether a process is behaving in an unusual way The quality of the individual points of a subset is determined unstable if any of the
following occurs
Rule 1 Any point falls beyond 3σ from the centreline(this is represented by the upper and
lower control limits)
Rule 2 Two out of three consecutive points fall beyond 2σ on the same side of the
centreline
Rule 3 Four out of five consecutive points fall beyond 1σ on the same side of the
centreline
Rule 4 Nine or more consecutive points fall on the same side of the centreline
(Ref Next page for sample)
37
READING THE CONTROL CHART
38
CONTROL CHARTS FOR ATTRIBUTES ndashP-CHARTS amp C-CHARTS
Attributes are discrete events yesno or passfail
Use P-Charts for quality characteristics that are discrete and involve yesno or goodbad decisions
Eg
Number of leaking caulking tubes in a box of 48
Number of broken eggs in a carton
Use C-Charts for discrete defects when there can be more than one defect per unit
Eg
Number of stains in a carpet sample cut from a production run
Number of complaints per customer at a hotel
39
P-CHART EXAMPLE A PRODUCTION MANAGER FOR A TIRE COMPANY HAS INSPECTED THE NUMBER OF
DEFECTIVE TIRES IN FIVE RANDOM SAMPLES WITH 20 TIRES IN EACH SAMPLE THE TABLE BELOW SHOWS THE
NUMBER OF DEFECTIVE TIRES IN EACH SAMPLE OF 20 TIRES CALCULATE THE CONTROL LIMITS
Sample Number of
Defective Tires
Number of Tires in each
Sample
Proportion Defective
1 3 20 15
2 2 20 10
3 1 20 05
4 2 20 10
5 2 20 05
Total 9 100 09
01023(064)09σzpLCL
2823(064)09σzpUCL
06420
(09)(91)
n
)p(1pσ
09100
9
Inspected Total
DefectivespCL
p
p
p
Solution
40
P- CONTROL CHART
41
C-CHART EXAMPLE THE NUMBER OF WEEKLY CUSTOMER COMPLAINTS ARE MONITORED IN A LARGE HOTEL USING A C-CHART DEVELOP THREE SIGMA CONTROL LIMITS USING THE DATA TABLE BELOW
Week Number of Complaints
1 3
2 2
3 3
4 1
5 3
6 3
7 2
8 1
9 3
10 1
Total 22
022522322ccLCL
66522322ccUCL
2210
22
samples of
complaintsc
c
c
z
z
Solution
42
C- CONTROL CHART
43
The ability of a process to meet product designtechnical specifications
Assessing capability involves evaluating process variability relative to preset product or service specifications
Process Capability ndash Cp and Cpk
Cp assumes that the process is centered in the specification range
Cpk helps to address a possible lack of centering of the process
PROCESS CAPABILITY
6σ
LSLUSL
width process
width ionspecificatCp
3σ
LSLμ
3σ
μUSLminCpk
44
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
45
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
46
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
47
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
--and an individual part is measured at 520rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
48
GRAPHING THE TOLERANCE AND MEASUREMENTS
Suppose we made and measured several more
units and they were all EXACTLY the same
We wouldnrsquot have very many part problems
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
X
X
X
49
GRAPHING THE TOLERANCE AND MEASUREMENTS
In the real world units are NOT EXACTLY the same
Everything VARIES
The question isnrsquot IF units vary
Itrsquos how much when and why
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
XX
XXX
XXXXX
XXXXXXX
50
The ldquonormal bell curverdquo
Widths heights depths thicknesses weights speeds strengths
and many other types of measurements when charted as a
histogram often form the shape of a bell
A ldquoperfect bellrdquo like a ldquoperfect circlerdquo doesnrsquot occur in nature but
many processes are close enough to make the bell curve useful
(A number of common industrial measurements such as flatness and straightness do NOT tend to distribute in a bell shape their proper statistical analysis is performed using models other than the bell curve)
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
51
What is a ldquostandard deviationrdquo
If we measure the DISTANCE from the CENTER of the bell
to each individual measurement that makes up the bell curve
we can find a TYPICAL DISTANCE
The most commonly used statistic to estimate this distance is the
Standard Deviation (also called ldquoSigmardquo)
Because of the natural shape of the bell curve the area of +1 to ndash1
standard deviations includes about 68 of the curve
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
Typical distance
from the center +1
standard deviation
Typical distance
from the center -1
standard deviation
52
How much of the curve is included in how many standard
deviations
From ndash1 to +1 is about 68 of the bell curve
From ndash2 to +2 is about 95
From ndash3 to +3 is about 9973
From ndash4 to +4 is about 9999
(NOTE We usually show the bell from ndash3 to +3 to make it easier to draw but in concept the ldquotailsrdquo of the bell get very thin and go on forever)
-6 -5 -4 -3 -2 -1 +1 +2 +3 +4 +5 +6 0
53
A
B
What is Cpk It is a measure of how well a process is within a specification
Cpk = A divided by B
A = Distance from process mean to closest spec limit
B = 3 Standard Deviations (also called ldquo3 Sigmardquo)
A bigger Cpk is better because fewer units will be beyond spec
(A bigger ldquoArdquo and a smaller ldquoBrdquo are better)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
54
A
B
ldquoProcess Capabilityrdquo is the ability of a process
to fit its output within the tolerances
hellipa LARGER ldquoArdquo
hellipand a SMALLER ldquoBrdquo
hellipmeans BETTER ldquoProcess Capabilityrdquo
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
55
A
B
An Analogy
Analogy
The bell curve is your automobile
The spec limits are the edges of your garage door
If A = B you are hitting the frame of your garage door with your car
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
56
A
B
How can we make Cpk (A divided by B) better
1 Design the product so a wider tolerance is functional (ldquorobust designrdquo)
2 Choose equipment and methods for a good safety margin (ldquoprocess capabilityrdquo)
3 Correctly adjust but only when needed (ldquocontrolrdquo)
4 Discover ways to narrow the natural variation (ldquoimprovementrdquo)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
57
A
B
What does a very good Cpk do for us
This process is producing good units with a good safety margin
Note that when Cpk = 2 our process mean is 6 standard deviations from
the nearest spec so we say it has ldquo6 Sigma Capabilityrdquo
Specification
Limit
Specification
Limit
This Cpk is
about 2
Very good
Mean
58
A
B
What does a problem Cpk look like
This process is in danger of producing some defects
It is too close to the specification limits
(Remember the bell curve tail goes further than Bhellip hellipwe only show the bell to 3-sigma to make it easier to draw)
Specification
Limit
Specification
Limit
This Cpk is just
slightly greater
than 1 Not good
59
A
B
What does a very bad Cpk look like
A significant part of the ldquotailrdquo is hanging out beyond the spec limits
This process is producing scrap rework and customer rejects
Notice that if distance ldquoArdquo approaches zerohellip
hellipthe Cpk would approach zero andhellip
hellipthe process would become 50 defective
Specification
Limit
Specification
Limit
This Cpk is less
than 1 We desire
a minimum of 133
and ultimately we
want 2 or more
60
-
Q amp A
61
MEASUREMENT SYSTEM ANALYSIS (MSA)
An MSA is a statistical tool used to determine if a measurement system is capable of precise measurement
What is It
Objective or Purpose
bull To determine how much error is in the measurement due to the measurement process itself
bull Quantifies the variability added by the measurement system
bull Applicable to attribute data and variable data
When to Use It
bull On the critical inputs and outputs prior to collecting data for analysis
bull For any new or modified process in order to ensure the quality of the data
Measurement System Analysis is an analysis of the measurement process not an analysis of the people
IMPORTANT
Who Should be Involved
Everyone that measures and makes decisions about these measurements should be involved in the MSA
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The observed variation in process output measurements is not simply the variation in the process itself it is the variation in the process plus the variation in measurement that results from an inadequate measurement system
Conducting an MSA reduces the likelihood of passing a bad part or rejecting a good part
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The output of the process measured by bull Cycle time bull Dimensional data bull Number of defects and others
Observed Variation
Process Variation
Measurement System
Variation
Reproducibility
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Accuracy (Central Location)
OBSERVED VARIATION
Calibration addresses accuracy
Measurement System Analysis (MSA)
MEASUREMENT SYSTEM ERRORS
Accuracy difference between the observed measurement and the actual measurement
Precision variation that occurs when measuring the same part with the same instrument
MEASUREMENT SYSTEM ERROR
Precise but not
accurate
Accurate but not
precise
Not accurate or
precise
Accurate and
precise
ACCURACY OF MEASUREMENT
Broken down into three components
aStability
The consistency of measurements over time
bBias
A measure of the amount of partiality in the system
cLinearity
A measure of the bias values through the expected
range of measurements
OBSERVED VARIATION
Observed Variation
Process Variation
Measurement System
Variation
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Reproducibility
Accuracy (Central Location)
Calibration Addresses Accuracy
Letrsquos take a closer look at Precision
Measurement System Analysis (MSA)
Measurement System Analysis (MSA)
Error in Resolution The inability to detect small changes
Possible Cause
Wrong measurement device selected - divisions on scale not fine enough to detect changes
Resolution
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Repeatability The inability to get the same answer from repeated measurements made of the same item under absolutely identical conditions
Possible Cause
Lack of standard operating procedures (SOP) lack of training measuring system variablilty
Repeatability
Equipment Variation
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Reproducibility The inability to get the same answer from repeated measurements made under various conditions from different inspectors
Possible Cause
Lack of SOP lack of training
Reproducibility
Appraiser Variation
VARIABLE MSA ndash GAGE RampR STUDY
bull Gage RampR is the combined estimate of
measurement system Repeatability and
Reproducibility
bull Typically a 3-person study is performed Each person randomly measures 10 marked parts per trial
Each person can perform up to 3 trials
bull There are 3 key indicators EV or Equipment Variation
AV or Appraiser Variation
Overall GRR
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
5 For the R Control Chart plot all R values on the R Control Chart
to see if all the Ranges are ldquobetween the control limitsrdquo If they are
then your process is considered to be in a state of statistical control
(as far as the variability of the process is concerned)
6 For the X-BAR Control Chart plot all the X-BARs on the X-BAR
control chart to see if all the X-BARs are ldquobetween the control
limitsrdquo If they are then your process is considered in a state of
statistical control (as far as the average of the process is
concerned)
PROCEDURE FOR X ndashBAR AND R BAR CHART
32
SAMPLE DATA FOR X BAR ndashR CHART
Sub Group 1 2 3 4 5 X -Bar Range reg
1 1195 1191 1211 1203 1198 1200 02
2 1201 1198 1198 1197 12 1199 004
3 1193 1206 1198 1196 1202 1199 013
4 1205 1198 1205 1206 1198 1202 008
5 1198 1203 1206 1201 1199 1201 008
6 1202 1205 1196 1201 1195 1200 01
7 1199 1206 1201 1204 1201 1202 007
8 1201 1197 1198 1204 1198 1200 007
9 1198 1204 1198 1204 1204 1202 006
10 1205 1195 1198 1204 1196 1200 01
` X Bar-Bar 1200 009
X Bar Chart
UCL = X BAR-BAR + A2 R Bar
1200 +(0577009) 1205
LCL= X BAR-BAR - A2 R Bar
1200 - (0577009) 1195
R Chart
UCL = D4R Bar 211 009 021
LCL = D3 R Bar 0009 0
33
PLOT DATA ON CONTROL CHARTS
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1 2 3 4 5 6 7 8 9 10
Ave
rage
(X
ba
r)
X Bar Chart
UCL
LCL
X Bar
34
PLOT DATA ON CONTROL CHARTS
001
003
005
007
009
011
013
015
017
019
021
023
025
1 2 3 4 5 6 7 8 9 10
R Chart
UCL
LCL
35
PROCEDURE TO DETERMINE IF PROCESS IS IN A STATE OF
STATISTICAL CONTROL
7 If process is determined to be ldquoNOT STABLErdquo then stop and find out what
an assignable cause might be fix and then repeat the complete process of
collecting new data
8 If the process is determined to be ldquoSTABLErdquo then you may use the
control charts you developed to monitor future production to ensure that the
process REMAINS stable
More Samples for Control charts
36
READING OF CONTROL CHART
Control charts can determine whether a process is behaving in an unusual way The quality of the individual points of a subset is determined unstable if any of the
following occurs
Rule 1 Any point falls beyond 3σ from the centreline(this is represented by the upper and
lower control limits)
Rule 2 Two out of three consecutive points fall beyond 2σ on the same side of the
centreline
Rule 3 Four out of five consecutive points fall beyond 1σ on the same side of the
centreline
Rule 4 Nine or more consecutive points fall on the same side of the centreline
(Ref Next page for sample)
37
READING THE CONTROL CHART
38
CONTROL CHARTS FOR ATTRIBUTES ndashP-CHARTS amp C-CHARTS
Attributes are discrete events yesno or passfail
Use P-Charts for quality characteristics that are discrete and involve yesno or goodbad decisions
Eg
Number of leaking caulking tubes in a box of 48
Number of broken eggs in a carton
Use C-Charts for discrete defects when there can be more than one defect per unit
Eg
Number of stains in a carpet sample cut from a production run
Number of complaints per customer at a hotel
39
P-CHART EXAMPLE A PRODUCTION MANAGER FOR A TIRE COMPANY HAS INSPECTED THE NUMBER OF
DEFECTIVE TIRES IN FIVE RANDOM SAMPLES WITH 20 TIRES IN EACH SAMPLE THE TABLE BELOW SHOWS THE
NUMBER OF DEFECTIVE TIRES IN EACH SAMPLE OF 20 TIRES CALCULATE THE CONTROL LIMITS
Sample Number of
Defective Tires
Number of Tires in each
Sample
Proportion Defective
1 3 20 15
2 2 20 10
3 1 20 05
4 2 20 10
5 2 20 05
Total 9 100 09
01023(064)09σzpLCL
2823(064)09σzpUCL
06420
(09)(91)
n
)p(1pσ
09100
9
Inspected Total
DefectivespCL
p
p
p
Solution
40
P- CONTROL CHART
41
C-CHART EXAMPLE THE NUMBER OF WEEKLY CUSTOMER COMPLAINTS ARE MONITORED IN A LARGE HOTEL USING A C-CHART DEVELOP THREE SIGMA CONTROL LIMITS USING THE DATA TABLE BELOW
Week Number of Complaints
1 3
2 2
3 3
4 1
5 3
6 3
7 2
8 1
9 3
10 1
Total 22
022522322ccLCL
66522322ccUCL
2210
22
samples of
complaintsc
c
c
z
z
Solution
42
C- CONTROL CHART
43
The ability of a process to meet product designtechnical specifications
Assessing capability involves evaluating process variability relative to preset product or service specifications
Process Capability ndash Cp and Cpk
Cp assumes that the process is centered in the specification range
Cpk helps to address a possible lack of centering of the process
PROCESS CAPABILITY
6σ
LSLUSL
width process
width ionspecificatCp
3σ
LSLμ
3σ
μUSLminCpk
44
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
45
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
46
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
47
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
--and an individual part is measured at 520rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
48
GRAPHING THE TOLERANCE AND MEASUREMENTS
Suppose we made and measured several more
units and they were all EXACTLY the same
We wouldnrsquot have very many part problems
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
X
X
X
49
GRAPHING THE TOLERANCE AND MEASUREMENTS
In the real world units are NOT EXACTLY the same
Everything VARIES
The question isnrsquot IF units vary
Itrsquos how much when and why
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
XX
XXX
XXXXX
XXXXXXX
50
The ldquonormal bell curverdquo
Widths heights depths thicknesses weights speeds strengths
and many other types of measurements when charted as a
histogram often form the shape of a bell
A ldquoperfect bellrdquo like a ldquoperfect circlerdquo doesnrsquot occur in nature but
many processes are close enough to make the bell curve useful
(A number of common industrial measurements such as flatness and straightness do NOT tend to distribute in a bell shape their proper statistical analysis is performed using models other than the bell curve)
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
51
What is a ldquostandard deviationrdquo
If we measure the DISTANCE from the CENTER of the bell
to each individual measurement that makes up the bell curve
we can find a TYPICAL DISTANCE
The most commonly used statistic to estimate this distance is the
Standard Deviation (also called ldquoSigmardquo)
Because of the natural shape of the bell curve the area of +1 to ndash1
standard deviations includes about 68 of the curve
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
Typical distance
from the center +1
standard deviation
Typical distance
from the center -1
standard deviation
52
How much of the curve is included in how many standard
deviations
From ndash1 to +1 is about 68 of the bell curve
From ndash2 to +2 is about 95
From ndash3 to +3 is about 9973
From ndash4 to +4 is about 9999
(NOTE We usually show the bell from ndash3 to +3 to make it easier to draw but in concept the ldquotailsrdquo of the bell get very thin and go on forever)
-6 -5 -4 -3 -2 -1 +1 +2 +3 +4 +5 +6 0
53
A
B
What is Cpk It is a measure of how well a process is within a specification
Cpk = A divided by B
A = Distance from process mean to closest spec limit
B = 3 Standard Deviations (also called ldquo3 Sigmardquo)
A bigger Cpk is better because fewer units will be beyond spec
(A bigger ldquoArdquo and a smaller ldquoBrdquo are better)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
54
A
B
ldquoProcess Capabilityrdquo is the ability of a process
to fit its output within the tolerances
hellipa LARGER ldquoArdquo
hellipand a SMALLER ldquoBrdquo
hellipmeans BETTER ldquoProcess Capabilityrdquo
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
55
A
B
An Analogy
Analogy
The bell curve is your automobile
The spec limits are the edges of your garage door
If A = B you are hitting the frame of your garage door with your car
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
56
A
B
How can we make Cpk (A divided by B) better
1 Design the product so a wider tolerance is functional (ldquorobust designrdquo)
2 Choose equipment and methods for a good safety margin (ldquoprocess capabilityrdquo)
3 Correctly adjust but only when needed (ldquocontrolrdquo)
4 Discover ways to narrow the natural variation (ldquoimprovementrdquo)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
57
A
B
What does a very good Cpk do for us
This process is producing good units with a good safety margin
Note that when Cpk = 2 our process mean is 6 standard deviations from
the nearest spec so we say it has ldquo6 Sigma Capabilityrdquo
Specification
Limit
Specification
Limit
This Cpk is
about 2
Very good
Mean
58
A
B
What does a problem Cpk look like
This process is in danger of producing some defects
It is too close to the specification limits
(Remember the bell curve tail goes further than Bhellip hellipwe only show the bell to 3-sigma to make it easier to draw)
Specification
Limit
Specification
Limit
This Cpk is just
slightly greater
than 1 Not good
59
A
B
What does a very bad Cpk look like
A significant part of the ldquotailrdquo is hanging out beyond the spec limits
This process is producing scrap rework and customer rejects
Notice that if distance ldquoArdquo approaches zerohellip
hellipthe Cpk would approach zero andhellip
hellipthe process would become 50 defective
Specification
Limit
Specification
Limit
This Cpk is less
than 1 We desire
a minimum of 133
and ultimately we
want 2 or more
60
-
Q amp A
61
MEASUREMENT SYSTEM ANALYSIS (MSA)
An MSA is a statistical tool used to determine if a measurement system is capable of precise measurement
What is It
Objective or Purpose
bull To determine how much error is in the measurement due to the measurement process itself
bull Quantifies the variability added by the measurement system
bull Applicable to attribute data and variable data
When to Use It
bull On the critical inputs and outputs prior to collecting data for analysis
bull For any new or modified process in order to ensure the quality of the data
Measurement System Analysis is an analysis of the measurement process not an analysis of the people
IMPORTANT
Who Should be Involved
Everyone that measures and makes decisions about these measurements should be involved in the MSA
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The observed variation in process output measurements is not simply the variation in the process itself it is the variation in the process plus the variation in measurement that results from an inadequate measurement system
Conducting an MSA reduces the likelihood of passing a bad part or rejecting a good part
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The output of the process measured by bull Cycle time bull Dimensional data bull Number of defects and others
Observed Variation
Process Variation
Measurement System
Variation
Reproducibility
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Accuracy (Central Location)
OBSERVED VARIATION
Calibration addresses accuracy
Measurement System Analysis (MSA)
MEASUREMENT SYSTEM ERRORS
Accuracy difference between the observed measurement and the actual measurement
Precision variation that occurs when measuring the same part with the same instrument
MEASUREMENT SYSTEM ERROR
Precise but not
accurate
Accurate but not
precise
Not accurate or
precise
Accurate and
precise
ACCURACY OF MEASUREMENT
Broken down into three components
aStability
The consistency of measurements over time
bBias
A measure of the amount of partiality in the system
cLinearity
A measure of the bias values through the expected
range of measurements
OBSERVED VARIATION
Observed Variation
Process Variation
Measurement System
Variation
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Reproducibility
Accuracy (Central Location)
Calibration Addresses Accuracy
Letrsquos take a closer look at Precision
Measurement System Analysis (MSA)
Measurement System Analysis (MSA)
Error in Resolution The inability to detect small changes
Possible Cause
Wrong measurement device selected - divisions on scale not fine enough to detect changes
Resolution
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Repeatability The inability to get the same answer from repeated measurements made of the same item under absolutely identical conditions
Possible Cause
Lack of standard operating procedures (SOP) lack of training measuring system variablilty
Repeatability
Equipment Variation
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Reproducibility The inability to get the same answer from repeated measurements made under various conditions from different inspectors
Possible Cause
Lack of SOP lack of training
Reproducibility
Appraiser Variation
VARIABLE MSA ndash GAGE RampR STUDY
bull Gage RampR is the combined estimate of
measurement system Repeatability and
Reproducibility
bull Typically a 3-person study is performed Each person randomly measures 10 marked parts per trial
Each person can perform up to 3 trials
bull There are 3 key indicators EV or Equipment Variation
AV or Appraiser Variation
Overall GRR
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
SAMPLE DATA FOR X BAR ndashR CHART
Sub Group 1 2 3 4 5 X -Bar Range reg
1 1195 1191 1211 1203 1198 1200 02
2 1201 1198 1198 1197 12 1199 004
3 1193 1206 1198 1196 1202 1199 013
4 1205 1198 1205 1206 1198 1202 008
5 1198 1203 1206 1201 1199 1201 008
6 1202 1205 1196 1201 1195 1200 01
7 1199 1206 1201 1204 1201 1202 007
8 1201 1197 1198 1204 1198 1200 007
9 1198 1204 1198 1204 1204 1202 006
10 1205 1195 1198 1204 1196 1200 01
` X Bar-Bar 1200 009
X Bar Chart
UCL = X BAR-BAR + A2 R Bar
1200 +(0577009) 1205
LCL= X BAR-BAR - A2 R Bar
1200 - (0577009) 1195
R Chart
UCL = D4R Bar 211 009 021
LCL = D3 R Bar 0009 0
33
PLOT DATA ON CONTROL CHARTS
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1 2 3 4 5 6 7 8 9 10
Ave
rage
(X
ba
r)
X Bar Chart
UCL
LCL
X Bar
34
PLOT DATA ON CONTROL CHARTS
001
003
005
007
009
011
013
015
017
019
021
023
025
1 2 3 4 5 6 7 8 9 10
R Chart
UCL
LCL
35
PROCEDURE TO DETERMINE IF PROCESS IS IN A STATE OF
STATISTICAL CONTROL
7 If process is determined to be ldquoNOT STABLErdquo then stop and find out what
an assignable cause might be fix and then repeat the complete process of
collecting new data
8 If the process is determined to be ldquoSTABLErdquo then you may use the
control charts you developed to monitor future production to ensure that the
process REMAINS stable
More Samples for Control charts
36
READING OF CONTROL CHART
Control charts can determine whether a process is behaving in an unusual way The quality of the individual points of a subset is determined unstable if any of the
following occurs
Rule 1 Any point falls beyond 3σ from the centreline(this is represented by the upper and
lower control limits)
Rule 2 Two out of three consecutive points fall beyond 2σ on the same side of the
centreline
Rule 3 Four out of five consecutive points fall beyond 1σ on the same side of the
centreline
Rule 4 Nine or more consecutive points fall on the same side of the centreline
(Ref Next page for sample)
37
READING THE CONTROL CHART
38
CONTROL CHARTS FOR ATTRIBUTES ndashP-CHARTS amp C-CHARTS
Attributes are discrete events yesno or passfail
Use P-Charts for quality characteristics that are discrete and involve yesno or goodbad decisions
Eg
Number of leaking caulking tubes in a box of 48
Number of broken eggs in a carton
Use C-Charts for discrete defects when there can be more than one defect per unit
Eg
Number of stains in a carpet sample cut from a production run
Number of complaints per customer at a hotel
39
P-CHART EXAMPLE A PRODUCTION MANAGER FOR A TIRE COMPANY HAS INSPECTED THE NUMBER OF
DEFECTIVE TIRES IN FIVE RANDOM SAMPLES WITH 20 TIRES IN EACH SAMPLE THE TABLE BELOW SHOWS THE
NUMBER OF DEFECTIVE TIRES IN EACH SAMPLE OF 20 TIRES CALCULATE THE CONTROL LIMITS
Sample Number of
Defective Tires
Number of Tires in each
Sample
Proportion Defective
1 3 20 15
2 2 20 10
3 1 20 05
4 2 20 10
5 2 20 05
Total 9 100 09
01023(064)09σzpLCL
2823(064)09σzpUCL
06420
(09)(91)
n
)p(1pσ
09100
9
Inspected Total
DefectivespCL
p
p
p
Solution
40
P- CONTROL CHART
41
C-CHART EXAMPLE THE NUMBER OF WEEKLY CUSTOMER COMPLAINTS ARE MONITORED IN A LARGE HOTEL USING A C-CHART DEVELOP THREE SIGMA CONTROL LIMITS USING THE DATA TABLE BELOW
Week Number of Complaints
1 3
2 2
3 3
4 1
5 3
6 3
7 2
8 1
9 3
10 1
Total 22
022522322ccLCL
66522322ccUCL
2210
22
samples of
complaintsc
c
c
z
z
Solution
42
C- CONTROL CHART
43
The ability of a process to meet product designtechnical specifications
Assessing capability involves evaluating process variability relative to preset product or service specifications
Process Capability ndash Cp and Cpk
Cp assumes that the process is centered in the specification range
Cpk helps to address a possible lack of centering of the process
PROCESS CAPABILITY
6σ
LSLUSL
width process
width ionspecificatCp
3σ
LSLμ
3σ
μUSLminCpk
44
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
45
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
46
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
47
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
--and an individual part is measured at 520rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
48
GRAPHING THE TOLERANCE AND MEASUREMENTS
Suppose we made and measured several more
units and they were all EXACTLY the same
We wouldnrsquot have very many part problems
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
X
X
X
49
GRAPHING THE TOLERANCE AND MEASUREMENTS
In the real world units are NOT EXACTLY the same
Everything VARIES
The question isnrsquot IF units vary
Itrsquos how much when and why
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
XX
XXX
XXXXX
XXXXXXX
50
The ldquonormal bell curverdquo
Widths heights depths thicknesses weights speeds strengths
and many other types of measurements when charted as a
histogram often form the shape of a bell
A ldquoperfect bellrdquo like a ldquoperfect circlerdquo doesnrsquot occur in nature but
many processes are close enough to make the bell curve useful
(A number of common industrial measurements such as flatness and straightness do NOT tend to distribute in a bell shape their proper statistical analysis is performed using models other than the bell curve)
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
51
What is a ldquostandard deviationrdquo
If we measure the DISTANCE from the CENTER of the bell
to each individual measurement that makes up the bell curve
we can find a TYPICAL DISTANCE
The most commonly used statistic to estimate this distance is the
Standard Deviation (also called ldquoSigmardquo)
Because of the natural shape of the bell curve the area of +1 to ndash1
standard deviations includes about 68 of the curve
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
Typical distance
from the center +1
standard deviation
Typical distance
from the center -1
standard deviation
52
How much of the curve is included in how many standard
deviations
From ndash1 to +1 is about 68 of the bell curve
From ndash2 to +2 is about 95
From ndash3 to +3 is about 9973
From ndash4 to +4 is about 9999
(NOTE We usually show the bell from ndash3 to +3 to make it easier to draw but in concept the ldquotailsrdquo of the bell get very thin and go on forever)
-6 -5 -4 -3 -2 -1 +1 +2 +3 +4 +5 +6 0
53
A
B
What is Cpk It is a measure of how well a process is within a specification
Cpk = A divided by B
A = Distance from process mean to closest spec limit
B = 3 Standard Deviations (also called ldquo3 Sigmardquo)
A bigger Cpk is better because fewer units will be beyond spec
(A bigger ldquoArdquo and a smaller ldquoBrdquo are better)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
54
A
B
ldquoProcess Capabilityrdquo is the ability of a process
to fit its output within the tolerances
hellipa LARGER ldquoArdquo
hellipand a SMALLER ldquoBrdquo
hellipmeans BETTER ldquoProcess Capabilityrdquo
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
55
A
B
An Analogy
Analogy
The bell curve is your automobile
The spec limits are the edges of your garage door
If A = B you are hitting the frame of your garage door with your car
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
56
A
B
How can we make Cpk (A divided by B) better
1 Design the product so a wider tolerance is functional (ldquorobust designrdquo)
2 Choose equipment and methods for a good safety margin (ldquoprocess capabilityrdquo)
3 Correctly adjust but only when needed (ldquocontrolrdquo)
4 Discover ways to narrow the natural variation (ldquoimprovementrdquo)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
57
A
B
What does a very good Cpk do for us
This process is producing good units with a good safety margin
Note that when Cpk = 2 our process mean is 6 standard deviations from
the nearest spec so we say it has ldquo6 Sigma Capabilityrdquo
Specification
Limit
Specification
Limit
This Cpk is
about 2
Very good
Mean
58
A
B
What does a problem Cpk look like
This process is in danger of producing some defects
It is too close to the specification limits
(Remember the bell curve tail goes further than Bhellip hellipwe only show the bell to 3-sigma to make it easier to draw)
Specification
Limit
Specification
Limit
This Cpk is just
slightly greater
than 1 Not good
59
A
B
What does a very bad Cpk look like
A significant part of the ldquotailrdquo is hanging out beyond the spec limits
This process is producing scrap rework and customer rejects
Notice that if distance ldquoArdquo approaches zerohellip
hellipthe Cpk would approach zero andhellip
hellipthe process would become 50 defective
Specification
Limit
Specification
Limit
This Cpk is less
than 1 We desire
a minimum of 133
and ultimately we
want 2 or more
60
-
Q amp A
61
MEASUREMENT SYSTEM ANALYSIS (MSA)
An MSA is a statistical tool used to determine if a measurement system is capable of precise measurement
What is It
Objective or Purpose
bull To determine how much error is in the measurement due to the measurement process itself
bull Quantifies the variability added by the measurement system
bull Applicable to attribute data and variable data
When to Use It
bull On the critical inputs and outputs prior to collecting data for analysis
bull For any new or modified process in order to ensure the quality of the data
Measurement System Analysis is an analysis of the measurement process not an analysis of the people
IMPORTANT
Who Should be Involved
Everyone that measures and makes decisions about these measurements should be involved in the MSA
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The observed variation in process output measurements is not simply the variation in the process itself it is the variation in the process plus the variation in measurement that results from an inadequate measurement system
Conducting an MSA reduces the likelihood of passing a bad part or rejecting a good part
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The output of the process measured by bull Cycle time bull Dimensional data bull Number of defects and others
Observed Variation
Process Variation
Measurement System
Variation
Reproducibility
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Accuracy (Central Location)
OBSERVED VARIATION
Calibration addresses accuracy
Measurement System Analysis (MSA)
MEASUREMENT SYSTEM ERRORS
Accuracy difference between the observed measurement and the actual measurement
Precision variation that occurs when measuring the same part with the same instrument
MEASUREMENT SYSTEM ERROR
Precise but not
accurate
Accurate but not
precise
Not accurate or
precise
Accurate and
precise
ACCURACY OF MEASUREMENT
Broken down into three components
aStability
The consistency of measurements over time
bBias
A measure of the amount of partiality in the system
cLinearity
A measure of the bias values through the expected
range of measurements
OBSERVED VARIATION
Observed Variation
Process Variation
Measurement System
Variation
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Reproducibility
Accuracy (Central Location)
Calibration Addresses Accuracy
Letrsquos take a closer look at Precision
Measurement System Analysis (MSA)
Measurement System Analysis (MSA)
Error in Resolution The inability to detect small changes
Possible Cause
Wrong measurement device selected - divisions on scale not fine enough to detect changes
Resolution
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Repeatability The inability to get the same answer from repeated measurements made of the same item under absolutely identical conditions
Possible Cause
Lack of standard operating procedures (SOP) lack of training measuring system variablilty
Repeatability
Equipment Variation
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Reproducibility The inability to get the same answer from repeated measurements made under various conditions from different inspectors
Possible Cause
Lack of SOP lack of training
Reproducibility
Appraiser Variation
VARIABLE MSA ndash GAGE RampR STUDY
bull Gage RampR is the combined estimate of
measurement system Repeatability and
Reproducibility
bull Typically a 3-person study is performed Each person randomly measures 10 marked parts per trial
Each person can perform up to 3 trials
bull There are 3 key indicators EV or Equipment Variation
AV or Appraiser Variation
Overall GRR
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
PLOT DATA ON CONTROL CHARTS
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1 2 3 4 5 6 7 8 9 10
Ave
rage
(X
ba
r)
X Bar Chart
UCL
LCL
X Bar
34
PLOT DATA ON CONTROL CHARTS
001
003
005
007
009
011
013
015
017
019
021
023
025
1 2 3 4 5 6 7 8 9 10
R Chart
UCL
LCL
35
PROCEDURE TO DETERMINE IF PROCESS IS IN A STATE OF
STATISTICAL CONTROL
7 If process is determined to be ldquoNOT STABLErdquo then stop and find out what
an assignable cause might be fix and then repeat the complete process of
collecting new data
8 If the process is determined to be ldquoSTABLErdquo then you may use the
control charts you developed to monitor future production to ensure that the
process REMAINS stable
More Samples for Control charts
36
READING OF CONTROL CHART
Control charts can determine whether a process is behaving in an unusual way The quality of the individual points of a subset is determined unstable if any of the
following occurs
Rule 1 Any point falls beyond 3σ from the centreline(this is represented by the upper and
lower control limits)
Rule 2 Two out of three consecutive points fall beyond 2σ on the same side of the
centreline
Rule 3 Four out of five consecutive points fall beyond 1σ on the same side of the
centreline
Rule 4 Nine or more consecutive points fall on the same side of the centreline
(Ref Next page for sample)
37
READING THE CONTROL CHART
38
CONTROL CHARTS FOR ATTRIBUTES ndashP-CHARTS amp C-CHARTS
Attributes are discrete events yesno or passfail
Use P-Charts for quality characteristics that are discrete and involve yesno or goodbad decisions
Eg
Number of leaking caulking tubes in a box of 48
Number of broken eggs in a carton
Use C-Charts for discrete defects when there can be more than one defect per unit
Eg
Number of stains in a carpet sample cut from a production run
Number of complaints per customer at a hotel
39
P-CHART EXAMPLE A PRODUCTION MANAGER FOR A TIRE COMPANY HAS INSPECTED THE NUMBER OF
DEFECTIVE TIRES IN FIVE RANDOM SAMPLES WITH 20 TIRES IN EACH SAMPLE THE TABLE BELOW SHOWS THE
NUMBER OF DEFECTIVE TIRES IN EACH SAMPLE OF 20 TIRES CALCULATE THE CONTROL LIMITS
Sample Number of
Defective Tires
Number of Tires in each
Sample
Proportion Defective
1 3 20 15
2 2 20 10
3 1 20 05
4 2 20 10
5 2 20 05
Total 9 100 09
01023(064)09σzpLCL
2823(064)09σzpUCL
06420
(09)(91)
n
)p(1pσ
09100
9
Inspected Total
DefectivespCL
p
p
p
Solution
40
P- CONTROL CHART
41
C-CHART EXAMPLE THE NUMBER OF WEEKLY CUSTOMER COMPLAINTS ARE MONITORED IN A LARGE HOTEL USING A C-CHART DEVELOP THREE SIGMA CONTROL LIMITS USING THE DATA TABLE BELOW
Week Number of Complaints
1 3
2 2
3 3
4 1
5 3
6 3
7 2
8 1
9 3
10 1
Total 22
022522322ccLCL
66522322ccUCL
2210
22
samples of
complaintsc
c
c
z
z
Solution
42
C- CONTROL CHART
43
The ability of a process to meet product designtechnical specifications
Assessing capability involves evaluating process variability relative to preset product or service specifications
Process Capability ndash Cp and Cpk
Cp assumes that the process is centered in the specification range
Cpk helps to address a possible lack of centering of the process
PROCESS CAPABILITY
6σ
LSLUSL
width process
width ionspecificatCp
3σ
LSLμ
3σ
μUSLminCpk
44
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
45
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
46
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
47
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
--and an individual part is measured at 520rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
48
GRAPHING THE TOLERANCE AND MEASUREMENTS
Suppose we made and measured several more
units and they were all EXACTLY the same
We wouldnrsquot have very many part problems
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
X
X
X
49
GRAPHING THE TOLERANCE AND MEASUREMENTS
In the real world units are NOT EXACTLY the same
Everything VARIES
The question isnrsquot IF units vary
Itrsquos how much when and why
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
XX
XXX
XXXXX
XXXXXXX
50
The ldquonormal bell curverdquo
Widths heights depths thicknesses weights speeds strengths
and many other types of measurements when charted as a
histogram often form the shape of a bell
A ldquoperfect bellrdquo like a ldquoperfect circlerdquo doesnrsquot occur in nature but
many processes are close enough to make the bell curve useful
(A number of common industrial measurements such as flatness and straightness do NOT tend to distribute in a bell shape their proper statistical analysis is performed using models other than the bell curve)
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
51
What is a ldquostandard deviationrdquo
If we measure the DISTANCE from the CENTER of the bell
to each individual measurement that makes up the bell curve
we can find a TYPICAL DISTANCE
The most commonly used statistic to estimate this distance is the
Standard Deviation (also called ldquoSigmardquo)
Because of the natural shape of the bell curve the area of +1 to ndash1
standard deviations includes about 68 of the curve
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
Typical distance
from the center +1
standard deviation
Typical distance
from the center -1
standard deviation
52
How much of the curve is included in how many standard
deviations
From ndash1 to +1 is about 68 of the bell curve
From ndash2 to +2 is about 95
From ndash3 to +3 is about 9973
From ndash4 to +4 is about 9999
(NOTE We usually show the bell from ndash3 to +3 to make it easier to draw but in concept the ldquotailsrdquo of the bell get very thin and go on forever)
-6 -5 -4 -3 -2 -1 +1 +2 +3 +4 +5 +6 0
53
A
B
What is Cpk It is a measure of how well a process is within a specification
Cpk = A divided by B
A = Distance from process mean to closest spec limit
B = 3 Standard Deviations (also called ldquo3 Sigmardquo)
A bigger Cpk is better because fewer units will be beyond spec
(A bigger ldquoArdquo and a smaller ldquoBrdquo are better)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
54
A
B
ldquoProcess Capabilityrdquo is the ability of a process
to fit its output within the tolerances
hellipa LARGER ldquoArdquo
hellipand a SMALLER ldquoBrdquo
hellipmeans BETTER ldquoProcess Capabilityrdquo
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
55
A
B
An Analogy
Analogy
The bell curve is your automobile
The spec limits are the edges of your garage door
If A = B you are hitting the frame of your garage door with your car
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
56
A
B
How can we make Cpk (A divided by B) better
1 Design the product so a wider tolerance is functional (ldquorobust designrdquo)
2 Choose equipment and methods for a good safety margin (ldquoprocess capabilityrdquo)
3 Correctly adjust but only when needed (ldquocontrolrdquo)
4 Discover ways to narrow the natural variation (ldquoimprovementrdquo)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
57
A
B
What does a very good Cpk do for us
This process is producing good units with a good safety margin
Note that when Cpk = 2 our process mean is 6 standard deviations from
the nearest spec so we say it has ldquo6 Sigma Capabilityrdquo
Specification
Limit
Specification
Limit
This Cpk is
about 2
Very good
Mean
58
A
B
What does a problem Cpk look like
This process is in danger of producing some defects
It is too close to the specification limits
(Remember the bell curve tail goes further than Bhellip hellipwe only show the bell to 3-sigma to make it easier to draw)
Specification
Limit
Specification
Limit
This Cpk is just
slightly greater
than 1 Not good
59
A
B
What does a very bad Cpk look like
A significant part of the ldquotailrdquo is hanging out beyond the spec limits
This process is producing scrap rework and customer rejects
Notice that if distance ldquoArdquo approaches zerohellip
hellipthe Cpk would approach zero andhellip
hellipthe process would become 50 defective
Specification
Limit
Specification
Limit
This Cpk is less
than 1 We desire
a minimum of 133
and ultimately we
want 2 or more
60
-
Q amp A
61
MEASUREMENT SYSTEM ANALYSIS (MSA)
An MSA is a statistical tool used to determine if a measurement system is capable of precise measurement
What is It
Objective or Purpose
bull To determine how much error is in the measurement due to the measurement process itself
bull Quantifies the variability added by the measurement system
bull Applicable to attribute data and variable data
When to Use It
bull On the critical inputs and outputs prior to collecting data for analysis
bull For any new or modified process in order to ensure the quality of the data
Measurement System Analysis is an analysis of the measurement process not an analysis of the people
IMPORTANT
Who Should be Involved
Everyone that measures and makes decisions about these measurements should be involved in the MSA
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The observed variation in process output measurements is not simply the variation in the process itself it is the variation in the process plus the variation in measurement that results from an inadequate measurement system
Conducting an MSA reduces the likelihood of passing a bad part or rejecting a good part
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The output of the process measured by bull Cycle time bull Dimensional data bull Number of defects and others
Observed Variation
Process Variation
Measurement System
Variation
Reproducibility
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Accuracy (Central Location)
OBSERVED VARIATION
Calibration addresses accuracy
Measurement System Analysis (MSA)
MEASUREMENT SYSTEM ERRORS
Accuracy difference between the observed measurement and the actual measurement
Precision variation that occurs when measuring the same part with the same instrument
MEASUREMENT SYSTEM ERROR
Precise but not
accurate
Accurate but not
precise
Not accurate or
precise
Accurate and
precise
ACCURACY OF MEASUREMENT
Broken down into three components
aStability
The consistency of measurements over time
bBias
A measure of the amount of partiality in the system
cLinearity
A measure of the bias values through the expected
range of measurements
OBSERVED VARIATION
Observed Variation
Process Variation
Measurement System
Variation
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Reproducibility
Accuracy (Central Location)
Calibration Addresses Accuracy
Letrsquos take a closer look at Precision
Measurement System Analysis (MSA)
Measurement System Analysis (MSA)
Error in Resolution The inability to detect small changes
Possible Cause
Wrong measurement device selected - divisions on scale not fine enough to detect changes
Resolution
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Repeatability The inability to get the same answer from repeated measurements made of the same item under absolutely identical conditions
Possible Cause
Lack of standard operating procedures (SOP) lack of training measuring system variablilty
Repeatability
Equipment Variation
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Reproducibility The inability to get the same answer from repeated measurements made under various conditions from different inspectors
Possible Cause
Lack of SOP lack of training
Reproducibility
Appraiser Variation
VARIABLE MSA ndash GAGE RampR STUDY
bull Gage RampR is the combined estimate of
measurement system Repeatability and
Reproducibility
bull Typically a 3-person study is performed Each person randomly measures 10 marked parts per trial
Each person can perform up to 3 trials
bull There are 3 key indicators EV or Equipment Variation
AV or Appraiser Variation
Overall GRR
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
PLOT DATA ON CONTROL CHARTS
001
003
005
007
009
011
013
015
017
019
021
023
025
1 2 3 4 5 6 7 8 9 10
R Chart
UCL
LCL
35
PROCEDURE TO DETERMINE IF PROCESS IS IN A STATE OF
STATISTICAL CONTROL
7 If process is determined to be ldquoNOT STABLErdquo then stop and find out what
an assignable cause might be fix and then repeat the complete process of
collecting new data
8 If the process is determined to be ldquoSTABLErdquo then you may use the
control charts you developed to monitor future production to ensure that the
process REMAINS stable
More Samples for Control charts
36
READING OF CONTROL CHART
Control charts can determine whether a process is behaving in an unusual way The quality of the individual points of a subset is determined unstable if any of the
following occurs
Rule 1 Any point falls beyond 3σ from the centreline(this is represented by the upper and
lower control limits)
Rule 2 Two out of three consecutive points fall beyond 2σ on the same side of the
centreline
Rule 3 Four out of five consecutive points fall beyond 1σ on the same side of the
centreline
Rule 4 Nine or more consecutive points fall on the same side of the centreline
(Ref Next page for sample)
37
READING THE CONTROL CHART
38
CONTROL CHARTS FOR ATTRIBUTES ndashP-CHARTS amp C-CHARTS
Attributes are discrete events yesno or passfail
Use P-Charts for quality characteristics that are discrete and involve yesno or goodbad decisions
Eg
Number of leaking caulking tubes in a box of 48
Number of broken eggs in a carton
Use C-Charts for discrete defects when there can be more than one defect per unit
Eg
Number of stains in a carpet sample cut from a production run
Number of complaints per customer at a hotel
39
P-CHART EXAMPLE A PRODUCTION MANAGER FOR A TIRE COMPANY HAS INSPECTED THE NUMBER OF
DEFECTIVE TIRES IN FIVE RANDOM SAMPLES WITH 20 TIRES IN EACH SAMPLE THE TABLE BELOW SHOWS THE
NUMBER OF DEFECTIVE TIRES IN EACH SAMPLE OF 20 TIRES CALCULATE THE CONTROL LIMITS
Sample Number of
Defective Tires
Number of Tires in each
Sample
Proportion Defective
1 3 20 15
2 2 20 10
3 1 20 05
4 2 20 10
5 2 20 05
Total 9 100 09
01023(064)09σzpLCL
2823(064)09σzpUCL
06420
(09)(91)
n
)p(1pσ
09100
9
Inspected Total
DefectivespCL
p
p
p
Solution
40
P- CONTROL CHART
41
C-CHART EXAMPLE THE NUMBER OF WEEKLY CUSTOMER COMPLAINTS ARE MONITORED IN A LARGE HOTEL USING A C-CHART DEVELOP THREE SIGMA CONTROL LIMITS USING THE DATA TABLE BELOW
Week Number of Complaints
1 3
2 2
3 3
4 1
5 3
6 3
7 2
8 1
9 3
10 1
Total 22
022522322ccLCL
66522322ccUCL
2210
22
samples of
complaintsc
c
c
z
z
Solution
42
C- CONTROL CHART
43
The ability of a process to meet product designtechnical specifications
Assessing capability involves evaluating process variability relative to preset product or service specifications
Process Capability ndash Cp and Cpk
Cp assumes that the process is centered in the specification range
Cpk helps to address a possible lack of centering of the process
PROCESS CAPABILITY
6σ
LSLUSL
width process
width ionspecificatCp
3σ
LSLμ
3σ
μUSLminCpk
44
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
45
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
46
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
47
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
--and an individual part is measured at 520rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
48
GRAPHING THE TOLERANCE AND MEASUREMENTS
Suppose we made and measured several more
units and they were all EXACTLY the same
We wouldnrsquot have very many part problems
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
X
X
X
49
GRAPHING THE TOLERANCE AND MEASUREMENTS
In the real world units are NOT EXACTLY the same
Everything VARIES
The question isnrsquot IF units vary
Itrsquos how much when and why
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
XX
XXX
XXXXX
XXXXXXX
50
The ldquonormal bell curverdquo
Widths heights depths thicknesses weights speeds strengths
and many other types of measurements when charted as a
histogram often form the shape of a bell
A ldquoperfect bellrdquo like a ldquoperfect circlerdquo doesnrsquot occur in nature but
many processes are close enough to make the bell curve useful
(A number of common industrial measurements such as flatness and straightness do NOT tend to distribute in a bell shape their proper statistical analysis is performed using models other than the bell curve)
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
51
What is a ldquostandard deviationrdquo
If we measure the DISTANCE from the CENTER of the bell
to each individual measurement that makes up the bell curve
we can find a TYPICAL DISTANCE
The most commonly used statistic to estimate this distance is the
Standard Deviation (also called ldquoSigmardquo)
Because of the natural shape of the bell curve the area of +1 to ndash1
standard deviations includes about 68 of the curve
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
Typical distance
from the center +1
standard deviation
Typical distance
from the center -1
standard deviation
52
How much of the curve is included in how many standard
deviations
From ndash1 to +1 is about 68 of the bell curve
From ndash2 to +2 is about 95
From ndash3 to +3 is about 9973
From ndash4 to +4 is about 9999
(NOTE We usually show the bell from ndash3 to +3 to make it easier to draw but in concept the ldquotailsrdquo of the bell get very thin and go on forever)
-6 -5 -4 -3 -2 -1 +1 +2 +3 +4 +5 +6 0
53
A
B
What is Cpk It is a measure of how well a process is within a specification
Cpk = A divided by B
A = Distance from process mean to closest spec limit
B = 3 Standard Deviations (also called ldquo3 Sigmardquo)
A bigger Cpk is better because fewer units will be beyond spec
(A bigger ldquoArdquo and a smaller ldquoBrdquo are better)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
54
A
B
ldquoProcess Capabilityrdquo is the ability of a process
to fit its output within the tolerances
hellipa LARGER ldquoArdquo
hellipand a SMALLER ldquoBrdquo
hellipmeans BETTER ldquoProcess Capabilityrdquo
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
55
A
B
An Analogy
Analogy
The bell curve is your automobile
The spec limits are the edges of your garage door
If A = B you are hitting the frame of your garage door with your car
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
56
A
B
How can we make Cpk (A divided by B) better
1 Design the product so a wider tolerance is functional (ldquorobust designrdquo)
2 Choose equipment and methods for a good safety margin (ldquoprocess capabilityrdquo)
3 Correctly adjust but only when needed (ldquocontrolrdquo)
4 Discover ways to narrow the natural variation (ldquoimprovementrdquo)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
57
A
B
What does a very good Cpk do for us
This process is producing good units with a good safety margin
Note that when Cpk = 2 our process mean is 6 standard deviations from
the nearest spec so we say it has ldquo6 Sigma Capabilityrdquo
Specification
Limit
Specification
Limit
This Cpk is
about 2
Very good
Mean
58
A
B
What does a problem Cpk look like
This process is in danger of producing some defects
It is too close to the specification limits
(Remember the bell curve tail goes further than Bhellip hellipwe only show the bell to 3-sigma to make it easier to draw)
Specification
Limit
Specification
Limit
This Cpk is just
slightly greater
than 1 Not good
59
A
B
What does a very bad Cpk look like
A significant part of the ldquotailrdquo is hanging out beyond the spec limits
This process is producing scrap rework and customer rejects
Notice that if distance ldquoArdquo approaches zerohellip
hellipthe Cpk would approach zero andhellip
hellipthe process would become 50 defective
Specification
Limit
Specification
Limit
This Cpk is less
than 1 We desire
a minimum of 133
and ultimately we
want 2 or more
60
-
Q amp A
61
MEASUREMENT SYSTEM ANALYSIS (MSA)
An MSA is a statistical tool used to determine if a measurement system is capable of precise measurement
What is It
Objective or Purpose
bull To determine how much error is in the measurement due to the measurement process itself
bull Quantifies the variability added by the measurement system
bull Applicable to attribute data and variable data
When to Use It
bull On the critical inputs and outputs prior to collecting data for analysis
bull For any new or modified process in order to ensure the quality of the data
Measurement System Analysis is an analysis of the measurement process not an analysis of the people
IMPORTANT
Who Should be Involved
Everyone that measures and makes decisions about these measurements should be involved in the MSA
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The observed variation in process output measurements is not simply the variation in the process itself it is the variation in the process plus the variation in measurement that results from an inadequate measurement system
Conducting an MSA reduces the likelihood of passing a bad part or rejecting a good part
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The output of the process measured by bull Cycle time bull Dimensional data bull Number of defects and others
Observed Variation
Process Variation
Measurement System
Variation
Reproducibility
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Accuracy (Central Location)
OBSERVED VARIATION
Calibration addresses accuracy
Measurement System Analysis (MSA)
MEASUREMENT SYSTEM ERRORS
Accuracy difference between the observed measurement and the actual measurement
Precision variation that occurs when measuring the same part with the same instrument
MEASUREMENT SYSTEM ERROR
Precise but not
accurate
Accurate but not
precise
Not accurate or
precise
Accurate and
precise
ACCURACY OF MEASUREMENT
Broken down into three components
aStability
The consistency of measurements over time
bBias
A measure of the amount of partiality in the system
cLinearity
A measure of the bias values through the expected
range of measurements
OBSERVED VARIATION
Observed Variation
Process Variation
Measurement System
Variation
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Reproducibility
Accuracy (Central Location)
Calibration Addresses Accuracy
Letrsquos take a closer look at Precision
Measurement System Analysis (MSA)
Measurement System Analysis (MSA)
Error in Resolution The inability to detect small changes
Possible Cause
Wrong measurement device selected - divisions on scale not fine enough to detect changes
Resolution
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Repeatability The inability to get the same answer from repeated measurements made of the same item under absolutely identical conditions
Possible Cause
Lack of standard operating procedures (SOP) lack of training measuring system variablilty
Repeatability
Equipment Variation
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Reproducibility The inability to get the same answer from repeated measurements made under various conditions from different inspectors
Possible Cause
Lack of SOP lack of training
Reproducibility
Appraiser Variation
VARIABLE MSA ndash GAGE RampR STUDY
bull Gage RampR is the combined estimate of
measurement system Repeatability and
Reproducibility
bull Typically a 3-person study is performed Each person randomly measures 10 marked parts per trial
Each person can perform up to 3 trials
bull There are 3 key indicators EV or Equipment Variation
AV or Appraiser Variation
Overall GRR
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
PROCEDURE TO DETERMINE IF PROCESS IS IN A STATE OF
STATISTICAL CONTROL
7 If process is determined to be ldquoNOT STABLErdquo then stop and find out what
an assignable cause might be fix and then repeat the complete process of
collecting new data
8 If the process is determined to be ldquoSTABLErdquo then you may use the
control charts you developed to monitor future production to ensure that the
process REMAINS stable
More Samples for Control charts
36
READING OF CONTROL CHART
Control charts can determine whether a process is behaving in an unusual way The quality of the individual points of a subset is determined unstable if any of the
following occurs
Rule 1 Any point falls beyond 3σ from the centreline(this is represented by the upper and
lower control limits)
Rule 2 Two out of three consecutive points fall beyond 2σ on the same side of the
centreline
Rule 3 Four out of five consecutive points fall beyond 1σ on the same side of the
centreline
Rule 4 Nine or more consecutive points fall on the same side of the centreline
(Ref Next page for sample)
37
READING THE CONTROL CHART
38
CONTROL CHARTS FOR ATTRIBUTES ndashP-CHARTS amp C-CHARTS
Attributes are discrete events yesno or passfail
Use P-Charts for quality characteristics that are discrete and involve yesno or goodbad decisions
Eg
Number of leaking caulking tubes in a box of 48
Number of broken eggs in a carton
Use C-Charts for discrete defects when there can be more than one defect per unit
Eg
Number of stains in a carpet sample cut from a production run
Number of complaints per customer at a hotel
39
P-CHART EXAMPLE A PRODUCTION MANAGER FOR A TIRE COMPANY HAS INSPECTED THE NUMBER OF
DEFECTIVE TIRES IN FIVE RANDOM SAMPLES WITH 20 TIRES IN EACH SAMPLE THE TABLE BELOW SHOWS THE
NUMBER OF DEFECTIVE TIRES IN EACH SAMPLE OF 20 TIRES CALCULATE THE CONTROL LIMITS
Sample Number of
Defective Tires
Number of Tires in each
Sample
Proportion Defective
1 3 20 15
2 2 20 10
3 1 20 05
4 2 20 10
5 2 20 05
Total 9 100 09
01023(064)09σzpLCL
2823(064)09σzpUCL
06420
(09)(91)
n
)p(1pσ
09100
9
Inspected Total
DefectivespCL
p
p
p
Solution
40
P- CONTROL CHART
41
C-CHART EXAMPLE THE NUMBER OF WEEKLY CUSTOMER COMPLAINTS ARE MONITORED IN A LARGE HOTEL USING A C-CHART DEVELOP THREE SIGMA CONTROL LIMITS USING THE DATA TABLE BELOW
Week Number of Complaints
1 3
2 2
3 3
4 1
5 3
6 3
7 2
8 1
9 3
10 1
Total 22
022522322ccLCL
66522322ccUCL
2210
22
samples of
complaintsc
c
c
z
z
Solution
42
C- CONTROL CHART
43
The ability of a process to meet product designtechnical specifications
Assessing capability involves evaluating process variability relative to preset product or service specifications
Process Capability ndash Cp and Cpk
Cp assumes that the process is centered in the specification range
Cpk helps to address a possible lack of centering of the process
PROCESS CAPABILITY
6σ
LSLUSL
width process
width ionspecificatCp
3σ
LSLμ
3σ
μUSLminCpk
44
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
45
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
46
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
47
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
--and an individual part is measured at 520rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
48
GRAPHING THE TOLERANCE AND MEASUREMENTS
Suppose we made and measured several more
units and they were all EXACTLY the same
We wouldnrsquot have very many part problems
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
X
X
X
49
GRAPHING THE TOLERANCE AND MEASUREMENTS
In the real world units are NOT EXACTLY the same
Everything VARIES
The question isnrsquot IF units vary
Itrsquos how much when and why
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
XX
XXX
XXXXX
XXXXXXX
50
The ldquonormal bell curverdquo
Widths heights depths thicknesses weights speeds strengths
and many other types of measurements when charted as a
histogram often form the shape of a bell
A ldquoperfect bellrdquo like a ldquoperfect circlerdquo doesnrsquot occur in nature but
many processes are close enough to make the bell curve useful
(A number of common industrial measurements such as flatness and straightness do NOT tend to distribute in a bell shape their proper statistical analysis is performed using models other than the bell curve)
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
51
What is a ldquostandard deviationrdquo
If we measure the DISTANCE from the CENTER of the bell
to each individual measurement that makes up the bell curve
we can find a TYPICAL DISTANCE
The most commonly used statistic to estimate this distance is the
Standard Deviation (also called ldquoSigmardquo)
Because of the natural shape of the bell curve the area of +1 to ndash1
standard deviations includes about 68 of the curve
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
Typical distance
from the center +1
standard deviation
Typical distance
from the center -1
standard deviation
52
How much of the curve is included in how many standard
deviations
From ndash1 to +1 is about 68 of the bell curve
From ndash2 to +2 is about 95
From ndash3 to +3 is about 9973
From ndash4 to +4 is about 9999
(NOTE We usually show the bell from ndash3 to +3 to make it easier to draw but in concept the ldquotailsrdquo of the bell get very thin and go on forever)
-6 -5 -4 -3 -2 -1 +1 +2 +3 +4 +5 +6 0
53
A
B
What is Cpk It is a measure of how well a process is within a specification
Cpk = A divided by B
A = Distance from process mean to closest spec limit
B = 3 Standard Deviations (also called ldquo3 Sigmardquo)
A bigger Cpk is better because fewer units will be beyond spec
(A bigger ldquoArdquo and a smaller ldquoBrdquo are better)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
54
A
B
ldquoProcess Capabilityrdquo is the ability of a process
to fit its output within the tolerances
hellipa LARGER ldquoArdquo
hellipand a SMALLER ldquoBrdquo
hellipmeans BETTER ldquoProcess Capabilityrdquo
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
55
A
B
An Analogy
Analogy
The bell curve is your automobile
The spec limits are the edges of your garage door
If A = B you are hitting the frame of your garage door with your car
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
56
A
B
How can we make Cpk (A divided by B) better
1 Design the product so a wider tolerance is functional (ldquorobust designrdquo)
2 Choose equipment and methods for a good safety margin (ldquoprocess capabilityrdquo)
3 Correctly adjust but only when needed (ldquocontrolrdquo)
4 Discover ways to narrow the natural variation (ldquoimprovementrdquo)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
57
A
B
What does a very good Cpk do for us
This process is producing good units with a good safety margin
Note that when Cpk = 2 our process mean is 6 standard deviations from
the nearest spec so we say it has ldquo6 Sigma Capabilityrdquo
Specification
Limit
Specification
Limit
This Cpk is
about 2
Very good
Mean
58
A
B
What does a problem Cpk look like
This process is in danger of producing some defects
It is too close to the specification limits
(Remember the bell curve tail goes further than Bhellip hellipwe only show the bell to 3-sigma to make it easier to draw)
Specification
Limit
Specification
Limit
This Cpk is just
slightly greater
than 1 Not good
59
A
B
What does a very bad Cpk look like
A significant part of the ldquotailrdquo is hanging out beyond the spec limits
This process is producing scrap rework and customer rejects
Notice that if distance ldquoArdquo approaches zerohellip
hellipthe Cpk would approach zero andhellip
hellipthe process would become 50 defective
Specification
Limit
Specification
Limit
This Cpk is less
than 1 We desire
a minimum of 133
and ultimately we
want 2 or more
60
-
Q amp A
61
MEASUREMENT SYSTEM ANALYSIS (MSA)
An MSA is a statistical tool used to determine if a measurement system is capable of precise measurement
What is It
Objective or Purpose
bull To determine how much error is in the measurement due to the measurement process itself
bull Quantifies the variability added by the measurement system
bull Applicable to attribute data and variable data
When to Use It
bull On the critical inputs and outputs prior to collecting data for analysis
bull For any new or modified process in order to ensure the quality of the data
Measurement System Analysis is an analysis of the measurement process not an analysis of the people
IMPORTANT
Who Should be Involved
Everyone that measures and makes decisions about these measurements should be involved in the MSA
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The observed variation in process output measurements is not simply the variation in the process itself it is the variation in the process plus the variation in measurement that results from an inadequate measurement system
Conducting an MSA reduces the likelihood of passing a bad part or rejecting a good part
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The output of the process measured by bull Cycle time bull Dimensional data bull Number of defects and others
Observed Variation
Process Variation
Measurement System
Variation
Reproducibility
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Accuracy (Central Location)
OBSERVED VARIATION
Calibration addresses accuracy
Measurement System Analysis (MSA)
MEASUREMENT SYSTEM ERRORS
Accuracy difference between the observed measurement and the actual measurement
Precision variation that occurs when measuring the same part with the same instrument
MEASUREMENT SYSTEM ERROR
Precise but not
accurate
Accurate but not
precise
Not accurate or
precise
Accurate and
precise
ACCURACY OF MEASUREMENT
Broken down into three components
aStability
The consistency of measurements over time
bBias
A measure of the amount of partiality in the system
cLinearity
A measure of the bias values through the expected
range of measurements
OBSERVED VARIATION
Observed Variation
Process Variation
Measurement System
Variation
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Reproducibility
Accuracy (Central Location)
Calibration Addresses Accuracy
Letrsquos take a closer look at Precision
Measurement System Analysis (MSA)
Measurement System Analysis (MSA)
Error in Resolution The inability to detect small changes
Possible Cause
Wrong measurement device selected - divisions on scale not fine enough to detect changes
Resolution
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Repeatability The inability to get the same answer from repeated measurements made of the same item under absolutely identical conditions
Possible Cause
Lack of standard operating procedures (SOP) lack of training measuring system variablilty
Repeatability
Equipment Variation
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Reproducibility The inability to get the same answer from repeated measurements made under various conditions from different inspectors
Possible Cause
Lack of SOP lack of training
Reproducibility
Appraiser Variation
VARIABLE MSA ndash GAGE RampR STUDY
bull Gage RampR is the combined estimate of
measurement system Repeatability and
Reproducibility
bull Typically a 3-person study is performed Each person randomly measures 10 marked parts per trial
Each person can perform up to 3 trials
bull There are 3 key indicators EV or Equipment Variation
AV or Appraiser Variation
Overall GRR
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
READING OF CONTROL CHART
Control charts can determine whether a process is behaving in an unusual way The quality of the individual points of a subset is determined unstable if any of the
following occurs
Rule 1 Any point falls beyond 3σ from the centreline(this is represented by the upper and
lower control limits)
Rule 2 Two out of three consecutive points fall beyond 2σ on the same side of the
centreline
Rule 3 Four out of five consecutive points fall beyond 1σ on the same side of the
centreline
Rule 4 Nine or more consecutive points fall on the same side of the centreline
(Ref Next page for sample)
37
READING THE CONTROL CHART
38
CONTROL CHARTS FOR ATTRIBUTES ndashP-CHARTS amp C-CHARTS
Attributes are discrete events yesno or passfail
Use P-Charts for quality characteristics that are discrete and involve yesno or goodbad decisions
Eg
Number of leaking caulking tubes in a box of 48
Number of broken eggs in a carton
Use C-Charts for discrete defects when there can be more than one defect per unit
Eg
Number of stains in a carpet sample cut from a production run
Number of complaints per customer at a hotel
39
P-CHART EXAMPLE A PRODUCTION MANAGER FOR A TIRE COMPANY HAS INSPECTED THE NUMBER OF
DEFECTIVE TIRES IN FIVE RANDOM SAMPLES WITH 20 TIRES IN EACH SAMPLE THE TABLE BELOW SHOWS THE
NUMBER OF DEFECTIVE TIRES IN EACH SAMPLE OF 20 TIRES CALCULATE THE CONTROL LIMITS
Sample Number of
Defective Tires
Number of Tires in each
Sample
Proportion Defective
1 3 20 15
2 2 20 10
3 1 20 05
4 2 20 10
5 2 20 05
Total 9 100 09
01023(064)09σzpLCL
2823(064)09σzpUCL
06420
(09)(91)
n
)p(1pσ
09100
9
Inspected Total
DefectivespCL
p
p
p
Solution
40
P- CONTROL CHART
41
C-CHART EXAMPLE THE NUMBER OF WEEKLY CUSTOMER COMPLAINTS ARE MONITORED IN A LARGE HOTEL USING A C-CHART DEVELOP THREE SIGMA CONTROL LIMITS USING THE DATA TABLE BELOW
Week Number of Complaints
1 3
2 2
3 3
4 1
5 3
6 3
7 2
8 1
9 3
10 1
Total 22
022522322ccLCL
66522322ccUCL
2210
22
samples of
complaintsc
c
c
z
z
Solution
42
C- CONTROL CHART
43
The ability of a process to meet product designtechnical specifications
Assessing capability involves evaluating process variability relative to preset product or service specifications
Process Capability ndash Cp and Cpk
Cp assumes that the process is centered in the specification range
Cpk helps to address a possible lack of centering of the process
PROCESS CAPABILITY
6σ
LSLUSL
width process
width ionspecificatCp
3σ
LSLμ
3σ
μUSLminCpk
44
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
45
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
46
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
47
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
--and an individual part is measured at 520rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
48
GRAPHING THE TOLERANCE AND MEASUREMENTS
Suppose we made and measured several more
units and they were all EXACTLY the same
We wouldnrsquot have very many part problems
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
X
X
X
49
GRAPHING THE TOLERANCE AND MEASUREMENTS
In the real world units are NOT EXACTLY the same
Everything VARIES
The question isnrsquot IF units vary
Itrsquos how much when and why
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
XX
XXX
XXXXX
XXXXXXX
50
The ldquonormal bell curverdquo
Widths heights depths thicknesses weights speeds strengths
and many other types of measurements when charted as a
histogram often form the shape of a bell
A ldquoperfect bellrdquo like a ldquoperfect circlerdquo doesnrsquot occur in nature but
many processes are close enough to make the bell curve useful
(A number of common industrial measurements such as flatness and straightness do NOT tend to distribute in a bell shape their proper statistical analysis is performed using models other than the bell curve)
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
51
What is a ldquostandard deviationrdquo
If we measure the DISTANCE from the CENTER of the bell
to each individual measurement that makes up the bell curve
we can find a TYPICAL DISTANCE
The most commonly used statistic to estimate this distance is the
Standard Deviation (also called ldquoSigmardquo)
Because of the natural shape of the bell curve the area of +1 to ndash1
standard deviations includes about 68 of the curve
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
Typical distance
from the center +1
standard deviation
Typical distance
from the center -1
standard deviation
52
How much of the curve is included in how many standard
deviations
From ndash1 to +1 is about 68 of the bell curve
From ndash2 to +2 is about 95
From ndash3 to +3 is about 9973
From ndash4 to +4 is about 9999
(NOTE We usually show the bell from ndash3 to +3 to make it easier to draw but in concept the ldquotailsrdquo of the bell get very thin and go on forever)
-6 -5 -4 -3 -2 -1 +1 +2 +3 +4 +5 +6 0
53
A
B
What is Cpk It is a measure of how well a process is within a specification
Cpk = A divided by B
A = Distance from process mean to closest spec limit
B = 3 Standard Deviations (also called ldquo3 Sigmardquo)
A bigger Cpk is better because fewer units will be beyond spec
(A bigger ldquoArdquo and a smaller ldquoBrdquo are better)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
54
A
B
ldquoProcess Capabilityrdquo is the ability of a process
to fit its output within the tolerances
hellipa LARGER ldquoArdquo
hellipand a SMALLER ldquoBrdquo
hellipmeans BETTER ldquoProcess Capabilityrdquo
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
55
A
B
An Analogy
Analogy
The bell curve is your automobile
The spec limits are the edges of your garage door
If A = B you are hitting the frame of your garage door with your car
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
56
A
B
How can we make Cpk (A divided by B) better
1 Design the product so a wider tolerance is functional (ldquorobust designrdquo)
2 Choose equipment and methods for a good safety margin (ldquoprocess capabilityrdquo)
3 Correctly adjust but only when needed (ldquocontrolrdquo)
4 Discover ways to narrow the natural variation (ldquoimprovementrdquo)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
57
A
B
What does a very good Cpk do for us
This process is producing good units with a good safety margin
Note that when Cpk = 2 our process mean is 6 standard deviations from
the nearest spec so we say it has ldquo6 Sigma Capabilityrdquo
Specification
Limit
Specification
Limit
This Cpk is
about 2
Very good
Mean
58
A
B
What does a problem Cpk look like
This process is in danger of producing some defects
It is too close to the specification limits
(Remember the bell curve tail goes further than Bhellip hellipwe only show the bell to 3-sigma to make it easier to draw)
Specification
Limit
Specification
Limit
This Cpk is just
slightly greater
than 1 Not good
59
A
B
What does a very bad Cpk look like
A significant part of the ldquotailrdquo is hanging out beyond the spec limits
This process is producing scrap rework and customer rejects
Notice that if distance ldquoArdquo approaches zerohellip
hellipthe Cpk would approach zero andhellip
hellipthe process would become 50 defective
Specification
Limit
Specification
Limit
This Cpk is less
than 1 We desire
a minimum of 133
and ultimately we
want 2 or more
60
-
Q amp A
61
MEASUREMENT SYSTEM ANALYSIS (MSA)
An MSA is a statistical tool used to determine if a measurement system is capable of precise measurement
What is It
Objective or Purpose
bull To determine how much error is in the measurement due to the measurement process itself
bull Quantifies the variability added by the measurement system
bull Applicable to attribute data and variable data
When to Use It
bull On the critical inputs and outputs prior to collecting data for analysis
bull For any new or modified process in order to ensure the quality of the data
Measurement System Analysis is an analysis of the measurement process not an analysis of the people
IMPORTANT
Who Should be Involved
Everyone that measures and makes decisions about these measurements should be involved in the MSA
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The observed variation in process output measurements is not simply the variation in the process itself it is the variation in the process plus the variation in measurement that results from an inadequate measurement system
Conducting an MSA reduces the likelihood of passing a bad part or rejecting a good part
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The output of the process measured by bull Cycle time bull Dimensional data bull Number of defects and others
Observed Variation
Process Variation
Measurement System
Variation
Reproducibility
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Accuracy (Central Location)
OBSERVED VARIATION
Calibration addresses accuracy
Measurement System Analysis (MSA)
MEASUREMENT SYSTEM ERRORS
Accuracy difference between the observed measurement and the actual measurement
Precision variation that occurs when measuring the same part with the same instrument
MEASUREMENT SYSTEM ERROR
Precise but not
accurate
Accurate but not
precise
Not accurate or
precise
Accurate and
precise
ACCURACY OF MEASUREMENT
Broken down into three components
aStability
The consistency of measurements over time
bBias
A measure of the amount of partiality in the system
cLinearity
A measure of the bias values through the expected
range of measurements
OBSERVED VARIATION
Observed Variation
Process Variation
Measurement System
Variation
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Reproducibility
Accuracy (Central Location)
Calibration Addresses Accuracy
Letrsquos take a closer look at Precision
Measurement System Analysis (MSA)
Measurement System Analysis (MSA)
Error in Resolution The inability to detect small changes
Possible Cause
Wrong measurement device selected - divisions on scale not fine enough to detect changes
Resolution
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Repeatability The inability to get the same answer from repeated measurements made of the same item under absolutely identical conditions
Possible Cause
Lack of standard operating procedures (SOP) lack of training measuring system variablilty
Repeatability
Equipment Variation
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Reproducibility The inability to get the same answer from repeated measurements made under various conditions from different inspectors
Possible Cause
Lack of SOP lack of training
Reproducibility
Appraiser Variation
VARIABLE MSA ndash GAGE RampR STUDY
bull Gage RampR is the combined estimate of
measurement system Repeatability and
Reproducibility
bull Typically a 3-person study is performed Each person randomly measures 10 marked parts per trial
Each person can perform up to 3 trials
bull There are 3 key indicators EV or Equipment Variation
AV or Appraiser Variation
Overall GRR
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
READING THE CONTROL CHART
38
CONTROL CHARTS FOR ATTRIBUTES ndashP-CHARTS amp C-CHARTS
Attributes are discrete events yesno or passfail
Use P-Charts for quality characteristics that are discrete and involve yesno or goodbad decisions
Eg
Number of leaking caulking tubes in a box of 48
Number of broken eggs in a carton
Use C-Charts for discrete defects when there can be more than one defect per unit
Eg
Number of stains in a carpet sample cut from a production run
Number of complaints per customer at a hotel
39
P-CHART EXAMPLE A PRODUCTION MANAGER FOR A TIRE COMPANY HAS INSPECTED THE NUMBER OF
DEFECTIVE TIRES IN FIVE RANDOM SAMPLES WITH 20 TIRES IN EACH SAMPLE THE TABLE BELOW SHOWS THE
NUMBER OF DEFECTIVE TIRES IN EACH SAMPLE OF 20 TIRES CALCULATE THE CONTROL LIMITS
Sample Number of
Defective Tires
Number of Tires in each
Sample
Proportion Defective
1 3 20 15
2 2 20 10
3 1 20 05
4 2 20 10
5 2 20 05
Total 9 100 09
01023(064)09σzpLCL
2823(064)09σzpUCL
06420
(09)(91)
n
)p(1pσ
09100
9
Inspected Total
DefectivespCL
p
p
p
Solution
40
P- CONTROL CHART
41
C-CHART EXAMPLE THE NUMBER OF WEEKLY CUSTOMER COMPLAINTS ARE MONITORED IN A LARGE HOTEL USING A C-CHART DEVELOP THREE SIGMA CONTROL LIMITS USING THE DATA TABLE BELOW
Week Number of Complaints
1 3
2 2
3 3
4 1
5 3
6 3
7 2
8 1
9 3
10 1
Total 22
022522322ccLCL
66522322ccUCL
2210
22
samples of
complaintsc
c
c
z
z
Solution
42
C- CONTROL CHART
43
The ability of a process to meet product designtechnical specifications
Assessing capability involves evaluating process variability relative to preset product or service specifications
Process Capability ndash Cp and Cpk
Cp assumes that the process is centered in the specification range
Cpk helps to address a possible lack of centering of the process
PROCESS CAPABILITY
6σ
LSLUSL
width process
width ionspecificatCp
3σ
LSLμ
3σ
μUSLminCpk
44
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
45
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
46
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
47
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
--and an individual part is measured at 520rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
48
GRAPHING THE TOLERANCE AND MEASUREMENTS
Suppose we made and measured several more
units and they were all EXACTLY the same
We wouldnrsquot have very many part problems
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
X
X
X
49
GRAPHING THE TOLERANCE AND MEASUREMENTS
In the real world units are NOT EXACTLY the same
Everything VARIES
The question isnrsquot IF units vary
Itrsquos how much when and why
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
XX
XXX
XXXXX
XXXXXXX
50
The ldquonormal bell curverdquo
Widths heights depths thicknesses weights speeds strengths
and many other types of measurements when charted as a
histogram often form the shape of a bell
A ldquoperfect bellrdquo like a ldquoperfect circlerdquo doesnrsquot occur in nature but
many processes are close enough to make the bell curve useful
(A number of common industrial measurements such as flatness and straightness do NOT tend to distribute in a bell shape their proper statistical analysis is performed using models other than the bell curve)
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
51
What is a ldquostandard deviationrdquo
If we measure the DISTANCE from the CENTER of the bell
to each individual measurement that makes up the bell curve
we can find a TYPICAL DISTANCE
The most commonly used statistic to estimate this distance is the
Standard Deviation (also called ldquoSigmardquo)
Because of the natural shape of the bell curve the area of +1 to ndash1
standard deviations includes about 68 of the curve
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
Typical distance
from the center +1
standard deviation
Typical distance
from the center -1
standard deviation
52
How much of the curve is included in how many standard
deviations
From ndash1 to +1 is about 68 of the bell curve
From ndash2 to +2 is about 95
From ndash3 to +3 is about 9973
From ndash4 to +4 is about 9999
(NOTE We usually show the bell from ndash3 to +3 to make it easier to draw but in concept the ldquotailsrdquo of the bell get very thin and go on forever)
-6 -5 -4 -3 -2 -1 +1 +2 +3 +4 +5 +6 0
53
A
B
What is Cpk It is a measure of how well a process is within a specification
Cpk = A divided by B
A = Distance from process mean to closest spec limit
B = 3 Standard Deviations (also called ldquo3 Sigmardquo)
A bigger Cpk is better because fewer units will be beyond spec
(A bigger ldquoArdquo and a smaller ldquoBrdquo are better)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
54
A
B
ldquoProcess Capabilityrdquo is the ability of a process
to fit its output within the tolerances
hellipa LARGER ldquoArdquo
hellipand a SMALLER ldquoBrdquo
hellipmeans BETTER ldquoProcess Capabilityrdquo
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
55
A
B
An Analogy
Analogy
The bell curve is your automobile
The spec limits are the edges of your garage door
If A = B you are hitting the frame of your garage door with your car
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
56
A
B
How can we make Cpk (A divided by B) better
1 Design the product so a wider tolerance is functional (ldquorobust designrdquo)
2 Choose equipment and methods for a good safety margin (ldquoprocess capabilityrdquo)
3 Correctly adjust but only when needed (ldquocontrolrdquo)
4 Discover ways to narrow the natural variation (ldquoimprovementrdquo)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
57
A
B
What does a very good Cpk do for us
This process is producing good units with a good safety margin
Note that when Cpk = 2 our process mean is 6 standard deviations from
the nearest spec so we say it has ldquo6 Sigma Capabilityrdquo
Specification
Limit
Specification
Limit
This Cpk is
about 2
Very good
Mean
58
A
B
What does a problem Cpk look like
This process is in danger of producing some defects
It is too close to the specification limits
(Remember the bell curve tail goes further than Bhellip hellipwe only show the bell to 3-sigma to make it easier to draw)
Specification
Limit
Specification
Limit
This Cpk is just
slightly greater
than 1 Not good
59
A
B
What does a very bad Cpk look like
A significant part of the ldquotailrdquo is hanging out beyond the spec limits
This process is producing scrap rework and customer rejects
Notice that if distance ldquoArdquo approaches zerohellip
hellipthe Cpk would approach zero andhellip
hellipthe process would become 50 defective
Specification
Limit
Specification
Limit
This Cpk is less
than 1 We desire
a minimum of 133
and ultimately we
want 2 or more
60
-
Q amp A
61
MEASUREMENT SYSTEM ANALYSIS (MSA)
An MSA is a statistical tool used to determine if a measurement system is capable of precise measurement
What is It
Objective or Purpose
bull To determine how much error is in the measurement due to the measurement process itself
bull Quantifies the variability added by the measurement system
bull Applicable to attribute data and variable data
When to Use It
bull On the critical inputs and outputs prior to collecting data for analysis
bull For any new or modified process in order to ensure the quality of the data
Measurement System Analysis is an analysis of the measurement process not an analysis of the people
IMPORTANT
Who Should be Involved
Everyone that measures and makes decisions about these measurements should be involved in the MSA
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The observed variation in process output measurements is not simply the variation in the process itself it is the variation in the process plus the variation in measurement that results from an inadequate measurement system
Conducting an MSA reduces the likelihood of passing a bad part or rejecting a good part
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The output of the process measured by bull Cycle time bull Dimensional data bull Number of defects and others
Observed Variation
Process Variation
Measurement System
Variation
Reproducibility
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Accuracy (Central Location)
OBSERVED VARIATION
Calibration addresses accuracy
Measurement System Analysis (MSA)
MEASUREMENT SYSTEM ERRORS
Accuracy difference between the observed measurement and the actual measurement
Precision variation that occurs when measuring the same part with the same instrument
MEASUREMENT SYSTEM ERROR
Precise but not
accurate
Accurate but not
precise
Not accurate or
precise
Accurate and
precise
ACCURACY OF MEASUREMENT
Broken down into three components
aStability
The consistency of measurements over time
bBias
A measure of the amount of partiality in the system
cLinearity
A measure of the bias values through the expected
range of measurements
OBSERVED VARIATION
Observed Variation
Process Variation
Measurement System
Variation
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Reproducibility
Accuracy (Central Location)
Calibration Addresses Accuracy
Letrsquos take a closer look at Precision
Measurement System Analysis (MSA)
Measurement System Analysis (MSA)
Error in Resolution The inability to detect small changes
Possible Cause
Wrong measurement device selected - divisions on scale not fine enough to detect changes
Resolution
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Repeatability The inability to get the same answer from repeated measurements made of the same item under absolutely identical conditions
Possible Cause
Lack of standard operating procedures (SOP) lack of training measuring system variablilty
Repeatability
Equipment Variation
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Reproducibility The inability to get the same answer from repeated measurements made under various conditions from different inspectors
Possible Cause
Lack of SOP lack of training
Reproducibility
Appraiser Variation
VARIABLE MSA ndash GAGE RampR STUDY
bull Gage RampR is the combined estimate of
measurement system Repeatability and
Reproducibility
bull Typically a 3-person study is performed Each person randomly measures 10 marked parts per trial
Each person can perform up to 3 trials
bull There are 3 key indicators EV or Equipment Variation
AV or Appraiser Variation
Overall GRR
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
CONTROL CHARTS FOR ATTRIBUTES ndashP-CHARTS amp C-CHARTS
Attributes are discrete events yesno or passfail
Use P-Charts for quality characteristics that are discrete and involve yesno or goodbad decisions
Eg
Number of leaking caulking tubes in a box of 48
Number of broken eggs in a carton
Use C-Charts for discrete defects when there can be more than one defect per unit
Eg
Number of stains in a carpet sample cut from a production run
Number of complaints per customer at a hotel
39
P-CHART EXAMPLE A PRODUCTION MANAGER FOR A TIRE COMPANY HAS INSPECTED THE NUMBER OF
DEFECTIVE TIRES IN FIVE RANDOM SAMPLES WITH 20 TIRES IN EACH SAMPLE THE TABLE BELOW SHOWS THE
NUMBER OF DEFECTIVE TIRES IN EACH SAMPLE OF 20 TIRES CALCULATE THE CONTROL LIMITS
Sample Number of
Defective Tires
Number of Tires in each
Sample
Proportion Defective
1 3 20 15
2 2 20 10
3 1 20 05
4 2 20 10
5 2 20 05
Total 9 100 09
01023(064)09σzpLCL
2823(064)09σzpUCL
06420
(09)(91)
n
)p(1pσ
09100
9
Inspected Total
DefectivespCL
p
p
p
Solution
40
P- CONTROL CHART
41
C-CHART EXAMPLE THE NUMBER OF WEEKLY CUSTOMER COMPLAINTS ARE MONITORED IN A LARGE HOTEL USING A C-CHART DEVELOP THREE SIGMA CONTROL LIMITS USING THE DATA TABLE BELOW
Week Number of Complaints
1 3
2 2
3 3
4 1
5 3
6 3
7 2
8 1
9 3
10 1
Total 22
022522322ccLCL
66522322ccUCL
2210
22
samples of
complaintsc
c
c
z
z
Solution
42
C- CONTROL CHART
43
The ability of a process to meet product designtechnical specifications
Assessing capability involves evaluating process variability relative to preset product or service specifications
Process Capability ndash Cp and Cpk
Cp assumes that the process is centered in the specification range
Cpk helps to address a possible lack of centering of the process
PROCESS CAPABILITY
6σ
LSLUSL
width process
width ionspecificatCp
3σ
LSLμ
3σ
μUSLminCpk
44
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
45
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
46
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
47
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
--and an individual part is measured at 520rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
48
GRAPHING THE TOLERANCE AND MEASUREMENTS
Suppose we made and measured several more
units and they were all EXACTLY the same
We wouldnrsquot have very many part problems
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
X
X
X
49
GRAPHING THE TOLERANCE AND MEASUREMENTS
In the real world units are NOT EXACTLY the same
Everything VARIES
The question isnrsquot IF units vary
Itrsquos how much when and why
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
XX
XXX
XXXXX
XXXXXXX
50
The ldquonormal bell curverdquo
Widths heights depths thicknesses weights speeds strengths
and many other types of measurements when charted as a
histogram often form the shape of a bell
A ldquoperfect bellrdquo like a ldquoperfect circlerdquo doesnrsquot occur in nature but
many processes are close enough to make the bell curve useful
(A number of common industrial measurements such as flatness and straightness do NOT tend to distribute in a bell shape their proper statistical analysis is performed using models other than the bell curve)
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
51
What is a ldquostandard deviationrdquo
If we measure the DISTANCE from the CENTER of the bell
to each individual measurement that makes up the bell curve
we can find a TYPICAL DISTANCE
The most commonly used statistic to estimate this distance is the
Standard Deviation (also called ldquoSigmardquo)
Because of the natural shape of the bell curve the area of +1 to ndash1
standard deviations includes about 68 of the curve
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
Typical distance
from the center +1
standard deviation
Typical distance
from the center -1
standard deviation
52
How much of the curve is included in how many standard
deviations
From ndash1 to +1 is about 68 of the bell curve
From ndash2 to +2 is about 95
From ndash3 to +3 is about 9973
From ndash4 to +4 is about 9999
(NOTE We usually show the bell from ndash3 to +3 to make it easier to draw but in concept the ldquotailsrdquo of the bell get very thin and go on forever)
-6 -5 -4 -3 -2 -1 +1 +2 +3 +4 +5 +6 0
53
A
B
What is Cpk It is a measure of how well a process is within a specification
Cpk = A divided by B
A = Distance from process mean to closest spec limit
B = 3 Standard Deviations (also called ldquo3 Sigmardquo)
A bigger Cpk is better because fewer units will be beyond spec
(A bigger ldquoArdquo and a smaller ldquoBrdquo are better)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
54
A
B
ldquoProcess Capabilityrdquo is the ability of a process
to fit its output within the tolerances
hellipa LARGER ldquoArdquo
hellipand a SMALLER ldquoBrdquo
hellipmeans BETTER ldquoProcess Capabilityrdquo
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
55
A
B
An Analogy
Analogy
The bell curve is your automobile
The spec limits are the edges of your garage door
If A = B you are hitting the frame of your garage door with your car
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
56
A
B
How can we make Cpk (A divided by B) better
1 Design the product so a wider tolerance is functional (ldquorobust designrdquo)
2 Choose equipment and methods for a good safety margin (ldquoprocess capabilityrdquo)
3 Correctly adjust but only when needed (ldquocontrolrdquo)
4 Discover ways to narrow the natural variation (ldquoimprovementrdquo)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
57
A
B
What does a very good Cpk do for us
This process is producing good units with a good safety margin
Note that when Cpk = 2 our process mean is 6 standard deviations from
the nearest spec so we say it has ldquo6 Sigma Capabilityrdquo
Specification
Limit
Specification
Limit
This Cpk is
about 2
Very good
Mean
58
A
B
What does a problem Cpk look like
This process is in danger of producing some defects
It is too close to the specification limits
(Remember the bell curve tail goes further than Bhellip hellipwe only show the bell to 3-sigma to make it easier to draw)
Specification
Limit
Specification
Limit
This Cpk is just
slightly greater
than 1 Not good
59
A
B
What does a very bad Cpk look like
A significant part of the ldquotailrdquo is hanging out beyond the spec limits
This process is producing scrap rework and customer rejects
Notice that if distance ldquoArdquo approaches zerohellip
hellipthe Cpk would approach zero andhellip
hellipthe process would become 50 defective
Specification
Limit
Specification
Limit
This Cpk is less
than 1 We desire
a minimum of 133
and ultimately we
want 2 or more
60
-
Q amp A
61
MEASUREMENT SYSTEM ANALYSIS (MSA)
An MSA is a statistical tool used to determine if a measurement system is capable of precise measurement
What is It
Objective or Purpose
bull To determine how much error is in the measurement due to the measurement process itself
bull Quantifies the variability added by the measurement system
bull Applicable to attribute data and variable data
When to Use It
bull On the critical inputs and outputs prior to collecting data for analysis
bull For any new or modified process in order to ensure the quality of the data
Measurement System Analysis is an analysis of the measurement process not an analysis of the people
IMPORTANT
Who Should be Involved
Everyone that measures and makes decisions about these measurements should be involved in the MSA
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The observed variation in process output measurements is not simply the variation in the process itself it is the variation in the process plus the variation in measurement that results from an inadequate measurement system
Conducting an MSA reduces the likelihood of passing a bad part or rejecting a good part
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The output of the process measured by bull Cycle time bull Dimensional data bull Number of defects and others
Observed Variation
Process Variation
Measurement System
Variation
Reproducibility
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Accuracy (Central Location)
OBSERVED VARIATION
Calibration addresses accuracy
Measurement System Analysis (MSA)
MEASUREMENT SYSTEM ERRORS
Accuracy difference between the observed measurement and the actual measurement
Precision variation that occurs when measuring the same part with the same instrument
MEASUREMENT SYSTEM ERROR
Precise but not
accurate
Accurate but not
precise
Not accurate or
precise
Accurate and
precise
ACCURACY OF MEASUREMENT
Broken down into three components
aStability
The consistency of measurements over time
bBias
A measure of the amount of partiality in the system
cLinearity
A measure of the bias values through the expected
range of measurements
OBSERVED VARIATION
Observed Variation
Process Variation
Measurement System
Variation
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Reproducibility
Accuracy (Central Location)
Calibration Addresses Accuracy
Letrsquos take a closer look at Precision
Measurement System Analysis (MSA)
Measurement System Analysis (MSA)
Error in Resolution The inability to detect small changes
Possible Cause
Wrong measurement device selected - divisions on scale not fine enough to detect changes
Resolution
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Repeatability The inability to get the same answer from repeated measurements made of the same item under absolutely identical conditions
Possible Cause
Lack of standard operating procedures (SOP) lack of training measuring system variablilty
Repeatability
Equipment Variation
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Reproducibility The inability to get the same answer from repeated measurements made under various conditions from different inspectors
Possible Cause
Lack of SOP lack of training
Reproducibility
Appraiser Variation
VARIABLE MSA ndash GAGE RampR STUDY
bull Gage RampR is the combined estimate of
measurement system Repeatability and
Reproducibility
bull Typically a 3-person study is performed Each person randomly measures 10 marked parts per trial
Each person can perform up to 3 trials
bull There are 3 key indicators EV or Equipment Variation
AV or Appraiser Variation
Overall GRR
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
P-CHART EXAMPLE A PRODUCTION MANAGER FOR A TIRE COMPANY HAS INSPECTED THE NUMBER OF
DEFECTIVE TIRES IN FIVE RANDOM SAMPLES WITH 20 TIRES IN EACH SAMPLE THE TABLE BELOW SHOWS THE
NUMBER OF DEFECTIVE TIRES IN EACH SAMPLE OF 20 TIRES CALCULATE THE CONTROL LIMITS
Sample Number of
Defective Tires
Number of Tires in each
Sample
Proportion Defective
1 3 20 15
2 2 20 10
3 1 20 05
4 2 20 10
5 2 20 05
Total 9 100 09
01023(064)09σzpLCL
2823(064)09σzpUCL
06420
(09)(91)
n
)p(1pσ
09100
9
Inspected Total
DefectivespCL
p
p
p
Solution
40
P- CONTROL CHART
41
C-CHART EXAMPLE THE NUMBER OF WEEKLY CUSTOMER COMPLAINTS ARE MONITORED IN A LARGE HOTEL USING A C-CHART DEVELOP THREE SIGMA CONTROL LIMITS USING THE DATA TABLE BELOW
Week Number of Complaints
1 3
2 2
3 3
4 1
5 3
6 3
7 2
8 1
9 3
10 1
Total 22
022522322ccLCL
66522322ccUCL
2210
22
samples of
complaintsc
c
c
z
z
Solution
42
C- CONTROL CHART
43
The ability of a process to meet product designtechnical specifications
Assessing capability involves evaluating process variability relative to preset product or service specifications
Process Capability ndash Cp and Cpk
Cp assumes that the process is centered in the specification range
Cpk helps to address a possible lack of centering of the process
PROCESS CAPABILITY
6σ
LSLUSL
width process
width ionspecificatCp
3σ
LSLμ
3σ
μUSLminCpk
44
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
45
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
46
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
47
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
--and an individual part is measured at 520rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
48
GRAPHING THE TOLERANCE AND MEASUREMENTS
Suppose we made and measured several more
units and they were all EXACTLY the same
We wouldnrsquot have very many part problems
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
X
X
X
49
GRAPHING THE TOLERANCE AND MEASUREMENTS
In the real world units are NOT EXACTLY the same
Everything VARIES
The question isnrsquot IF units vary
Itrsquos how much when and why
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
XX
XXX
XXXXX
XXXXXXX
50
The ldquonormal bell curverdquo
Widths heights depths thicknesses weights speeds strengths
and many other types of measurements when charted as a
histogram often form the shape of a bell
A ldquoperfect bellrdquo like a ldquoperfect circlerdquo doesnrsquot occur in nature but
many processes are close enough to make the bell curve useful
(A number of common industrial measurements such as flatness and straightness do NOT tend to distribute in a bell shape their proper statistical analysis is performed using models other than the bell curve)
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
51
What is a ldquostandard deviationrdquo
If we measure the DISTANCE from the CENTER of the bell
to each individual measurement that makes up the bell curve
we can find a TYPICAL DISTANCE
The most commonly used statistic to estimate this distance is the
Standard Deviation (also called ldquoSigmardquo)
Because of the natural shape of the bell curve the area of +1 to ndash1
standard deviations includes about 68 of the curve
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
Typical distance
from the center +1
standard deviation
Typical distance
from the center -1
standard deviation
52
How much of the curve is included in how many standard
deviations
From ndash1 to +1 is about 68 of the bell curve
From ndash2 to +2 is about 95
From ndash3 to +3 is about 9973
From ndash4 to +4 is about 9999
(NOTE We usually show the bell from ndash3 to +3 to make it easier to draw but in concept the ldquotailsrdquo of the bell get very thin and go on forever)
-6 -5 -4 -3 -2 -1 +1 +2 +3 +4 +5 +6 0
53
A
B
What is Cpk It is a measure of how well a process is within a specification
Cpk = A divided by B
A = Distance from process mean to closest spec limit
B = 3 Standard Deviations (also called ldquo3 Sigmardquo)
A bigger Cpk is better because fewer units will be beyond spec
(A bigger ldquoArdquo and a smaller ldquoBrdquo are better)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
54
A
B
ldquoProcess Capabilityrdquo is the ability of a process
to fit its output within the tolerances
hellipa LARGER ldquoArdquo
hellipand a SMALLER ldquoBrdquo
hellipmeans BETTER ldquoProcess Capabilityrdquo
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
55
A
B
An Analogy
Analogy
The bell curve is your automobile
The spec limits are the edges of your garage door
If A = B you are hitting the frame of your garage door with your car
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
56
A
B
How can we make Cpk (A divided by B) better
1 Design the product so a wider tolerance is functional (ldquorobust designrdquo)
2 Choose equipment and methods for a good safety margin (ldquoprocess capabilityrdquo)
3 Correctly adjust but only when needed (ldquocontrolrdquo)
4 Discover ways to narrow the natural variation (ldquoimprovementrdquo)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
57
A
B
What does a very good Cpk do for us
This process is producing good units with a good safety margin
Note that when Cpk = 2 our process mean is 6 standard deviations from
the nearest spec so we say it has ldquo6 Sigma Capabilityrdquo
Specification
Limit
Specification
Limit
This Cpk is
about 2
Very good
Mean
58
A
B
What does a problem Cpk look like
This process is in danger of producing some defects
It is too close to the specification limits
(Remember the bell curve tail goes further than Bhellip hellipwe only show the bell to 3-sigma to make it easier to draw)
Specification
Limit
Specification
Limit
This Cpk is just
slightly greater
than 1 Not good
59
A
B
What does a very bad Cpk look like
A significant part of the ldquotailrdquo is hanging out beyond the spec limits
This process is producing scrap rework and customer rejects
Notice that if distance ldquoArdquo approaches zerohellip
hellipthe Cpk would approach zero andhellip
hellipthe process would become 50 defective
Specification
Limit
Specification
Limit
This Cpk is less
than 1 We desire
a minimum of 133
and ultimately we
want 2 or more
60
-
Q amp A
61
MEASUREMENT SYSTEM ANALYSIS (MSA)
An MSA is a statistical tool used to determine if a measurement system is capable of precise measurement
What is It
Objective or Purpose
bull To determine how much error is in the measurement due to the measurement process itself
bull Quantifies the variability added by the measurement system
bull Applicable to attribute data and variable data
When to Use It
bull On the critical inputs and outputs prior to collecting data for analysis
bull For any new or modified process in order to ensure the quality of the data
Measurement System Analysis is an analysis of the measurement process not an analysis of the people
IMPORTANT
Who Should be Involved
Everyone that measures and makes decisions about these measurements should be involved in the MSA
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The observed variation in process output measurements is not simply the variation in the process itself it is the variation in the process plus the variation in measurement that results from an inadequate measurement system
Conducting an MSA reduces the likelihood of passing a bad part or rejecting a good part
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The output of the process measured by bull Cycle time bull Dimensional data bull Number of defects and others
Observed Variation
Process Variation
Measurement System
Variation
Reproducibility
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Accuracy (Central Location)
OBSERVED VARIATION
Calibration addresses accuracy
Measurement System Analysis (MSA)
MEASUREMENT SYSTEM ERRORS
Accuracy difference between the observed measurement and the actual measurement
Precision variation that occurs when measuring the same part with the same instrument
MEASUREMENT SYSTEM ERROR
Precise but not
accurate
Accurate but not
precise
Not accurate or
precise
Accurate and
precise
ACCURACY OF MEASUREMENT
Broken down into three components
aStability
The consistency of measurements over time
bBias
A measure of the amount of partiality in the system
cLinearity
A measure of the bias values through the expected
range of measurements
OBSERVED VARIATION
Observed Variation
Process Variation
Measurement System
Variation
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Reproducibility
Accuracy (Central Location)
Calibration Addresses Accuracy
Letrsquos take a closer look at Precision
Measurement System Analysis (MSA)
Measurement System Analysis (MSA)
Error in Resolution The inability to detect small changes
Possible Cause
Wrong measurement device selected - divisions on scale not fine enough to detect changes
Resolution
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Repeatability The inability to get the same answer from repeated measurements made of the same item under absolutely identical conditions
Possible Cause
Lack of standard operating procedures (SOP) lack of training measuring system variablilty
Repeatability
Equipment Variation
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Reproducibility The inability to get the same answer from repeated measurements made under various conditions from different inspectors
Possible Cause
Lack of SOP lack of training
Reproducibility
Appraiser Variation
VARIABLE MSA ndash GAGE RampR STUDY
bull Gage RampR is the combined estimate of
measurement system Repeatability and
Reproducibility
bull Typically a 3-person study is performed Each person randomly measures 10 marked parts per trial
Each person can perform up to 3 trials
bull There are 3 key indicators EV or Equipment Variation
AV or Appraiser Variation
Overall GRR
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
P- CONTROL CHART
41
C-CHART EXAMPLE THE NUMBER OF WEEKLY CUSTOMER COMPLAINTS ARE MONITORED IN A LARGE HOTEL USING A C-CHART DEVELOP THREE SIGMA CONTROL LIMITS USING THE DATA TABLE BELOW
Week Number of Complaints
1 3
2 2
3 3
4 1
5 3
6 3
7 2
8 1
9 3
10 1
Total 22
022522322ccLCL
66522322ccUCL
2210
22
samples of
complaintsc
c
c
z
z
Solution
42
C- CONTROL CHART
43
The ability of a process to meet product designtechnical specifications
Assessing capability involves evaluating process variability relative to preset product or service specifications
Process Capability ndash Cp and Cpk
Cp assumes that the process is centered in the specification range
Cpk helps to address a possible lack of centering of the process
PROCESS CAPABILITY
6σ
LSLUSL
width process
width ionspecificatCp
3σ
LSLμ
3σ
μUSLminCpk
44
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
45
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
46
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
47
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
--and an individual part is measured at 520rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
48
GRAPHING THE TOLERANCE AND MEASUREMENTS
Suppose we made and measured several more
units and they were all EXACTLY the same
We wouldnrsquot have very many part problems
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
X
X
X
49
GRAPHING THE TOLERANCE AND MEASUREMENTS
In the real world units are NOT EXACTLY the same
Everything VARIES
The question isnrsquot IF units vary
Itrsquos how much when and why
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
XX
XXX
XXXXX
XXXXXXX
50
The ldquonormal bell curverdquo
Widths heights depths thicknesses weights speeds strengths
and many other types of measurements when charted as a
histogram often form the shape of a bell
A ldquoperfect bellrdquo like a ldquoperfect circlerdquo doesnrsquot occur in nature but
many processes are close enough to make the bell curve useful
(A number of common industrial measurements such as flatness and straightness do NOT tend to distribute in a bell shape their proper statistical analysis is performed using models other than the bell curve)
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
51
What is a ldquostandard deviationrdquo
If we measure the DISTANCE from the CENTER of the bell
to each individual measurement that makes up the bell curve
we can find a TYPICAL DISTANCE
The most commonly used statistic to estimate this distance is the
Standard Deviation (also called ldquoSigmardquo)
Because of the natural shape of the bell curve the area of +1 to ndash1
standard deviations includes about 68 of the curve
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
Typical distance
from the center +1
standard deviation
Typical distance
from the center -1
standard deviation
52
How much of the curve is included in how many standard
deviations
From ndash1 to +1 is about 68 of the bell curve
From ndash2 to +2 is about 95
From ndash3 to +3 is about 9973
From ndash4 to +4 is about 9999
(NOTE We usually show the bell from ndash3 to +3 to make it easier to draw but in concept the ldquotailsrdquo of the bell get very thin and go on forever)
-6 -5 -4 -3 -2 -1 +1 +2 +3 +4 +5 +6 0
53
A
B
What is Cpk It is a measure of how well a process is within a specification
Cpk = A divided by B
A = Distance from process mean to closest spec limit
B = 3 Standard Deviations (also called ldquo3 Sigmardquo)
A bigger Cpk is better because fewer units will be beyond spec
(A bigger ldquoArdquo and a smaller ldquoBrdquo are better)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
54
A
B
ldquoProcess Capabilityrdquo is the ability of a process
to fit its output within the tolerances
hellipa LARGER ldquoArdquo
hellipand a SMALLER ldquoBrdquo
hellipmeans BETTER ldquoProcess Capabilityrdquo
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
55
A
B
An Analogy
Analogy
The bell curve is your automobile
The spec limits are the edges of your garage door
If A = B you are hitting the frame of your garage door with your car
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
56
A
B
How can we make Cpk (A divided by B) better
1 Design the product so a wider tolerance is functional (ldquorobust designrdquo)
2 Choose equipment and methods for a good safety margin (ldquoprocess capabilityrdquo)
3 Correctly adjust but only when needed (ldquocontrolrdquo)
4 Discover ways to narrow the natural variation (ldquoimprovementrdquo)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
57
A
B
What does a very good Cpk do for us
This process is producing good units with a good safety margin
Note that when Cpk = 2 our process mean is 6 standard deviations from
the nearest spec so we say it has ldquo6 Sigma Capabilityrdquo
Specification
Limit
Specification
Limit
This Cpk is
about 2
Very good
Mean
58
A
B
What does a problem Cpk look like
This process is in danger of producing some defects
It is too close to the specification limits
(Remember the bell curve tail goes further than Bhellip hellipwe only show the bell to 3-sigma to make it easier to draw)
Specification
Limit
Specification
Limit
This Cpk is just
slightly greater
than 1 Not good
59
A
B
What does a very bad Cpk look like
A significant part of the ldquotailrdquo is hanging out beyond the spec limits
This process is producing scrap rework and customer rejects
Notice that if distance ldquoArdquo approaches zerohellip
hellipthe Cpk would approach zero andhellip
hellipthe process would become 50 defective
Specification
Limit
Specification
Limit
This Cpk is less
than 1 We desire
a minimum of 133
and ultimately we
want 2 or more
60
-
Q amp A
61
MEASUREMENT SYSTEM ANALYSIS (MSA)
An MSA is a statistical tool used to determine if a measurement system is capable of precise measurement
What is It
Objective or Purpose
bull To determine how much error is in the measurement due to the measurement process itself
bull Quantifies the variability added by the measurement system
bull Applicable to attribute data and variable data
When to Use It
bull On the critical inputs and outputs prior to collecting data for analysis
bull For any new or modified process in order to ensure the quality of the data
Measurement System Analysis is an analysis of the measurement process not an analysis of the people
IMPORTANT
Who Should be Involved
Everyone that measures and makes decisions about these measurements should be involved in the MSA
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The observed variation in process output measurements is not simply the variation in the process itself it is the variation in the process plus the variation in measurement that results from an inadequate measurement system
Conducting an MSA reduces the likelihood of passing a bad part or rejecting a good part
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The output of the process measured by bull Cycle time bull Dimensional data bull Number of defects and others
Observed Variation
Process Variation
Measurement System
Variation
Reproducibility
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Accuracy (Central Location)
OBSERVED VARIATION
Calibration addresses accuracy
Measurement System Analysis (MSA)
MEASUREMENT SYSTEM ERRORS
Accuracy difference between the observed measurement and the actual measurement
Precision variation that occurs when measuring the same part with the same instrument
MEASUREMENT SYSTEM ERROR
Precise but not
accurate
Accurate but not
precise
Not accurate or
precise
Accurate and
precise
ACCURACY OF MEASUREMENT
Broken down into three components
aStability
The consistency of measurements over time
bBias
A measure of the amount of partiality in the system
cLinearity
A measure of the bias values through the expected
range of measurements
OBSERVED VARIATION
Observed Variation
Process Variation
Measurement System
Variation
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Reproducibility
Accuracy (Central Location)
Calibration Addresses Accuracy
Letrsquos take a closer look at Precision
Measurement System Analysis (MSA)
Measurement System Analysis (MSA)
Error in Resolution The inability to detect small changes
Possible Cause
Wrong measurement device selected - divisions on scale not fine enough to detect changes
Resolution
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Repeatability The inability to get the same answer from repeated measurements made of the same item under absolutely identical conditions
Possible Cause
Lack of standard operating procedures (SOP) lack of training measuring system variablilty
Repeatability
Equipment Variation
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Reproducibility The inability to get the same answer from repeated measurements made under various conditions from different inspectors
Possible Cause
Lack of SOP lack of training
Reproducibility
Appraiser Variation
VARIABLE MSA ndash GAGE RampR STUDY
bull Gage RampR is the combined estimate of
measurement system Repeatability and
Reproducibility
bull Typically a 3-person study is performed Each person randomly measures 10 marked parts per trial
Each person can perform up to 3 trials
bull There are 3 key indicators EV or Equipment Variation
AV or Appraiser Variation
Overall GRR
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
C-CHART EXAMPLE THE NUMBER OF WEEKLY CUSTOMER COMPLAINTS ARE MONITORED IN A LARGE HOTEL USING A C-CHART DEVELOP THREE SIGMA CONTROL LIMITS USING THE DATA TABLE BELOW
Week Number of Complaints
1 3
2 2
3 3
4 1
5 3
6 3
7 2
8 1
9 3
10 1
Total 22
022522322ccLCL
66522322ccUCL
2210
22
samples of
complaintsc
c
c
z
z
Solution
42
C- CONTROL CHART
43
The ability of a process to meet product designtechnical specifications
Assessing capability involves evaluating process variability relative to preset product or service specifications
Process Capability ndash Cp and Cpk
Cp assumes that the process is centered in the specification range
Cpk helps to address a possible lack of centering of the process
PROCESS CAPABILITY
6σ
LSLUSL
width process
width ionspecificatCp
3σ
LSLμ
3σ
μUSLminCpk
44
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
45
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
46
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
47
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
--and an individual part is measured at 520rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
48
GRAPHING THE TOLERANCE AND MEASUREMENTS
Suppose we made and measured several more
units and they were all EXACTLY the same
We wouldnrsquot have very many part problems
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
X
X
X
49
GRAPHING THE TOLERANCE AND MEASUREMENTS
In the real world units are NOT EXACTLY the same
Everything VARIES
The question isnrsquot IF units vary
Itrsquos how much when and why
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
XX
XXX
XXXXX
XXXXXXX
50
The ldquonormal bell curverdquo
Widths heights depths thicknesses weights speeds strengths
and many other types of measurements when charted as a
histogram often form the shape of a bell
A ldquoperfect bellrdquo like a ldquoperfect circlerdquo doesnrsquot occur in nature but
many processes are close enough to make the bell curve useful
(A number of common industrial measurements such as flatness and straightness do NOT tend to distribute in a bell shape their proper statistical analysis is performed using models other than the bell curve)
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
51
What is a ldquostandard deviationrdquo
If we measure the DISTANCE from the CENTER of the bell
to each individual measurement that makes up the bell curve
we can find a TYPICAL DISTANCE
The most commonly used statistic to estimate this distance is the
Standard Deviation (also called ldquoSigmardquo)
Because of the natural shape of the bell curve the area of +1 to ndash1
standard deviations includes about 68 of the curve
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
Typical distance
from the center +1
standard deviation
Typical distance
from the center -1
standard deviation
52
How much of the curve is included in how many standard
deviations
From ndash1 to +1 is about 68 of the bell curve
From ndash2 to +2 is about 95
From ndash3 to +3 is about 9973
From ndash4 to +4 is about 9999
(NOTE We usually show the bell from ndash3 to +3 to make it easier to draw but in concept the ldquotailsrdquo of the bell get very thin and go on forever)
-6 -5 -4 -3 -2 -1 +1 +2 +3 +4 +5 +6 0
53
A
B
What is Cpk It is a measure of how well a process is within a specification
Cpk = A divided by B
A = Distance from process mean to closest spec limit
B = 3 Standard Deviations (also called ldquo3 Sigmardquo)
A bigger Cpk is better because fewer units will be beyond spec
(A bigger ldquoArdquo and a smaller ldquoBrdquo are better)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
54
A
B
ldquoProcess Capabilityrdquo is the ability of a process
to fit its output within the tolerances
hellipa LARGER ldquoArdquo
hellipand a SMALLER ldquoBrdquo
hellipmeans BETTER ldquoProcess Capabilityrdquo
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
55
A
B
An Analogy
Analogy
The bell curve is your automobile
The spec limits are the edges of your garage door
If A = B you are hitting the frame of your garage door with your car
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
56
A
B
How can we make Cpk (A divided by B) better
1 Design the product so a wider tolerance is functional (ldquorobust designrdquo)
2 Choose equipment and methods for a good safety margin (ldquoprocess capabilityrdquo)
3 Correctly adjust but only when needed (ldquocontrolrdquo)
4 Discover ways to narrow the natural variation (ldquoimprovementrdquo)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
57
A
B
What does a very good Cpk do for us
This process is producing good units with a good safety margin
Note that when Cpk = 2 our process mean is 6 standard deviations from
the nearest spec so we say it has ldquo6 Sigma Capabilityrdquo
Specification
Limit
Specification
Limit
This Cpk is
about 2
Very good
Mean
58
A
B
What does a problem Cpk look like
This process is in danger of producing some defects
It is too close to the specification limits
(Remember the bell curve tail goes further than Bhellip hellipwe only show the bell to 3-sigma to make it easier to draw)
Specification
Limit
Specification
Limit
This Cpk is just
slightly greater
than 1 Not good
59
A
B
What does a very bad Cpk look like
A significant part of the ldquotailrdquo is hanging out beyond the spec limits
This process is producing scrap rework and customer rejects
Notice that if distance ldquoArdquo approaches zerohellip
hellipthe Cpk would approach zero andhellip
hellipthe process would become 50 defective
Specification
Limit
Specification
Limit
This Cpk is less
than 1 We desire
a minimum of 133
and ultimately we
want 2 or more
60
-
Q amp A
61
MEASUREMENT SYSTEM ANALYSIS (MSA)
An MSA is a statistical tool used to determine if a measurement system is capable of precise measurement
What is It
Objective or Purpose
bull To determine how much error is in the measurement due to the measurement process itself
bull Quantifies the variability added by the measurement system
bull Applicable to attribute data and variable data
When to Use It
bull On the critical inputs and outputs prior to collecting data for analysis
bull For any new or modified process in order to ensure the quality of the data
Measurement System Analysis is an analysis of the measurement process not an analysis of the people
IMPORTANT
Who Should be Involved
Everyone that measures and makes decisions about these measurements should be involved in the MSA
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The observed variation in process output measurements is not simply the variation in the process itself it is the variation in the process plus the variation in measurement that results from an inadequate measurement system
Conducting an MSA reduces the likelihood of passing a bad part or rejecting a good part
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The output of the process measured by bull Cycle time bull Dimensional data bull Number of defects and others
Observed Variation
Process Variation
Measurement System
Variation
Reproducibility
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Accuracy (Central Location)
OBSERVED VARIATION
Calibration addresses accuracy
Measurement System Analysis (MSA)
MEASUREMENT SYSTEM ERRORS
Accuracy difference between the observed measurement and the actual measurement
Precision variation that occurs when measuring the same part with the same instrument
MEASUREMENT SYSTEM ERROR
Precise but not
accurate
Accurate but not
precise
Not accurate or
precise
Accurate and
precise
ACCURACY OF MEASUREMENT
Broken down into three components
aStability
The consistency of measurements over time
bBias
A measure of the amount of partiality in the system
cLinearity
A measure of the bias values through the expected
range of measurements
OBSERVED VARIATION
Observed Variation
Process Variation
Measurement System
Variation
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Reproducibility
Accuracy (Central Location)
Calibration Addresses Accuracy
Letrsquos take a closer look at Precision
Measurement System Analysis (MSA)
Measurement System Analysis (MSA)
Error in Resolution The inability to detect small changes
Possible Cause
Wrong measurement device selected - divisions on scale not fine enough to detect changes
Resolution
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Repeatability The inability to get the same answer from repeated measurements made of the same item under absolutely identical conditions
Possible Cause
Lack of standard operating procedures (SOP) lack of training measuring system variablilty
Repeatability
Equipment Variation
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Reproducibility The inability to get the same answer from repeated measurements made under various conditions from different inspectors
Possible Cause
Lack of SOP lack of training
Reproducibility
Appraiser Variation
VARIABLE MSA ndash GAGE RampR STUDY
bull Gage RampR is the combined estimate of
measurement system Repeatability and
Reproducibility
bull Typically a 3-person study is performed Each person randomly measures 10 marked parts per trial
Each person can perform up to 3 trials
bull There are 3 key indicators EV or Equipment Variation
AV or Appraiser Variation
Overall GRR
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
C- CONTROL CHART
43
The ability of a process to meet product designtechnical specifications
Assessing capability involves evaluating process variability relative to preset product or service specifications
Process Capability ndash Cp and Cpk
Cp assumes that the process is centered in the specification range
Cpk helps to address a possible lack of centering of the process
PROCESS CAPABILITY
6σ
LSLUSL
width process
width ionspecificatCp
3σ
LSLμ
3σ
μUSLminCpk
44
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
45
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
46
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
47
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
--and an individual part is measured at 520rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
48
GRAPHING THE TOLERANCE AND MEASUREMENTS
Suppose we made and measured several more
units and they were all EXACTLY the same
We wouldnrsquot have very many part problems
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
X
X
X
49
GRAPHING THE TOLERANCE AND MEASUREMENTS
In the real world units are NOT EXACTLY the same
Everything VARIES
The question isnrsquot IF units vary
Itrsquos how much when and why
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
XX
XXX
XXXXX
XXXXXXX
50
The ldquonormal bell curverdquo
Widths heights depths thicknesses weights speeds strengths
and many other types of measurements when charted as a
histogram often form the shape of a bell
A ldquoperfect bellrdquo like a ldquoperfect circlerdquo doesnrsquot occur in nature but
many processes are close enough to make the bell curve useful
(A number of common industrial measurements such as flatness and straightness do NOT tend to distribute in a bell shape their proper statistical analysis is performed using models other than the bell curve)
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
51
What is a ldquostandard deviationrdquo
If we measure the DISTANCE from the CENTER of the bell
to each individual measurement that makes up the bell curve
we can find a TYPICAL DISTANCE
The most commonly used statistic to estimate this distance is the
Standard Deviation (also called ldquoSigmardquo)
Because of the natural shape of the bell curve the area of +1 to ndash1
standard deviations includes about 68 of the curve
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
Typical distance
from the center +1
standard deviation
Typical distance
from the center -1
standard deviation
52
How much of the curve is included in how many standard
deviations
From ndash1 to +1 is about 68 of the bell curve
From ndash2 to +2 is about 95
From ndash3 to +3 is about 9973
From ndash4 to +4 is about 9999
(NOTE We usually show the bell from ndash3 to +3 to make it easier to draw but in concept the ldquotailsrdquo of the bell get very thin and go on forever)
-6 -5 -4 -3 -2 -1 +1 +2 +3 +4 +5 +6 0
53
A
B
What is Cpk It is a measure of how well a process is within a specification
Cpk = A divided by B
A = Distance from process mean to closest spec limit
B = 3 Standard Deviations (also called ldquo3 Sigmardquo)
A bigger Cpk is better because fewer units will be beyond spec
(A bigger ldquoArdquo and a smaller ldquoBrdquo are better)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
54
A
B
ldquoProcess Capabilityrdquo is the ability of a process
to fit its output within the tolerances
hellipa LARGER ldquoArdquo
hellipand a SMALLER ldquoBrdquo
hellipmeans BETTER ldquoProcess Capabilityrdquo
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
55
A
B
An Analogy
Analogy
The bell curve is your automobile
The spec limits are the edges of your garage door
If A = B you are hitting the frame of your garage door with your car
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
56
A
B
How can we make Cpk (A divided by B) better
1 Design the product so a wider tolerance is functional (ldquorobust designrdquo)
2 Choose equipment and methods for a good safety margin (ldquoprocess capabilityrdquo)
3 Correctly adjust but only when needed (ldquocontrolrdquo)
4 Discover ways to narrow the natural variation (ldquoimprovementrdquo)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
57
A
B
What does a very good Cpk do for us
This process is producing good units with a good safety margin
Note that when Cpk = 2 our process mean is 6 standard deviations from
the nearest spec so we say it has ldquo6 Sigma Capabilityrdquo
Specification
Limit
Specification
Limit
This Cpk is
about 2
Very good
Mean
58
A
B
What does a problem Cpk look like
This process is in danger of producing some defects
It is too close to the specification limits
(Remember the bell curve tail goes further than Bhellip hellipwe only show the bell to 3-sigma to make it easier to draw)
Specification
Limit
Specification
Limit
This Cpk is just
slightly greater
than 1 Not good
59
A
B
What does a very bad Cpk look like
A significant part of the ldquotailrdquo is hanging out beyond the spec limits
This process is producing scrap rework and customer rejects
Notice that if distance ldquoArdquo approaches zerohellip
hellipthe Cpk would approach zero andhellip
hellipthe process would become 50 defective
Specification
Limit
Specification
Limit
This Cpk is less
than 1 We desire
a minimum of 133
and ultimately we
want 2 or more
60
-
Q amp A
61
MEASUREMENT SYSTEM ANALYSIS (MSA)
An MSA is a statistical tool used to determine if a measurement system is capable of precise measurement
What is It
Objective or Purpose
bull To determine how much error is in the measurement due to the measurement process itself
bull Quantifies the variability added by the measurement system
bull Applicable to attribute data and variable data
When to Use It
bull On the critical inputs and outputs prior to collecting data for analysis
bull For any new or modified process in order to ensure the quality of the data
Measurement System Analysis is an analysis of the measurement process not an analysis of the people
IMPORTANT
Who Should be Involved
Everyone that measures and makes decisions about these measurements should be involved in the MSA
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The observed variation in process output measurements is not simply the variation in the process itself it is the variation in the process plus the variation in measurement that results from an inadequate measurement system
Conducting an MSA reduces the likelihood of passing a bad part or rejecting a good part
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The output of the process measured by bull Cycle time bull Dimensional data bull Number of defects and others
Observed Variation
Process Variation
Measurement System
Variation
Reproducibility
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Accuracy (Central Location)
OBSERVED VARIATION
Calibration addresses accuracy
Measurement System Analysis (MSA)
MEASUREMENT SYSTEM ERRORS
Accuracy difference between the observed measurement and the actual measurement
Precision variation that occurs when measuring the same part with the same instrument
MEASUREMENT SYSTEM ERROR
Precise but not
accurate
Accurate but not
precise
Not accurate or
precise
Accurate and
precise
ACCURACY OF MEASUREMENT
Broken down into three components
aStability
The consistency of measurements over time
bBias
A measure of the amount of partiality in the system
cLinearity
A measure of the bias values through the expected
range of measurements
OBSERVED VARIATION
Observed Variation
Process Variation
Measurement System
Variation
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Reproducibility
Accuracy (Central Location)
Calibration Addresses Accuracy
Letrsquos take a closer look at Precision
Measurement System Analysis (MSA)
Measurement System Analysis (MSA)
Error in Resolution The inability to detect small changes
Possible Cause
Wrong measurement device selected - divisions on scale not fine enough to detect changes
Resolution
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Repeatability The inability to get the same answer from repeated measurements made of the same item under absolutely identical conditions
Possible Cause
Lack of standard operating procedures (SOP) lack of training measuring system variablilty
Repeatability
Equipment Variation
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Reproducibility The inability to get the same answer from repeated measurements made under various conditions from different inspectors
Possible Cause
Lack of SOP lack of training
Reproducibility
Appraiser Variation
VARIABLE MSA ndash GAGE RampR STUDY
bull Gage RampR is the combined estimate of
measurement system Repeatability and
Reproducibility
bull Typically a 3-person study is performed Each person randomly measures 10 marked parts per trial
Each person can perform up to 3 trials
bull There are 3 key indicators EV or Equipment Variation
AV or Appraiser Variation
Overall GRR
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
The ability of a process to meet product designtechnical specifications
Assessing capability involves evaluating process variability relative to preset product or service specifications
Process Capability ndash Cp and Cpk
Cp assumes that the process is centered in the specification range
Cpk helps to address a possible lack of centering of the process
PROCESS CAPABILITY
6σ
LSLUSL
width process
width ionspecificatCp
3σ
LSLμ
3σ
μUSLminCpk
44
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
45
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
46
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
47
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
--and an individual part is measured at 520rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
48
GRAPHING THE TOLERANCE AND MEASUREMENTS
Suppose we made and measured several more
units and they were all EXACTLY the same
We wouldnrsquot have very many part problems
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
X
X
X
49
GRAPHING THE TOLERANCE AND MEASUREMENTS
In the real world units are NOT EXACTLY the same
Everything VARIES
The question isnrsquot IF units vary
Itrsquos how much when and why
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
XX
XXX
XXXXX
XXXXXXX
50
The ldquonormal bell curverdquo
Widths heights depths thicknesses weights speeds strengths
and many other types of measurements when charted as a
histogram often form the shape of a bell
A ldquoperfect bellrdquo like a ldquoperfect circlerdquo doesnrsquot occur in nature but
many processes are close enough to make the bell curve useful
(A number of common industrial measurements such as flatness and straightness do NOT tend to distribute in a bell shape their proper statistical analysis is performed using models other than the bell curve)
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
51
What is a ldquostandard deviationrdquo
If we measure the DISTANCE from the CENTER of the bell
to each individual measurement that makes up the bell curve
we can find a TYPICAL DISTANCE
The most commonly used statistic to estimate this distance is the
Standard Deviation (also called ldquoSigmardquo)
Because of the natural shape of the bell curve the area of +1 to ndash1
standard deviations includes about 68 of the curve
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
Typical distance
from the center +1
standard deviation
Typical distance
from the center -1
standard deviation
52
How much of the curve is included in how many standard
deviations
From ndash1 to +1 is about 68 of the bell curve
From ndash2 to +2 is about 95
From ndash3 to +3 is about 9973
From ndash4 to +4 is about 9999
(NOTE We usually show the bell from ndash3 to +3 to make it easier to draw but in concept the ldquotailsrdquo of the bell get very thin and go on forever)
-6 -5 -4 -3 -2 -1 +1 +2 +3 +4 +5 +6 0
53
A
B
What is Cpk It is a measure of how well a process is within a specification
Cpk = A divided by B
A = Distance from process mean to closest spec limit
B = 3 Standard Deviations (also called ldquo3 Sigmardquo)
A bigger Cpk is better because fewer units will be beyond spec
(A bigger ldquoArdquo and a smaller ldquoBrdquo are better)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
54
A
B
ldquoProcess Capabilityrdquo is the ability of a process
to fit its output within the tolerances
hellipa LARGER ldquoArdquo
hellipand a SMALLER ldquoBrdquo
hellipmeans BETTER ldquoProcess Capabilityrdquo
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
55
A
B
An Analogy
Analogy
The bell curve is your automobile
The spec limits are the edges of your garage door
If A = B you are hitting the frame of your garage door with your car
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
56
A
B
How can we make Cpk (A divided by B) better
1 Design the product so a wider tolerance is functional (ldquorobust designrdquo)
2 Choose equipment and methods for a good safety margin (ldquoprocess capabilityrdquo)
3 Correctly adjust but only when needed (ldquocontrolrdquo)
4 Discover ways to narrow the natural variation (ldquoimprovementrdquo)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
57
A
B
What does a very good Cpk do for us
This process is producing good units with a good safety margin
Note that when Cpk = 2 our process mean is 6 standard deviations from
the nearest spec so we say it has ldquo6 Sigma Capabilityrdquo
Specification
Limit
Specification
Limit
This Cpk is
about 2
Very good
Mean
58
A
B
What does a problem Cpk look like
This process is in danger of producing some defects
It is too close to the specification limits
(Remember the bell curve tail goes further than Bhellip hellipwe only show the bell to 3-sigma to make it easier to draw)
Specification
Limit
Specification
Limit
This Cpk is just
slightly greater
than 1 Not good
59
A
B
What does a very bad Cpk look like
A significant part of the ldquotailrdquo is hanging out beyond the spec limits
This process is producing scrap rework and customer rejects
Notice that if distance ldquoArdquo approaches zerohellip
hellipthe Cpk would approach zero andhellip
hellipthe process would become 50 defective
Specification
Limit
Specification
Limit
This Cpk is less
than 1 We desire
a minimum of 133
and ultimately we
want 2 or more
60
-
Q amp A
61
MEASUREMENT SYSTEM ANALYSIS (MSA)
An MSA is a statistical tool used to determine if a measurement system is capable of precise measurement
What is It
Objective or Purpose
bull To determine how much error is in the measurement due to the measurement process itself
bull Quantifies the variability added by the measurement system
bull Applicable to attribute data and variable data
When to Use It
bull On the critical inputs and outputs prior to collecting data for analysis
bull For any new or modified process in order to ensure the quality of the data
Measurement System Analysis is an analysis of the measurement process not an analysis of the people
IMPORTANT
Who Should be Involved
Everyone that measures and makes decisions about these measurements should be involved in the MSA
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The observed variation in process output measurements is not simply the variation in the process itself it is the variation in the process plus the variation in measurement that results from an inadequate measurement system
Conducting an MSA reduces the likelihood of passing a bad part or rejecting a good part
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The output of the process measured by bull Cycle time bull Dimensional data bull Number of defects and others
Observed Variation
Process Variation
Measurement System
Variation
Reproducibility
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Accuracy (Central Location)
OBSERVED VARIATION
Calibration addresses accuracy
Measurement System Analysis (MSA)
MEASUREMENT SYSTEM ERRORS
Accuracy difference between the observed measurement and the actual measurement
Precision variation that occurs when measuring the same part with the same instrument
MEASUREMENT SYSTEM ERROR
Precise but not
accurate
Accurate but not
precise
Not accurate or
precise
Accurate and
precise
ACCURACY OF MEASUREMENT
Broken down into three components
aStability
The consistency of measurements over time
bBias
A measure of the amount of partiality in the system
cLinearity
A measure of the bias values through the expected
range of measurements
OBSERVED VARIATION
Observed Variation
Process Variation
Measurement System
Variation
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Reproducibility
Accuracy (Central Location)
Calibration Addresses Accuracy
Letrsquos take a closer look at Precision
Measurement System Analysis (MSA)
Measurement System Analysis (MSA)
Error in Resolution The inability to detect small changes
Possible Cause
Wrong measurement device selected - divisions on scale not fine enough to detect changes
Resolution
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Repeatability The inability to get the same answer from repeated measurements made of the same item under absolutely identical conditions
Possible Cause
Lack of standard operating procedures (SOP) lack of training measuring system variablilty
Repeatability
Equipment Variation
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Reproducibility The inability to get the same answer from repeated measurements made under various conditions from different inspectors
Possible Cause
Lack of SOP lack of training
Reproducibility
Appraiser Variation
VARIABLE MSA ndash GAGE RampR STUDY
bull Gage RampR is the combined estimate of
measurement system Repeatability and
Reproducibility
bull Typically a 3-person study is performed Each person randomly measures 10 marked parts per trial
Each person can perform up to 3 trials
bull There are 3 key indicators EV or Equipment Variation
AV or Appraiser Variation
Overall GRR
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
45
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
46
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
47
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
--and an individual part is measured at 520rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
48
GRAPHING THE TOLERANCE AND MEASUREMENTS
Suppose we made and measured several more
units and they were all EXACTLY the same
We wouldnrsquot have very many part problems
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
X
X
X
49
GRAPHING THE TOLERANCE AND MEASUREMENTS
In the real world units are NOT EXACTLY the same
Everything VARIES
The question isnrsquot IF units vary
Itrsquos how much when and why
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
XX
XXX
XXXXX
XXXXXXX
50
The ldquonormal bell curverdquo
Widths heights depths thicknesses weights speeds strengths
and many other types of measurements when charted as a
histogram often form the shape of a bell
A ldquoperfect bellrdquo like a ldquoperfect circlerdquo doesnrsquot occur in nature but
many processes are close enough to make the bell curve useful
(A number of common industrial measurements such as flatness and straightness do NOT tend to distribute in a bell shape their proper statistical analysis is performed using models other than the bell curve)
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
51
What is a ldquostandard deviationrdquo
If we measure the DISTANCE from the CENTER of the bell
to each individual measurement that makes up the bell curve
we can find a TYPICAL DISTANCE
The most commonly used statistic to estimate this distance is the
Standard Deviation (also called ldquoSigmardquo)
Because of the natural shape of the bell curve the area of +1 to ndash1
standard deviations includes about 68 of the curve
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
Typical distance
from the center +1
standard deviation
Typical distance
from the center -1
standard deviation
52
How much of the curve is included in how many standard
deviations
From ndash1 to +1 is about 68 of the bell curve
From ndash2 to +2 is about 95
From ndash3 to +3 is about 9973
From ndash4 to +4 is about 9999
(NOTE We usually show the bell from ndash3 to +3 to make it easier to draw but in concept the ldquotailsrdquo of the bell get very thin and go on forever)
-6 -5 -4 -3 -2 -1 +1 +2 +3 +4 +5 +6 0
53
A
B
What is Cpk It is a measure of how well a process is within a specification
Cpk = A divided by B
A = Distance from process mean to closest spec limit
B = 3 Standard Deviations (also called ldquo3 Sigmardquo)
A bigger Cpk is better because fewer units will be beyond spec
(A bigger ldquoArdquo and a smaller ldquoBrdquo are better)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
54
A
B
ldquoProcess Capabilityrdquo is the ability of a process
to fit its output within the tolerances
hellipa LARGER ldquoArdquo
hellipand a SMALLER ldquoBrdquo
hellipmeans BETTER ldquoProcess Capabilityrdquo
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
55
A
B
An Analogy
Analogy
The bell curve is your automobile
The spec limits are the edges of your garage door
If A = B you are hitting the frame of your garage door with your car
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
56
A
B
How can we make Cpk (A divided by B) better
1 Design the product so a wider tolerance is functional (ldquorobust designrdquo)
2 Choose equipment and methods for a good safety margin (ldquoprocess capabilityrdquo)
3 Correctly adjust but only when needed (ldquocontrolrdquo)
4 Discover ways to narrow the natural variation (ldquoimprovementrdquo)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
57
A
B
What does a very good Cpk do for us
This process is producing good units with a good safety margin
Note that when Cpk = 2 our process mean is 6 standard deviations from
the nearest spec so we say it has ldquo6 Sigma Capabilityrdquo
Specification
Limit
Specification
Limit
This Cpk is
about 2
Very good
Mean
58
A
B
What does a problem Cpk look like
This process is in danger of producing some defects
It is too close to the specification limits
(Remember the bell curve tail goes further than Bhellip hellipwe only show the bell to 3-sigma to make it easier to draw)
Specification
Limit
Specification
Limit
This Cpk is just
slightly greater
than 1 Not good
59
A
B
What does a very bad Cpk look like
A significant part of the ldquotailrdquo is hanging out beyond the spec limits
This process is producing scrap rework and customer rejects
Notice that if distance ldquoArdquo approaches zerohellip
hellipthe Cpk would approach zero andhellip
hellipthe process would become 50 defective
Specification
Limit
Specification
Limit
This Cpk is less
than 1 We desire
a minimum of 133
and ultimately we
want 2 or more
60
-
Q amp A
61
MEASUREMENT SYSTEM ANALYSIS (MSA)
An MSA is a statistical tool used to determine if a measurement system is capable of precise measurement
What is It
Objective or Purpose
bull To determine how much error is in the measurement due to the measurement process itself
bull Quantifies the variability added by the measurement system
bull Applicable to attribute data and variable data
When to Use It
bull On the critical inputs and outputs prior to collecting data for analysis
bull For any new or modified process in order to ensure the quality of the data
Measurement System Analysis is an analysis of the measurement process not an analysis of the people
IMPORTANT
Who Should be Involved
Everyone that measures and makes decisions about these measurements should be involved in the MSA
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The observed variation in process output measurements is not simply the variation in the process itself it is the variation in the process plus the variation in measurement that results from an inadequate measurement system
Conducting an MSA reduces the likelihood of passing a bad part or rejecting a good part
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The output of the process measured by bull Cycle time bull Dimensional data bull Number of defects and others
Observed Variation
Process Variation
Measurement System
Variation
Reproducibility
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Accuracy (Central Location)
OBSERVED VARIATION
Calibration addresses accuracy
Measurement System Analysis (MSA)
MEASUREMENT SYSTEM ERRORS
Accuracy difference between the observed measurement and the actual measurement
Precision variation that occurs when measuring the same part with the same instrument
MEASUREMENT SYSTEM ERROR
Precise but not
accurate
Accurate but not
precise
Not accurate or
precise
Accurate and
precise
ACCURACY OF MEASUREMENT
Broken down into three components
aStability
The consistency of measurements over time
bBias
A measure of the amount of partiality in the system
cLinearity
A measure of the bias values through the expected
range of measurements
OBSERVED VARIATION
Observed Variation
Process Variation
Measurement System
Variation
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Reproducibility
Accuracy (Central Location)
Calibration Addresses Accuracy
Letrsquos take a closer look at Precision
Measurement System Analysis (MSA)
Measurement System Analysis (MSA)
Error in Resolution The inability to detect small changes
Possible Cause
Wrong measurement device selected - divisions on scale not fine enough to detect changes
Resolution
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Repeatability The inability to get the same answer from repeated measurements made of the same item under absolutely identical conditions
Possible Cause
Lack of standard operating procedures (SOP) lack of training measuring system variablilty
Repeatability
Equipment Variation
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Reproducibility The inability to get the same answer from repeated measurements made under various conditions from different inspectors
Possible Cause
Lack of SOP lack of training
Reproducibility
Appraiser Variation
VARIABLE MSA ndash GAGE RampR STUDY
bull Gage RampR is the combined estimate of
measurement system Repeatability and
Reproducibility
bull Typically a 3-person study is performed Each person randomly measures 10 marked parts per trial
Each person can perform up to 3 trials
bull There are 3 key indicators EV or Equipment Variation
AV or Appraiser Variation
Overall GRR
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
46
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
47
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
--and an individual part is measured at 520rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
48
GRAPHING THE TOLERANCE AND MEASUREMENTS
Suppose we made and measured several more
units and they were all EXACTLY the same
We wouldnrsquot have very many part problems
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
X
X
X
49
GRAPHING THE TOLERANCE AND MEASUREMENTS
In the real world units are NOT EXACTLY the same
Everything VARIES
The question isnrsquot IF units vary
Itrsquos how much when and why
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
XX
XXX
XXXXX
XXXXXXX
50
The ldquonormal bell curverdquo
Widths heights depths thicknesses weights speeds strengths
and many other types of measurements when charted as a
histogram often form the shape of a bell
A ldquoperfect bellrdquo like a ldquoperfect circlerdquo doesnrsquot occur in nature but
many processes are close enough to make the bell curve useful
(A number of common industrial measurements such as flatness and straightness do NOT tend to distribute in a bell shape their proper statistical analysis is performed using models other than the bell curve)
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
51
What is a ldquostandard deviationrdquo
If we measure the DISTANCE from the CENTER of the bell
to each individual measurement that makes up the bell curve
we can find a TYPICAL DISTANCE
The most commonly used statistic to estimate this distance is the
Standard Deviation (also called ldquoSigmardquo)
Because of the natural shape of the bell curve the area of +1 to ndash1
standard deviations includes about 68 of the curve
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
Typical distance
from the center +1
standard deviation
Typical distance
from the center -1
standard deviation
52
How much of the curve is included in how many standard
deviations
From ndash1 to +1 is about 68 of the bell curve
From ndash2 to +2 is about 95
From ndash3 to +3 is about 9973
From ndash4 to +4 is about 9999
(NOTE We usually show the bell from ndash3 to +3 to make it easier to draw but in concept the ldquotailsrdquo of the bell get very thin and go on forever)
-6 -5 -4 -3 -2 -1 +1 +2 +3 +4 +5 +6 0
53
A
B
What is Cpk It is a measure of how well a process is within a specification
Cpk = A divided by B
A = Distance from process mean to closest spec limit
B = 3 Standard Deviations (also called ldquo3 Sigmardquo)
A bigger Cpk is better because fewer units will be beyond spec
(A bigger ldquoArdquo and a smaller ldquoBrdquo are better)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
54
A
B
ldquoProcess Capabilityrdquo is the ability of a process
to fit its output within the tolerances
hellipa LARGER ldquoArdquo
hellipand a SMALLER ldquoBrdquo
hellipmeans BETTER ldquoProcess Capabilityrdquo
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
55
A
B
An Analogy
Analogy
The bell curve is your automobile
The spec limits are the edges of your garage door
If A = B you are hitting the frame of your garage door with your car
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
56
A
B
How can we make Cpk (A divided by B) better
1 Design the product so a wider tolerance is functional (ldquorobust designrdquo)
2 Choose equipment and methods for a good safety margin (ldquoprocess capabilityrdquo)
3 Correctly adjust but only when needed (ldquocontrolrdquo)
4 Discover ways to narrow the natural variation (ldquoimprovementrdquo)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
57
A
B
What does a very good Cpk do for us
This process is producing good units with a good safety margin
Note that when Cpk = 2 our process mean is 6 standard deviations from
the nearest spec so we say it has ldquo6 Sigma Capabilityrdquo
Specification
Limit
Specification
Limit
This Cpk is
about 2
Very good
Mean
58
A
B
What does a problem Cpk look like
This process is in danger of producing some defects
It is too close to the specification limits
(Remember the bell curve tail goes further than Bhellip hellipwe only show the bell to 3-sigma to make it easier to draw)
Specification
Limit
Specification
Limit
This Cpk is just
slightly greater
than 1 Not good
59
A
B
What does a very bad Cpk look like
A significant part of the ldquotailrdquo is hanging out beyond the spec limits
This process is producing scrap rework and customer rejects
Notice that if distance ldquoArdquo approaches zerohellip
hellipthe Cpk would approach zero andhellip
hellipthe process would become 50 defective
Specification
Limit
Specification
Limit
This Cpk is less
than 1 We desire
a minimum of 133
and ultimately we
want 2 or more
60
-
Q amp A
61
MEASUREMENT SYSTEM ANALYSIS (MSA)
An MSA is a statistical tool used to determine if a measurement system is capable of precise measurement
What is It
Objective or Purpose
bull To determine how much error is in the measurement due to the measurement process itself
bull Quantifies the variability added by the measurement system
bull Applicable to attribute data and variable data
When to Use It
bull On the critical inputs and outputs prior to collecting data for analysis
bull For any new or modified process in order to ensure the quality of the data
Measurement System Analysis is an analysis of the measurement process not an analysis of the people
IMPORTANT
Who Should be Involved
Everyone that measures and makes decisions about these measurements should be involved in the MSA
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The observed variation in process output measurements is not simply the variation in the process itself it is the variation in the process plus the variation in measurement that results from an inadequate measurement system
Conducting an MSA reduces the likelihood of passing a bad part or rejecting a good part
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The output of the process measured by bull Cycle time bull Dimensional data bull Number of defects and others
Observed Variation
Process Variation
Measurement System
Variation
Reproducibility
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Accuracy (Central Location)
OBSERVED VARIATION
Calibration addresses accuracy
Measurement System Analysis (MSA)
MEASUREMENT SYSTEM ERRORS
Accuracy difference between the observed measurement and the actual measurement
Precision variation that occurs when measuring the same part with the same instrument
MEASUREMENT SYSTEM ERROR
Precise but not
accurate
Accurate but not
precise
Not accurate or
precise
Accurate and
precise
ACCURACY OF MEASUREMENT
Broken down into three components
aStability
The consistency of measurements over time
bBias
A measure of the amount of partiality in the system
cLinearity
A measure of the bias values through the expected
range of measurements
OBSERVED VARIATION
Observed Variation
Process Variation
Measurement System
Variation
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Reproducibility
Accuracy (Central Location)
Calibration Addresses Accuracy
Letrsquos take a closer look at Precision
Measurement System Analysis (MSA)
Measurement System Analysis (MSA)
Error in Resolution The inability to detect small changes
Possible Cause
Wrong measurement device selected - divisions on scale not fine enough to detect changes
Resolution
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Repeatability The inability to get the same answer from repeated measurements made of the same item under absolutely identical conditions
Possible Cause
Lack of standard operating procedures (SOP) lack of training measuring system variablilty
Repeatability
Equipment Variation
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Reproducibility The inability to get the same answer from repeated measurements made under various conditions from different inspectors
Possible Cause
Lack of SOP lack of training
Reproducibility
Appraiser Variation
VARIABLE MSA ndash GAGE RampR STUDY
bull Gage RampR is the combined estimate of
measurement system Repeatability and
Reproducibility
bull Typically a 3-person study is performed Each person randomly measures 10 marked parts per trial
Each person can perform up to 3 trials
bull There are 3 key indicators EV or Equipment Variation
AV or Appraiser Variation
Overall GRR
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
47
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
--and an individual part is measured at 520rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
48
GRAPHING THE TOLERANCE AND MEASUREMENTS
Suppose we made and measured several more
units and they were all EXACTLY the same
We wouldnrsquot have very many part problems
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
X
X
X
49
GRAPHING THE TOLERANCE AND MEASUREMENTS
In the real world units are NOT EXACTLY the same
Everything VARIES
The question isnrsquot IF units vary
Itrsquos how much when and why
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
XX
XXX
XXXXX
XXXXXXX
50
The ldquonormal bell curverdquo
Widths heights depths thicknesses weights speeds strengths
and many other types of measurements when charted as a
histogram often form the shape of a bell
A ldquoperfect bellrdquo like a ldquoperfect circlerdquo doesnrsquot occur in nature but
many processes are close enough to make the bell curve useful
(A number of common industrial measurements such as flatness and straightness do NOT tend to distribute in a bell shape their proper statistical analysis is performed using models other than the bell curve)
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
51
What is a ldquostandard deviationrdquo
If we measure the DISTANCE from the CENTER of the bell
to each individual measurement that makes up the bell curve
we can find a TYPICAL DISTANCE
The most commonly used statistic to estimate this distance is the
Standard Deviation (also called ldquoSigmardquo)
Because of the natural shape of the bell curve the area of +1 to ndash1
standard deviations includes about 68 of the curve
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
Typical distance
from the center +1
standard deviation
Typical distance
from the center -1
standard deviation
52
How much of the curve is included in how many standard
deviations
From ndash1 to +1 is about 68 of the bell curve
From ndash2 to +2 is about 95
From ndash3 to +3 is about 9973
From ndash4 to +4 is about 9999
(NOTE We usually show the bell from ndash3 to +3 to make it easier to draw but in concept the ldquotailsrdquo of the bell get very thin and go on forever)
-6 -5 -4 -3 -2 -1 +1 +2 +3 +4 +5 +6 0
53
A
B
What is Cpk It is a measure of how well a process is within a specification
Cpk = A divided by B
A = Distance from process mean to closest spec limit
B = 3 Standard Deviations (also called ldquo3 Sigmardquo)
A bigger Cpk is better because fewer units will be beyond spec
(A bigger ldquoArdquo and a smaller ldquoBrdquo are better)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
54
A
B
ldquoProcess Capabilityrdquo is the ability of a process
to fit its output within the tolerances
hellipa LARGER ldquoArdquo
hellipand a SMALLER ldquoBrdquo
hellipmeans BETTER ldquoProcess Capabilityrdquo
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
55
A
B
An Analogy
Analogy
The bell curve is your automobile
The spec limits are the edges of your garage door
If A = B you are hitting the frame of your garage door with your car
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
56
A
B
How can we make Cpk (A divided by B) better
1 Design the product so a wider tolerance is functional (ldquorobust designrdquo)
2 Choose equipment and methods for a good safety margin (ldquoprocess capabilityrdquo)
3 Correctly adjust but only when needed (ldquocontrolrdquo)
4 Discover ways to narrow the natural variation (ldquoimprovementrdquo)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
57
A
B
What does a very good Cpk do for us
This process is producing good units with a good safety margin
Note that when Cpk = 2 our process mean is 6 standard deviations from
the nearest spec so we say it has ldquo6 Sigma Capabilityrdquo
Specification
Limit
Specification
Limit
This Cpk is
about 2
Very good
Mean
58
A
B
What does a problem Cpk look like
This process is in danger of producing some defects
It is too close to the specification limits
(Remember the bell curve tail goes further than Bhellip hellipwe only show the bell to 3-sigma to make it easier to draw)
Specification
Limit
Specification
Limit
This Cpk is just
slightly greater
than 1 Not good
59
A
B
What does a very bad Cpk look like
A significant part of the ldquotailrdquo is hanging out beyond the spec limits
This process is producing scrap rework and customer rejects
Notice that if distance ldquoArdquo approaches zerohellip
hellipthe Cpk would approach zero andhellip
hellipthe process would become 50 defective
Specification
Limit
Specification
Limit
This Cpk is less
than 1 We desire
a minimum of 133
and ultimately we
want 2 or more
60
-
Q amp A
61
MEASUREMENT SYSTEM ANALYSIS (MSA)
An MSA is a statistical tool used to determine if a measurement system is capable of precise measurement
What is It
Objective or Purpose
bull To determine how much error is in the measurement due to the measurement process itself
bull Quantifies the variability added by the measurement system
bull Applicable to attribute data and variable data
When to Use It
bull On the critical inputs and outputs prior to collecting data for analysis
bull For any new or modified process in order to ensure the quality of the data
Measurement System Analysis is an analysis of the measurement process not an analysis of the people
IMPORTANT
Who Should be Involved
Everyone that measures and makes decisions about these measurements should be involved in the MSA
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The observed variation in process output measurements is not simply the variation in the process itself it is the variation in the process plus the variation in measurement that results from an inadequate measurement system
Conducting an MSA reduces the likelihood of passing a bad part or rejecting a good part
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The output of the process measured by bull Cycle time bull Dimensional data bull Number of defects and others
Observed Variation
Process Variation
Measurement System
Variation
Reproducibility
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Accuracy (Central Location)
OBSERVED VARIATION
Calibration addresses accuracy
Measurement System Analysis (MSA)
MEASUREMENT SYSTEM ERRORS
Accuracy difference between the observed measurement and the actual measurement
Precision variation that occurs when measuring the same part with the same instrument
MEASUREMENT SYSTEM ERROR
Precise but not
accurate
Accurate but not
precise
Not accurate or
precise
Accurate and
precise
ACCURACY OF MEASUREMENT
Broken down into three components
aStability
The consistency of measurements over time
bBias
A measure of the amount of partiality in the system
cLinearity
A measure of the bias values through the expected
range of measurements
OBSERVED VARIATION
Observed Variation
Process Variation
Measurement System
Variation
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Reproducibility
Accuracy (Central Location)
Calibration Addresses Accuracy
Letrsquos take a closer look at Precision
Measurement System Analysis (MSA)
Measurement System Analysis (MSA)
Error in Resolution The inability to detect small changes
Possible Cause
Wrong measurement device selected - divisions on scale not fine enough to detect changes
Resolution
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Repeatability The inability to get the same answer from repeated measurements made of the same item under absolutely identical conditions
Possible Cause
Lack of standard operating procedures (SOP) lack of training measuring system variablilty
Repeatability
Equipment Variation
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Reproducibility The inability to get the same answer from repeated measurements made under various conditions from different inspectors
Possible Cause
Lack of SOP lack of training
Reproducibility
Appraiser Variation
VARIABLE MSA ndash GAGE RampR STUDY
bull Gage RampR is the combined estimate of
measurement system Repeatability and
Reproducibility
bull Typically a 3-person study is performed Each person randomly measures 10 marked parts per trial
Each person can perform up to 3 trials
bull There are 3 key indicators EV or Equipment Variation
AV or Appraiser Variation
Overall GRR
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
GRAPHING THE TOLERANCE AND A MEASUREMENT
Itrsquos useful to see the tolerance and the part measurement on a graph
Suppose that
--the tolerance is 515rdquo to 525rdquo
--and an individual part is measured at 520rdquo
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
48
GRAPHING THE TOLERANCE AND MEASUREMENTS
Suppose we made and measured several more
units and they were all EXACTLY the same
We wouldnrsquot have very many part problems
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
X
X
X
49
GRAPHING THE TOLERANCE AND MEASUREMENTS
In the real world units are NOT EXACTLY the same
Everything VARIES
The question isnrsquot IF units vary
Itrsquos how much when and why
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
XX
XXX
XXXXX
XXXXXXX
50
The ldquonormal bell curverdquo
Widths heights depths thicknesses weights speeds strengths
and many other types of measurements when charted as a
histogram often form the shape of a bell
A ldquoperfect bellrdquo like a ldquoperfect circlerdquo doesnrsquot occur in nature but
many processes are close enough to make the bell curve useful
(A number of common industrial measurements such as flatness and straightness do NOT tend to distribute in a bell shape their proper statistical analysis is performed using models other than the bell curve)
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
51
What is a ldquostandard deviationrdquo
If we measure the DISTANCE from the CENTER of the bell
to each individual measurement that makes up the bell curve
we can find a TYPICAL DISTANCE
The most commonly used statistic to estimate this distance is the
Standard Deviation (also called ldquoSigmardquo)
Because of the natural shape of the bell curve the area of +1 to ndash1
standard deviations includes about 68 of the curve
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
Typical distance
from the center +1
standard deviation
Typical distance
from the center -1
standard deviation
52
How much of the curve is included in how many standard
deviations
From ndash1 to +1 is about 68 of the bell curve
From ndash2 to +2 is about 95
From ndash3 to +3 is about 9973
From ndash4 to +4 is about 9999
(NOTE We usually show the bell from ndash3 to +3 to make it easier to draw but in concept the ldquotailsrdquo of the bell get very thin and go on forever)
-6 -5 -4 -3 -2 -1 +1 +2 +3 +4 +5 +6 0
53
A
B
What is Cpk It is a measure of how well a process is within a specification
Cpk = A divided by B
A = Distance from process mean to closest spec limit
B = 3 Standard Deviations (also called ldquo3 Sigmardquo)
A bigger Cpk is better because fewer units will be beyond spec
(A bigger ldquoArdquo and a smaller ldquoBrdquo are better)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
54
A
B
ldquoProcess Capabilityrdquo is the ability of a process
to fit its output within the tolerances
hellipa LARGER ldquoArdquo
hellipand a SMALLER ldquoBrdquo
hellipmeans BETTER ldquoProcess Capabilityrdquo
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
55
A
B
An Analogy
Analogy
The bell curve is your automobile
The spec limits are the edges of your garage door
If A = B you are hitting the frame of your garage door with your car
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
56
A
B
How can we make Cpk (A divided by B) better
1 Design the product so a wider tolerance is functional (ldquorobust designrdquo)
2 Choose equipment and methods for a good safety margin (ldquoprocess capabilityrdquo)
3 Correctly adjust but only when needed (ldquocontrolrdquo)
4 Discover ways to narrow the natural variation (ldquoimprovementrdquo)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
57
A
B
What does a very good Cpk do for us
This process is producing good units with a good safety margin
Note that when Cpk = 2 our process mean is 6 standard deviations from
the nearest spec so we say it has ldquo6 Sigma Capabilityrdquo
Specification
Limit
Specification
Limit
This Cpk is
about 2
Very good
Mean
58
A
B
What does a problem Cpk look like
This process is in danger of producing some defects
It is too close to the specification limits
(Remember the bell curve tail goes further than Bhellip hellipwe only show the bell to 3-sigma to make it easier to draw)
Specification
Limit
Specification
Limit
This Cpk is just
slightly greater
than 1 Not good
59
A
B
What does a very bad Cpk look like
A significant part of the ldquotailrdquo is hanging out beyond the spec limits
This process is producing scrap rework and customer rejects
Notice that if distance ldquoArdquo approaches zerohellip
hellipthe Cpk would approach zero andhellip
hellipthe process would become 50 defective
Specification
Limit
Specification
Limit
This Cpk is less
than 1 We desire
a minimum of 133
and ultimately we
want 2 or more
60
-
Q amp A
61
MEASUREMENT SYSTEM ANALYSIS (MSA)
An MSA is a statistical tool used to determine if a measurement system is capable of precise measurement
What is It
Objective or Purpose
bull To determine how much error is in the measurement due to the measurement process itself
bull Quantifies the variability added by the measurement system
bull Applicable to attribute data and variable data
When to Use It
bull On the critical inputs and outputs prior to collecting data for analysis
bull For any new or modified process in order to ensure the quality of the data
Measurement System Analysis is an analysis of the measurement process not an analysis of the people
IMPORTANT
Who Should be Involved
Everyone that measures and makes decisions about these measurements should be involved in the MSA
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The observed variation in process output measurements is not simply the variation in the process itself it is the variation in the process plus the variation in measurement that results from an inadequate measurement system
Conducting an MSA reduces the likelihood of passing a bad part or rejecting a good part
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The output of the process measured by bull Cycle time bull Dimensional data bull Number of defects and others
Observed Variation
Process Variation
Measurement System
Variation
Reproducibility
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Accuracy (Central Location)
OBSERVED VARIATION
Calibration addresses accuracy
Measurement System Analysis (MSA)
MEASUREMENT SYSTEM ERRORS
Accuracy difference between the observed measurement and the actual measurement
Precision variation that occurs when measuring the same part with the same instrument
MEASUREMENT SYSTEM ERROR
Precise but not
accurate
Accurate but not
precise
Not accurate or
precise
Accurate and
precise
ACCURACY OF MEASUREMENT
Broken down into three components
aStability
The consistency of measurements over time
bBias
A measure of the amount of partiality in the system
cLinearity
A measure of the bias values through the expected
range of measurements
OBSERVED VARIATION
Observed Variation
Process Variation
Measurement System
Variation
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Reproducibility
Accuracy (Central Location)
Calibration Addresses Accuracy
Letrsquos take a closer look at Precision
Measurement System Analysis (MSA)
Measurement System Analysis (MSA)
Error in Resolution The inability to detect small changes
Possible Cause
Wrong measurement device selected - divisions on scale not fine enough to detect changes
Resolution
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Repeatability The inability to get the same answer from repeated measurements made of the same item under absolutely identical conditions
Possible Cause
Lack of standard operating procedures (SOP) lack of training measuring system variablilty
Repeatability
Equipment Variation
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Reproducibility The inability to get the same answer from repeated measurements made under various conditions from different inspectors
Possible Cause
Lack of SOP lack of training
Reproducibility
Appraiser Variation
VARIABLE MSA ndash GAGE RampR STUDY
bull Gage RampR is the combined estimate of
measurement system Repeatability and
Reproducibility
bull Typically a 3-person study is performed Each person randomly measures 10 marked parts per trial
Each person can perform up to 3 trials
bull There are 3 key indicators EV or Equipment Variation
AV or Appraiser Variation
Overall GRR
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
GRAPHING THE TOLERANCE AND MEASUREMENTS
Suppose we made and measured several more
units and they were all EXACTLY the same
We wouldnrsquot have very many part problems
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
X
X
X
X
49
GRAPHING THE TOLERANCE AND MEASUREMENTS
In the real world units are NOT EXACTLY the same
Everything VARIES
The question isnrsquot IF units vary
Itrsquos how much when and why
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
XX
XXX
XXXXX
XXXXXXX
50
The ldquonormal bell curverdquo
Widths heights depths thicknesses weights speeds strengths
and many other types of measurements when charted as a
histogram often form the shape of a bell
A ldquoperfect bellrdquo like a ldquoperfect circlerdquo doesnrsquot occur in nature but
many processes are close enough to make the bell curve useful
(A number of common industrial measurements such as flatness and straightness do NOT tend to distribute in a bell shape their proper statistical analysis is performed using models other than the bell curve)
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
51
What is a ldquostandard deviationrdquo
If we measure the DISTANCE from the CENTER of the bell
to each individual measurement that makes up the bell curve
we can find a TYPICAL DISTANCE
The most commonly used statistic to estimate this distance is the
Standard Deviation (also called ldquoSigmardquo)
Because of the natural shape of the bell curve the area of +1 to ndash1
standard deviations includes about 68 of the curve
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
Typical distance
from the center +1
standard deviation
Typical distance
from the center -1
standard deviation
52
How much of the curve is included in how many standard
deviations
From ndash1 to +1 is about 68 of the bell curve
From ndash2 to +2 is about 95
From ndash3 to +3 is about 9973
From ndash4 to +4 is about 9999
(NOTE We usually show the bell from ndash3 to +3 to make it easier to draw but in concept the ldquotailsrdquo of the bell get very thin and go on forever)
-6 -5 -4 -3 -2 -1 +1 +2 +3 +4 +5 +6 0
53
A
B
What is Cpk It is a measure of how well a process is within a specification
Cpk = A divided by B
A = Distance from process mean to closest spec limit
B = 3 Standard Deviations (also called ldquo3 Sigmardquo)
A bigger Cpk is better because fewer units will be beyond spec
(A bigger ldquoArdquo and a smaller ldquoBrdquo are better)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
54
A
B
ldquoProcess Capabilityrdquo is the ability of a process
to fit its output within the tolerances
hellipa LARGER ldquoArdquo
hellipand a SMALLER ldquoBrdquo
hellipmeans BETTER ldquoProcess Capabilityrdquo
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
55
A
B
An Analogy
Analogy
The bell curve is your automobile
The spec limits are the edges of your garage door
If A = B you are hitting the frame of your garage door with your car
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
56
A
B
How can we make Cpk (A divided by B) better
1 Design the product so a wider tolerance is functional (ldquorobust designrdquo)
2 Choose equipment and methods for a good safety margin (ldquoprocess capabilityrdquo)
3 Correctly adjust but only when needed (ldquocontrolrdquo)
4 Discover ways to narrow the natural variation (ldquoimprovementrdquo)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
57
A
B
What does a very good Cpk do for us
This process is producing good units with a good safety margin
Note that when Cpk = 2 our process mean is 6 standard deviations from
the nearest spec so we say it has ldquo6 Sigma Capabilityrdquo
Specification
Limit
Specification
Limit
This Cpk is
about 2
Very good
Mean
58
A
B
What does a problem Cpk look like
This process is in danger of producing some defects
It is too close to the specification limits
(Remember the bell curve tail goes further than Bhellip hellipwe only show the bell to 3-sigma to make it easier to draw)
Specification
Limit
Specification
Limit
This Cpk is just
slightly greater
than 1 Not good
59
A
B
What does a very bad Cpk look like
A significant part of the ldquotailrdquo is hanging out beyond the spec limits
This process is producing scrap rework and customer rejects
Notice that if distance ldquoArdquo approaches zerohellip
hellipthe Cpk would approach zero andhellip
hellipthe process would become 50 defective
Specification
Limit
Specification
Limit
This Cpk is less
than 1 We desire
a minimum of 133
and ultimately we
want 2 or more
60
-
Q amp A
61
MEASUREMENT SYSTEM ANALYSIS (MSA)
An MSA is a statistical tool used to determine if a measurement system is capable of precise measurement
What is It
Objective or Purpose
bull To determine how much error is in the measurement due to the measurement process itself
bull Quantifies the variability added by the measurement system
bull Applicable to attribute data and variable data
When to Use It
bull On the critical inputs and outputs prior to collecting data for analysis
bull For any new or modified process in order to ensure the quality of the data
Measurement System Analysis is an analysis of the measurement process not an analysis of the people
IMPORTANT
Who Should be Involved
Everyone that measures and makes decisions about these measurements should be involved in the MSA
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The observed variation in process output measurements is not simply the variation in the process itself it is the variation in the process plus the variation in measurement that results from an inadequate measurement system
Conducting an MSA reduces the likelihood of passing a bad part or rejecting a good part
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The output of the process measured by bull Cycle time bull Dimensional data bull Number of defects and others
Observed Variation
Process Variation
Measurement System
Variation
Reproducibility
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Accuracy (Central Location)
OBSERVED VARIATION
Calibration addresses accuracy
Measurement System Analysis (MSA)
MEASUREMENT SYSTEM ERRORS
Accuracy difference between the observed measurement and the actual measurement
Precision variation that occurs when measuring the same part with the same instrument
MEASUREMENT SYSTEM ERROR
Precise but not
accurate
Accurate but not
precise
Not accurate or
precise
Accurate and
precise
ACCURACY OF MEASUREMENT
Broken down into three components
aStability
The consistency of measurements over time
bBias
A measure of the amount of partiality in the system
cLinearity
A measure of the bias values through the expected
range of measurements
OBSERVED VARIATION
Observed Variation
Process Variation
Measurement System
Variation
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Reproducibility
Accuracy (Central Location)
Calibration Addresses Accuracy
Letrsquos take a closer look at Precision
Measurement System Analysis (MSA)
Measurement System Analysis (MSA)
Error in Resolution The inability to detect small changes
Possible Cause
Wrong measurement device selected - divisions on scale not fine enough to detect changes
Resolution
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Repeatability The inability to get the same answer from repeated measurements made of the same item under absolutely identical conditions
Possible Cause
Lack of standard operating procedures (SOP) lack of training measuring system variablilty
Repeatability
Equipment Variation
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Reproducibility The inability to get the same answer from repeated measurements made under various conditions from different inspectors
Possible Cause
Lack of SOP lack of training
Reproducibility
Appraiser Variation
VARIABLE MSA ndash GAGE RampR STUDY
bull Gage RampR is the combined estimate of
measurement system Repeatability and
Reproducibility
bull Typically a 3-person study is performed Each person randomly measures 10 marked parts per trial
Each person can perform up to 3 trials
bull There are 3 key indicators EV or Equipment Variation
AV or Appraiser Variation
Overall GRR
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
GRAPHING THE TOLERANCE AND MEASUREMENTS
In the real world units are NOT EXACTLY the same
Everything VARIES
The question isnrsquot IF units vary
Itrsquos how much when and why
Specification
Limit MAX
Specification
Limit MIN
512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
XX
XXX
XXXXX
XXXXXXX
50
The ldquonormal bell curverdquo
Widths heights depths thicknesses weights speeds strengths
and many other types of measurements when charted as a
histogram often form the shape of a bell
A ldquoperfect bellrdquo like a ldquoperfect circlerdquo doesnrsquot occur in nature but
many processes are close enough to make the bell curve useful
(A number of common industrial measurements such as flatness and straightness do NOT tend to distribute in a bell shape their proper statistical analysis is performed using models other than the bell curve)
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
51
What is a ldquostandard deviationrdquo
If we measure the DISTANCE from the CENTER of the bell
to each individual measurement that makes up the bell curve
we can find a TYPICAL DISTANCE
The most commonly used statistic to estimate this distance is the
Standard Deviation (also called ldquoSigmardquo)
Because of the natural shape of the bell curve the area of +1 to ndash1
standard deviations includes about 68 of the curve
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
Typical distance
from the center +1
standard deviation
Typical distance
from the center -1
standard deviation
52
How much of the curve is included in how many standard
deviations
From ndash1 to +1 is about 68 of the bell curve
From ndash2 to +2 is about 95
From ndash3 to +3 is about 9973
From ndash4 to +4 is about 9999
(NOTE We usually show the bell from ndash3 to +3 to make it easier to draw but in concept the ldquotailsrdquo of the bell get very thin and go on forever)
-6 -5 -4 -3 -2 -1 +1 +2 +3 +4 +5 +6 0
53
A
B
What is Cpk It is a measure of how well a process is within a specification
Cpk = A divided by B
A = Distance from process mean to closest spec limit
B = 3 Standard Deviations (also called ldquo3 Sigmardquo)
A bigger Cpk is better because fewer units will be beyond spec
(A bigger ldquoArdquo and a smaller ldquoBrdquo are better)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
54
A
B
ldquoProcess Capabilityrdquo is the ability of a process
to fit its output within the tolerances
hellipa LARGER ldquoArdquo
hellipand a SMALLER ldquoBrdquo
hellipmeans BETTER ldquoProcess Capabilityrdquo
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
55
A
B
An Analogy
Analogy
The bell curve is your automobile
The spec limits are the edges of your garage door
If A = B you are hitting the frame of your garage door with your car
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
56
A
B
How can we make Cpk (A divided by B) better
1 Design the product so a wider tolerance is functional (ldquorobust designrdquo)
2 Choose equipment and methods for a good safety margin (ldquoprocess capabilityrdquo)
3 Correctly adjust but only when needed (ldquocontrolrdquo)
4 Discover ways to narrow the natural variation (ldquoimprovementrdquo)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
57
A
B
What does a very good Cpk do for us
This process is producing good units with a good safety margin
Note that when Cpk = 2 our process mean is 6 standard deviations from
the nearest spec so we say it has ldquo6 Sigma Capabilityrdquo
Specification
Limit
Specification
Limit
This Cpk is
about 2
Very good
Mean
58
A
B
What does a problem Cpk look like
This process is in danger of producing some defects
It is too close to the specification limits
(Remember the bell curve tail goes further than Bhellip hellipwe only show the bell to 3-sigma to make it easier to draw)
Specification
Limit
Specification
Limit
This Cpk is just
slightly greater
than 1 Not good
59
A
B
What does a very bad Cpk look like
A significant part of the ldquotailrdquo is hanging out beyond the spec limits
This process is producing scrap rework and customer rejects
Notice that if distance ldquoArdquo approaches zerohellip
hellipthe Cpk would approach zero andhellip
hellipthe process would become 50 defective
Specification
Limit
Specification
Limit
This Cpk is less
than 1 We desire
a minimum of 133
and ultimately we
want 2 or more
60
-
Q amp A
61
MEASUREMENT SYSTEM ANALYSIS (MSA)
An MSA is a statistical tool used to determine if a measurement system is capable of precise measurement
What is It
Objective or Purpose
bull To determine how much error is in the measurement due to the measurement process itself
bull Quantifies the variability added by the measurement system
bull Applicable to attribute data and variable data
When to Use It
bull On the critical inputs and outputs prior to collecting data for analysis
bull For any new or modified process in order to ensure the quality of the data
Measurement System Analysis is an analysis of the measurement process not an analysis of the people
IMPORTANT
Who Should be Involved
Everyone that measures and makes decisions about these measurements should be involved in the MSA
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The observed variation in process output measurements is not simply the variation in the process itself it is the variation in the process plus the variation in measurement that results from an inadequate measurement system
Conducting an MSA reduces the likelihood of passing a bad part or rejecting a good part
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The output of the process measured by bull Cycle time bull Dimensional data bull Number of defects and others
Observed Variation
Process Variation
Measurement System
Variation
Reproducibility
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Accuracy (Central Location)
OBSERVED VARIATION
Calibration addresses accuracy
Measurement System Analysis (MSA)
MEASUREMENT SYSTEM ERRORS
Accuracy difference between the observed measurement and the actual measurement
Precision variation that occurs when measuring the same part with the same instrument
MEASUREMENT SYSTEM ERROR
Precise but not
accurate
Accurate but not
precise
Not accurate or
precise
Accurate and
precise
ACCURACY OF MEASUREMENT
Broken down into three components
aStability
The consistency of measurements over time
bBias
A measure of the amount of partiality in the system
cLinearity
A measure of the bias values through the expected
range of measurements
OBSERVED VARIATION
Observed Variation
Process Variation
Measurement System
Variation
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Reproducibility
Accuracy (Central Location)
Calibration Addresses Accuracy
Letrsquos take a closer look at Precision
Measurement System Analysis (MSA)
Measurement System Analysis (MSA)
Error in Resolution The inability to detect small changes
Possible Cause
Wrong measurement device selected - divisions on scale not fine enough to detect changes
Resolution
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Repeatability The inability to get the same answer from repeated measurements made of the same item under absolutely identical conditions
Possible Cause
Lack of standard operating procedures (SOP) lack of training measuring system variablilty
Repeatability
Equipment Variation
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Reproducibility The inability to get the same answer from repeated measurements made under various conditions from different inspectors
Possible Cause
Lack of SOP lack of training
Reproducibility
Appraiser Variation
VARIABLE MSA ndash GAGE RampR STUDY
bull Gage RampR is the combined estimate of
measurement system Repeatability and
Reproducibility
bull Typically a 3-person study is performed Each person randomly measures 10 marked parts per trial
Each person can perform up to 3 trials
bull There are 3 key indicators EV or Equipment Variation
AV or Appraiser Variation
Overall GRR
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
The ldquonormal bell curverdquo
Widths heights depths thicknesses weights speeds strengths
and many other types of measurements when charted as a
histogram often form the shape of a bell
A ldquoperfect bellrdquo like a ldquoperfect circlerdquo doesnrsquot occur in nature but
many processes are close enough to make the bell curve useful
(A number of common industrial measurements such as flatness and straightness do NOT tend to distribute in a bell shape their proper statistical analysis is performed using models other than the bell curve)
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
51
What is a ldquostandard deviationrdquo
If we measure the DISTANCE from the CENTER of the bell
to each individual measurement that makes up the bell curve
we can find a TYPICAL DISTANCE
The most commonly used statistic to estimate this distance is the
Standard Deviation (also called ldquoSigmardquo)
Because of the natural shape of the bell curve the area of +1 to ndash1
standard deviations includes about 68 of the curve
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
Typical distance
from the center +1
standard deviation
Typical distance
from the center -1
standard deviation
52
How much of the curve is included in how many standard
deviations
From ndash1 to +1 is about 68 of the bell curve
From ndash2 to +2 is about 95
From ndash3 to +3 is about 9973
From ndash4 to +4 is about 9999
(NOTE We usually show the bell from ndash3 to +3 to make it easier to draw but in concept the ldquotailsrdquo of the bell get very thin and go on forever)
-6 -5 -4 -3 -2 -1 +1 +2 +3 +4 +5 +6 0
53
A
B
What is Cpk It is a measure of how well a process is within a specification
Cpk = A divided by B
A = Distance from process mean to closest spec limit
B = 3 Standard Deviations (also called ldquo3 Sigmardquo)
A bigger Cpk is better because fewer units will be beyond spec
(A bigger ldquoArdquo and a smaller ldquoBrdquo are better)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
54
A
B
ldquoProcess Capabilityrdquo is the ability of a process
to fit its output within the tolerances
hellipa LARGER ldquoArdquo
hellipand a SMALLER ldquoBrdquo
hellipmeans BETTER ldquoProcess Capabilityrdquo
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
55
A
B
An Analogy
Analogy
The bell curve is your automobile
The spec limits are the edges of your garage door
If A = B you are hitting the frame of your garage door with your car
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
56
A
B
How can we make Cpk (A divided by B) better
1 Design the product so a wider tolerance is functional (ldquorobust designrdquo)
2 Choose equipment and methods for a good safety margin (ldquoprocess capabilityrdquo)
3 Correctly adjust but only when needed (ldquocontrolrdquo)
4 Discover ways to narrow the natural variation (ldquoimprovementrdquo)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
57
A
B
What does a very good Cpk do for us
This process is producing good units with a good safety margin
Note that when Cpk = 2 our process mean is 6 standard deviations from
the nearest spec so we say it has ldquo6 Sigma Capabilityrdquo
Specification
Limit
Specification
Limit
This Cpk is
about 2
Very good
Mean
58
A
B
What does a problem Cpk look like
This process is in danger of producing some defects
It is too close to the specification limits
(Remember the bell curve tail goes further than Bhellip hellipwe only show the bell to 3-sigma to make it easier to draw)
Specification
Limit
Specification
Limit
This Cpk is just
slightly greater
than 1 Not good
59
A
B
What does a very bad Cpk look like
A significant part of the ldquotailrdquo is hanging out beyond the spec limits
This process is producing scrap rework and customer rejects
Notice that if distance ldquoArdquo approaches zerohellip
hellipthe Cpk would approach zero andhellip
hellipthe process would become 50 defective
Specification
Limit
Specification
Limit
This Cpk is less
than 1 We desire
a minimum of 133
and ultimately we
want 2 or more
60
-
Q amp A
61
MEASUREMENT SYSTEM ANALYSIS (MSA)
An MSA is a statistical tool used to determine if a measurement system is capable of precise measurement
What is It
Objective or Purpose
bull To determine how much error is in the measurement due to the measurement process itself
bull Quantifies the variability added by the measurement system
bull Applicable to attribute data and variable data
When to Use It
bull On the critical inputs and outputs prior to collecting data for analysis
bull For any new or modified process in order to ensure the quality of the data
Measurement System Analysis is an analysis of the measurement process not an analysis of the people
IMPORTANT
Who Should be Involved
Everyone that measures and makes decisions about these measurements should be involved in the MSA
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The observed variation in process output measurements is not simply the variation in the process itself it is the variation in the process plus the variation in measurement that results from an inadequate measurement system
Conducting an MSA reduces the likelihood of passing a bad part or rejecting a good part
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The output of the process measured by bull Cycle time bull Dimensional data bull Number of defects and others
Observed Variation
Process Variation
Measurement System
Variation
Reproducibility
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Accuracy (Central Location)
OBSERVED VARIATION
Calibration addresses accuracy
Measurement System Analysis (MSA)
MEASUREMENT SYSTEM ERRORS
Accuracy difference between the observed measurement and the actual measurement
Precision variation that occurs when measuring the same part with the same instrument
MEASUREMENT SYSTEM ERROR
Precise but not
accurate
Accurate but not
precise
Not accurate or
precise
Accurate and
precise
ACCURACY OF MEASUREMENT
Broken down into three components
aStability
The consistency of measurements over time
bBias
A measure of the amount of partiality in the system
cLinearity
A measure of the bias values through the expected
range of measurements
OBSERVED VARIATION
Observed Variation
Process Variation
Measurement System
Variation
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Reproducibility
Accuracy (Central Location)
Calibration Addresses Accuracy
Letrsquos take a closer look at Precision
Measurement System Analysis (MSA)
Measurement System Analysis (MSA)
Error in Resolution The inability to detect small changes
Possible Cause
Wrong measurement device selected - divisions on scale not fine enough to detect changes
Resolution
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Repeatability The inability to get the same answer from repeated measurements made of the same item under absolutely identical conditions
Possible Cause
Lack of standard operating procedures (SOP) lack of training measuring system variablilty
Repeatability
Equipment Variation
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Reproducibility The inability to get the same answer from repeated measurements made under various conditions from different inspectors
Possible Cause
Lack of SOP lack of training
Reproducibility
Appraiser Variation
VARIABLE MSA ndash GAGE RampR STUDY
bull Gage RampR is the combined estimate of
measurement system Repeatability and
Reproducibility
bull Typically a 3-person study is performed Each person randomly measures 10 marked parts per trial
Each person can perform up to 3 trials
bull There are 3 key indicators EV or Equipment Variation
AV or Appraiser Variation
Overall GRR
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
What is a ldquostandard deviationrdquo
If we measure the DISTANCE from the CENTER of the bell
to each individual measurement that makes up the bell curve
we can find a TYPICAL DISTANCE
The most commonly used statistic to estimate this distance is the
Standard Deviation (also called ldquoSigmardquo)
Because of the natural shape of the bell curve the area of +1 to ndash1
standard deviations includes about 68 of the curve
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
XX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXXXXX
Typical distance
from the center +1
standard deviation
Typical distance
from the center -1
standard deviation
52
How much of the curve is included in how many standard
deviations
From ndash1 to +1 is about 68 of the bell curve
From ndash2 to +2 is about 95
From ndash3 to +3 is about 9973
From ndash4 to +4 is about 9999
(NOTE We usually show the bell from ndash3 to +3 to make it easier to draw but in concept the ldquotailsrdquo of the bell get very thin and go on forever)
-6 -5 -4 -3 -2 -1 +1 +2 +3 +4 +5 +6 0
53
A
B
What is Cpk It is a measure of how well a process is within a specification
Cpk = A divided by B
A = Distance from process mean to closest spec limit
B = 3 Standard Deviations (also called ldquo3 Sigmardquo)
A bigger Cpk is better because fewer units will be beyond spec
(A bigger ldquoArdquo and a smaller ldquoBrdquo are better)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
54
A
B
ldquoProcess Capabilityrdquo is the ability of a process
to fit its output within the tolerances
hellipa LARGER ldquoArdquo
hellipand a SMALLER ldquoBrdquo
hellipmeans BETTER ldquoProcess Capabilityrdquo
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
55
A
B
An Analogy
Analogy
The bell curve is your automobile
The spec limits are the edges of your garage door
If A = B you are hitting the frame of your garage door with your car
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
56
A
B
How can we make Cpk (A divided by B) better
1 Design the product so a wider tolerance is functional (ldquorobust designrdquo)
2 Choose equipment and methods for a good safety margin (ldquoprocess capabilityrdquo)
3 Correctly adjust but only when needed (ldquocontrolrdquo)
4 Discover ways to narrow the natural variation (ldquoimprovementrdquo)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
57
A
B
What does a very good Cpk do for us
This process is producing good units with a good safety margin
Note that when Cpk = 2 our process mean is 6 standard deviations from
the nearest spec so we say it has ldquo6 Sigma Capabilityrdquo
Specification
Limit
Specification
Limit
This Cpk is
about 2
Very good
Mean
58
A
B
What does a problem Cpk look like
This process is in danger of producing some defects
It is too close to the specification limits
(Remember the bell curve tail goes further than Bhellip hellipwe only show the bell to 3-sigma to make it easier to draw)
Specification
Limit
Specification
Limit
This Cpk is just
slightly greater
than 1 Not good
59
A
B
What does a very bad Cpk look like
A significant part of the ldquotailrdquo is hanging out beyond the spec limits
This process is producing scrap rework and customer rejects
Notice that if distance ldquoArdquo approaches zerohellip
hellipthe Cpk would approach zero andhellip
hellipthe process would become 50 defective
Specification
Limit
Specification
Limit
This Cpk is less
than 1 We desire
a minimum of 133
and ultimately we
want 2 or more
60
-
Q amp A
61
MEASUREMENT SYSTEM ANALYSIS (MSA)
An MSA is a statistical tool used to determine if a measurement system is capable of precise measurement
What is It
Objective or Purpose
bull To determine how much error is in the measurement due to the measurement process itself
bull Quantifies the variability added by the measurement system
bull Applicable to attribute data and variable data
When to Use It
bull On the critical inputs and outputs prior to collecting data for analysis
bull For any new or modified process in order to ensure the quality of the data
Measurement System Analysis is an analysis of the measurement process not an analysis of the people
IMPORTANT
Who Should be Involved
Everyone that measures and makes decisions about these measurements should be involved in the MSA
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The observed variation in process output measurements is not simply the variation in the process itself it is the variation in the process plus the variation in measurement that results from an inadequate measurement system
Conducting an MSA reduces the likelihood of passing a bad part or rejecting a good part
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The output of the process measured by bull Cycle time bull Dimensional data bull Number of defects and others
Observed Variation
Process Variation
Measurement System
Variation
Reproducibility
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Accuracy (Central Location)
OBSERVED VARIATION
Calibration addresses accuracy
Measurement System Analysis (MSA)
MEASUREMENT SYSTEM ERRORS
Accuracy difference between the observed measurement and the actual measurement
Precision variation that occurs when measuring the same part with the same instrument
MEASUREMENT SYSTEM ERROR
Precise but not
accurate
Accurate but not
precise
Not accurate or
precise
Accurate and
precise
ACCURACY OF MEASUREMENT
Broken down into three components
aStability
The consistency of measurements over time
bBias
A measure of the amount of partiality in the system
cLinearity
A measure of the bias values through the expected
range of measurements
OBSERVED VARIATION
Observed Variation
Process Variation
Measurement System
Variation
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Reproducibility
Accuracy (Central Location)
Calibration Addresses Accuracy
Letrsquos take a closer look at Precision
Measurement System Analysis (MSA)
Measurement System Analysis (MSA)
Error in Resolution The inability to detect small changes
Possible Cause
Wrong measurement device selected - divisions on scale not fine enough to detect changes
Resolution
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Repeatability The inability to get the same answer from repeated measurements made of the same item under absolutely identical conditions
Possible Cause
Lack of standard operating procedures (SOP) lack of training measuring system variablilty
Repeatability
Equipment Variation
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Reproducibility The inability to get the same answer from repeated measurements made under various conditions from different inspectors
Possible Cause
Lack of SOP lack of training
Reproducibility
Appraiser Variation
VARIABLE MSA ndash GAGE RampR STUDY
bull Gage RampR is the combined estimate of
measurement system Repeatability and
Reproducibility
bull Typically a 3-person study is performed Each person randomly measures 10 marked parts per trial
Each person can perform up to 3 trials
bull There are 3 key indicators EV or Equipment Variation
AV or Appraiser Variation
Overall GRR
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
How much of the curve is included in how many standard
deviations
From ndash1 to +1 is about 68 of the bell curve
From ndash2 to +2 is about 95
From ndash3 to +3 is about 9973
From ndash4 to +4 is about 9999
(NOTE We usually show the bell from ndash3 to +3 to make it easier to draw but in concept the ldquotailsrdquo of the bell get very thin and go on forever)
-6 -5 -4 -3 -2 -1 +1 +2 +3 +4 +5 +6 0
53
A
B
What is Cpk It is a measure of how well a process is within a specification
Cpk = A divided by B
A = Distance from process mean to closest spec limit
B = 3 Standard Deviations (also called ldquo3 Sigmardquo)
A bigger Cpk is better because fewer units will be beyond spec
(A bigger ldquoArdquo and a smaller ldquoBrdquo are better)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
54
A
B
ldquoProcess Capabilityrdquo is the ability of a process
to fit its output within the tolerances
hellipa LARGER ldquoArdquo
hellipand a SMALLER ldquoBrdquo
hellipmeans BETTER ldquoProcess Capabilityrdquo
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
55
A
B
An Analogy
Analogy
The bell curve is your automobile
The spec limits are the edges of your garage door
If A = B you are hitting the frame of your garage door with your car
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
56
A
B
How can we make Cpk (A divided by B) better
1 Design the product so a wider tolerance is functional (ldquorobust designrdquo)
2 Choose equipment and methods for a good safety margin (ldquoprocess capabilityrdquo)
3 Correctly adjust but only when needed (ldquocontrolrdquo)
4 Discover ways to narrow the natural variation (ldquoimprovementrdquo)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
57
A
B
What does a very good Cpk do for us
This process is producing good units with a good safety margin
Note that when Cpk = 2 our process mean is 6 standard deviations from
the nearest spec so we say it has ldquo6 Sigma Capabilityrdquo
Specification
Limit
Specification
Limit
This Cpk is
about 2
Very good
Mean
58
A
B
What does a problem Cpk look like
This process is in danger of producing some defects
It is too close to the specification limits
(Remember the bell curve tail goes further than Bhellip hellipwe only show the bell to 3-sigma to make it easier to draw)
Specification
Limit
Specification
Limit
This Cpk is just
slightly greater
than 1 Not good
59
A
B
What does a very bad Cpk look like
A significant part of the ldquotailrdquo is hanging out beyond the spec limits
This process is producing scrap rework and customer rejects
Notice that if distance ldquoArdquo approaches zerohellip
hellipthe Cpk would approach zero andhellip
hellipthe process would become 50 defective
Specification
Limit
Specification
Limit
This Cpk is less
than 1 We desire
a minimum of 133
and ultimately we
want 2 or more
60
-
Q amp A
61
MEASUREMENT SYSTEM ANALYSIS (MSA)
An MSA is a statistical tool used to determine if a measurement system is capable of precise measurement
What is It
Objective or Purpose
bull To determine how much error is in the measurement due to the measurement process itself
bull Quantifies the variability added by the measurement system
bull Applicable to attribute data and variable data
When to Use It
bull On the critical inputs and outputs prior to collecting data for analysis
bull For any new or modified process in order to ensure the quality of the data
Measurement System Analysis is an analysis of the measurement process not an analysis of the people
IMPORTANT
Who Should be Involved
Everyone that measures and makes decisions about these measurements should be involved in the MSA
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The observed variation in process output measurements is not simply the variation in the process itself it is the variation in the process plus the variation in measurement that results from an inadequate measurement system
Conducting an MSA reduces the likelihood of passing a bad part or rejecting a good part
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The output of the process measured by bull Cycle time bull Dimensional data bull Number of defects and others
Observed Variation
Process Variation
Measurement System
Variation
Reproducibility
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Accuracy (Central Location)
OBSERVED VARIATION
Calibration addresses accuracy
Measurement System Analysis (MSA)
MEASUREMENT SYSTEM ERRORS
Accuracy difference between the observed measurement and the actual measurement
Precision variation that occurs when measuring the same part with the same instrument
MEASUREMENT SYSTEM ERROR
Precise but not
accurate
Accurate but not
precise
Not accurate or
precise
Accurate and
precise
ACCURACY OF MEASUREMENT
Broken down into three components
aStability
The consistency of measurements over time
bBias
A measure of the amount of partiality in the system
cLinearity
A measure of the bias values through the expected
range of measurements
OBSERVED VARIATION
Observed Variation
Process Variation
Measurement System
Variation
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Reproducibility
Accuracy (Central Location)
Calibration Addresses Accuracy
Letrsquos take a closer look at Precision
Measurement System Analysis (MSA)
Measurement System Analysis (MSA)
Error in Resolution The inability to detect small changes
Possible Cause
Wrong measurement device selected - divisions on scale not fine enough to detect changes
Resolution
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Repeatability The inability to get the same answer from repeated measurements made of the same item under absolutely identical conditions
Possible Cause
Lack of standard operating procedures (SOP) lack of training measuring system variablilty
Repeatability
Equipment Variation
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Reproducibility The inability to get the same answer from repeated measurements made under various conditions from different inspectors
Possible Cause
Lack of SOP lack of training
Reproducibility
Appraiser Variation
VARIABLE MSA ndash GAGE RampR STUDY
bull Gage RampR is the combined estimate of
measurement system Repeatability and
Reproducibility
bull Typically a 3-person study is performed Each person randomly measures 10 marked parts per trial
Each person can perform up to 3 trials
bull There are 3 key indicators EV or Equipment Variation
AV or Appraiser Variation
Overall GRR
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
A
B
What is Cpk It is a measure of how well a process is within a specification
Cpk = A divided by B
A = Distance from process mean to closest spec limit
B = 3 Standard Deviations (also called ldquo3 Sigmardquo)
A bigger Cpk is better because fewer units will be beyond spec
(A bigger ldquoArdquo and a smaller ldquoBrdquo are better)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
54
A
B
ldquoProcess Capabilityrdquo is the ability of a process
to fit its output within the tolerances
hellipa LARGER ldquoArdquo
hellipand a SMALLER ldquoBrdquo
hellipmeans BETTER ldquoProcess Capabilityrdquo
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
55
A
B
An Analogy
Analogy
The bell curve is your automobile
The spec limits are the edges of your garage door
If A = B you are hitting the frame of your garage door with your car
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
56
A
B
How can we make Cpk (A divided by B) better
1 Design the product so a wider tolerance is functional (ldquorobust designrdquo)
2 Choose equipment and methods for a good safety margin (ldquoprocess capabilityrdquo)
3 Correctly adjust but only when needed (ldquocontrolrdquo)
4 Discover ways to narrow the natural variation (ldquoimprovementrdquo)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
57
A
B
What does a very good Cpk do for us
This process is producing good units with a good safety margin
Note that when Cpk = 2 our process mean is 6 standard deviations from
the nearest spec so we say it has ldquo6 Sigma Capabilityrdquo
Specification
Limit
Specification
Limit
This Cpk is
about 2
Very good
Mean
58
A
B
What does a problem Cpk look like
This process is in danger of producing some defects
It is too close to the specification limits
(Remember the bell curve tail goes further than Bhellip hellipwe only show the bell to 3-sigma to make it easier to draw)
Specification
Limit
Specification
Limit
This Cpk is just
slightly greater
than 1 Not good
59
A
B
What does a very bad Cpk look like
A significant part of the ldquotailrdquo is hanging out beyond the spec limits
This process is producing scrap rework and customer rejects
Notice that if distance ldquoArdquo approaches zerohellip
hellipthe Cpk would approach zero andhellip
hellipthe process would become 50 defective
Specification
Limit
Specification
Limit
This Cpk is less
than 1 We desire
a minimum of 133
and ultimately we
want 2 or more
60
-
Q amp A
61
MEASUREMENT SYSTEM ANALYSIS (MSA)
An MSA is a statistical tool used to determine if a measurement system is capable of precise measurement
What is It
Objective or Purpose
bull To determine how much error is in the measurement due to the measurement process itself
bull Quantifies the variability added by the measurement system
bull Applicable to attribute data and variable data
When to Use It
bull On the critical inputs and outputs prior to collecting data for analysis
bull For any new or modified process in order to ensure the quality of the data
Measurement System Analysis is an analysis of the measurement process not an analysis of the people
IMPORTANT
Who Should be Involved
Everyone that measures and makes decisions about these measurements should be involved in the MSA
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The observed variation in process output measurements is not simply the variation in the process itself it is the variation in the process plus the variation in measurement that results from an inadequate measurement system
Conducting an MSA reduces the likelihood of passing a bad part or rejecting a good part
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The output of the process measured by bull Cycle time bull Dimensional data bull Number of defects and others
Observed Variation
Process Variation
Measurement System
Variation
Reproducibility
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Accuracy (Central Location)
OBSERVED VARIATION
Calibration addresses accuracy
Measurement System Analysis (MSA)
MEASUREMENT SYSTEM ERRORS
Accuracy difference between the observed measurement and the actual measurement
Precision variation that occurs when measuring the same part with the same instrument
MEASUREMENT SYSTEM ERROR
Precise but not
accurate
Accurate but not
precise
Not accurate or
precise
Accurate and
precise
ACCURACY OF MEASUREMENT
Broken down into three components
aStability
The consistency of measurements over time
bBias
A measure of the amount of partiality in the system
cLinearity
A measure of the bias values through the expected
range of measurements
OBSERVED VARIATION
Observed Variation
Process Variation
Measurement System
Variation
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Reproducibility
Accuracy (Central Location)
Calibration Addresses Accuracy
Letrsquos take a closer look at Precision
Measurement System Analysis (MSA)
Measurement System Analysis (MSA)
Error in Resolution The inability to detect small changes
Possible Cause
Wrong measurement device selected - divisions on scale not fine enough to detect changes
Resolution
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Repeatability The inability to get the same answer from repeated measurements made of the same item under absolutely identical conditions
Possible Cause
Lack of standard operating procedures (SOP) lack of training measuring system variablilty
Repeatability
Equipment Variation
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Reproducibility The inability to get the same answer from repeated measurements made under various conditions from different inspectors
Possible Cause
Lack of SOP lack of training
Reproducibility
Appraiser Variation
VARIABLE MSA ndash GAGE RampR STUDY
bull Gage RampR is the combined estimate of
measurement system Repeatability and
Reproducibility
bull Typically a 3-person study is performed Each person randomly measures 10 marked parts per trial
Each person can perform up to 3 trials
bull There are 3 key indicators EV or Equipment Variation
AV or Appraiser Variation
Overall GRR
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
A
B
ldquoProcess Capabilityrdquo is the ability of a process
to fit its output within the tolerances
hellipa LARGER ldquoArdquo
hellipand a SMALLER ldquoBrdquo
hellipmeans BETTER ldquoProcess Capabilityrdquo
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
55
A
B
An Analogy
Analogy
The bell curve is your automobile
The spec limits are the edges of your garage door
If A = B you are hitting the frame of your garage door with your car
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
56
A
B
How can we make Cpk (A divided by B) better
1 Design the product so a wider tolerance is functional (ldquorobust designrdquo)
2 Choose equipment and methods for a good safety margin (ldquoprocess capabilityrdquo)
3 Correctly adjust but only when needed (ldquocontrolrdquo)
4 Discover ways to narrow the natural variation (ldquoimprovementrdquo)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
57
A
B
What does a very good Cpk do for us
This process is producing good units with a good safety margin
Note that when Cpk = 2 our process mean is 6 standard deviations from
the nearest spec so we say it has ldquo6 Sigma Capabilityrdquo
Specification
Limit
Specification
Limit
This Cpk is
about 2
Very good
Mean
58
A
B
What does a problem Cpk look like
This process is in danger of producing some defects
It is too close to the specification limits
(Remember the bell curve tail goes further than Bhellip hellipwe only show the bell to 3-sigma to make it easier to draw)
Specification
Limit
Specification
Limit
This Cpk is just
slightly greater
than 1 Not good
59
A
B
What does a very bad Cpk look like
A significant part of the ldquotailrdquo is hanging out beyond the spec limits
This process is producing scrap rework and customer rejects
Notice that if distance ldquoArdquo approaches zerohellip
hellipthe Cpk would approach zero andhellip
hellipthe process would become 50 defective
Specification
Limit
Specification
Limit
This Cpk is less
than 1 We desire
a minimum of 133
and ultimately we
want 2 or more
60
-
Q amp A
61
MEASUREMENT SYSTEM ANALYSIS (MSA)
An MSA is a statistical tool used to determine if a measurement system is capable of precise measurement
What is It
Objective or Purpose
bull To determine how much error is in the measurement due to the measurement process itself
bull Quantifies the variability added by the measurement system
bull Applicable to attribute data and variable data
When to Use It
bull On the critical inputs and outputs prior to collecting data for analysis
bull For any new or modified process in order to ensure the quality of the data
Measurement System Analysis is an analysis of the measurement process not an analysis of the people
IMPORTANT
Who Should be Involved
Everyone that measures and makes decisions about these measurements should be involved in the MSA
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The observed variation in process output measurements is not simply the variation in the process itself it is the variation in the process plus the variation in measurement that results from an inadequate measurement system
Conducting an MSA reduces the likelihood of passing a bad part or rejecting a good part
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The output of the process measured by bull Cycle time bull Dimensional data bull Number of defects and others
Observed Variation
Process Variation
Measurement System
Variation
Reproducibility
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Accuracy (Central Location)
OBSERVED VARIATION
Calibration addresses accuracy
Measurement System Analysis (MSA)
MEASUREMENT SYSTEM ERRORS
Accuracy difference between the observed measurement and the actual measurement
Precision variation that occurs when measuring the same part with the same instrument
MEASUREMENT SYSTEM ERROR
Precise but not
accurate
Accurate but not
precise
Not accurate or
precise
Accurate and
precise
ACCURACY OF MEASUREMENT
Broken down into three components
aStability
The consistency of measurements over time
bBias
A measure of the amount of partiality in the system
cLinearity
A measure of the bias values through the expected
range of measurements
OBSERVED VARIATION
Observed Variation
Process Variation
Measurement System
Variation
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Reproducibility
Accuracy (Central Location)
Calibration Addresses Accuracy
Letrsquos take a closer look at Precision
Measurement System Analysis (MSA)
Measurement System Analysis (MSA)
Error in Resolution The inability to detect small changes
Possible Cause
Wrong measurement device selected - divisions on scale not fine enough to detect changes
Resolution
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Repeatability The inability to get the same answer from repeated measurements made of the same item under absolutely identical conditions
Possible Cause
Lack of standard operating procedures (SOP) lack of training measuring system variablilty
Repeatability
Equipment Variation
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Reproducibility The inability to get the same answer from repeated measurements made under various conditions from different inspectors
Possible Cause
Lack of SOP lack of training
Reproducibility
Appraiser Variation
VARIABLE MSA ndash GAGE RampR STUDY
bull Gage RampR is the combined estimate of
measurement system Repeatability and
Reproducibility
bull Typically a 3-person study is performed Each person randomly measures 10 marked parts per trial
Each person can perform up to 3 trials
bull There are 3 key indicators EV or Equipment Variation
AV or Appraiser Variation
Overall GRR
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
A
B
An Analogy
Analogy
The bell curve is your automobile
The spec limits are the edges of your garage door
If A = B you are hitting the frame of your garage door with your car
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
56
A
B
How can we make Cpk (A divided by B) better
1 Design the product so a wider tolerance is functional (ldquorobust designrdquo)
2 Choose equipment and methods for a good safety margin (ldquoprocess capabilityrdquo)
3 Correctly adjust but only when needed (ldquocontrolrdquo)
4 Discover ways to narrow the natural variation (ldquoimprovementrdquo)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
57
A
B
What does a very good Cpk do for us
This process is producing good units with a good safety margin
Note that when Cpk = 2 our process mean is 6 standard deviations from
the nearest spec so we say it has ldquo6 Sigma Capabilityrdquo
Specification
Limit
Specification
Limit
This Cpk is
about 2
Very good
Mean
58
A
B
What does a problem Cpk look like
This process is in danger of producing some defects
It is too close to the specification limits
(Remember the bell curve tail goes further than Bhellip hellipwe only show the bell to 3-sigma to make it easier to draw)
Specification
Limit
Specification
Limit
This Cpk is just
slightly greater
than 1 Not good
59
A
B
What does a very bad Cpk look like
A significant part of the ldquotailrdquo is hanging out beyond the spec limits
This process is producing scrap rework and customer rejects
Notice that if distance ldquoArdquo approaches zerohellip
hellipthe Cpk would approach zero andhellip
hellipthe process would become 50 defective
Specification
Limit
Specification
Limit
This Cpk is less
than 1 We desire
a minimum of 133
and ultimately we
want 2 or more
60
-
Q amp A
61
MEASUREMENT SYSTEM ANALYSIS (MSA)
An MSA is a statistical tool used to determine if a measurement system is capable of precise measurement
What is It
Objective or Purpose
bull To determine how much error is in the measurement due to the measurement process itself
bull Quantifies the variability added by the measurement system
bull Applicable to attribute data and variable data
When to Use It
bull On the critical inputs and outputs prior to collecting data for analysis
bull For any new or modified process in order to ensure the quality of the data
Measurement System Analysis is an analysis of the measurement process not an analysis of the people
IMPORTANT
Who Should be Involved
Everyone that measures and makes decisions about these measurements should be involved in the MSA
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The observed variation in process output measurements is not simply the variation in the process itself it is the variation in the process plus the variation in measurement that results from an inadequate measurement system
Conducting an MSA reduces the likelihood of passing a bad part or rejecting a good part
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The output of the process measured by bull Cycle time bull Dimensional data bull Number of defects and others
Observed Variation
Process Variation
Measurement System
Variation
Reproducibility
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Accuracy (Central Location)
OBSERVED VARIATION
Calibration addresses accuracy
Measurement System Analysis (MSA)
MEASUREMENT SYSTEM ERRORS
Accuracy difference between the observed measurement and the actual measurement
Precision variation that occurs when measuring the same part with the same instrument
MEASUREMENT SYSTEM ERROR
Precise but not
accurate
Accurate but not
precise
Not accurate or
precise
Accurate and
precise
ACCURACY OF MEASUREMENT
Broken down into three components
aStability
The consistency of measurements over time
bBias
A measure of the amount of partiality in the system
cLinearity
A measure of the bias values through the expected
range of measurements
OBSERVED VARIATION
Observed Variation
Process Variation
Measurement System
Variation
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Reproducibility
Accuracy (Central Location)
Calibration Addresses Accuracy
Letrsquos take a closer look at Precision
Measurement System Analysis (MSA)
Measurement System Analysis (MSA)
Error in Resolution The inability to detect small changes
Possible Cause
Wrong measurement device selected - divisions on scale not fine enough to detect changes
Resolution
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Repeatability The inability to get the same answer from repeated measurements made of the same item under absolutely identical conditions
Possible Cause
Lack of standard operating procedures (SOP) lack of training measuring system variablilty
Repeatability
Equipment Variation
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Reproducibility The inability to get the same answer from repeated measurements made under various conditions from different inspectors
Possible Cause
Lack of SOP lack of training
Reproducibility
Appraiser Variation
VARIABLE MSA ndash GAGE RampR STUDY
bull Gage RampR is the combined estimate of
measurement system Repeatability and
Reproducibility
bull Typically a 3-person study is performed Each person randomly measures 10 marked parts per trial
Each person can perform up to 3 trials
bull There are 3 key indicators EV or Equipment Variation
AV or Appraiser Variation
Overall GRR
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
A
B
How can we make Cpk (A divided by B) better
1 Design the product so a wider tolerance is functional (ldquorobust designrdquo)
2 Choose equipment and methods for a good safety margin (ldquoprocess capabilityrdquo)
3 Correctly adjust but only when needed (ldquocontrolrdquo)
4 Discover ways to narrow the natural variation (ldquoimprovementrdquo)
Specification
Limit
Specification
Limit
Cpk =
A divided by
B
57
A
B
What does a very good Cpk do for us
This process is producing good units with a good safety margin
Note that when Cpk = 2 our process mean is 6 standard deviations from
the nearest spec so we say it has ldquo6 Sigma Capabilityrdquo
Specification
Limit
Specification
Limit
This Cpk is
about 2
Very good
Mean
58
A
B
What does a problem Cpk look like
This process is in danger of producing some defects
It is too close to the specification limits
(Remember the bell curve tail goes further than Bhellip hellipwe only show the bell to 3-sigma to make it easier to draw)
Specification
Limit
Specification
Limit
This Cpk is just
slightly greater
than 1 Not good
59
A
B
What does a very bad Cpk look like
A significant part of the ldquotailrdquo is hanging out beyond the spec limits
This process is producing scrap rework and customer rejects
Notice that if distance ldquoArdquo approaches zerohellip
hellipthe Cpk would approach zero andhellip
hellipthe process would become 50 defective
Specification
Limit
Specification
Limit
This Cpk is less
than 1 We desire
a minimum of 133
and ultimately we
want 2 or more
60
-
Q amp A
61
MEASUREMENT SYSTEM ANALYSIS (MSA)
An MSA is a statistical tool used to determine if a measurement system is capable of precise measurement
What is It
Objective or Purpose
bull To determine how much error is in the measurement due to the measurement process itself
bull Quantifies the variability added by the measurement system
bull Applicable to attribute data and variable data
When to Use It
bull On the critical inputs and outputs prior to collecting data for analysis
bull For any new or modified process in order to ensure the quality of the data
Measurement System Analysis is an analysis of the measurement process not an analysis of the people
IMPORTANT
Who Should be Involved
Everyone that measures and makes decisions about these measurements should be involved in the MSA
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The observed variation in process output measurements is not simply the variation in the process itself it is the variation in the process plus the variation in measurement that results from an inadequate measurement system
Conducting an MSA reduces the likelihood of passing a bad part or rejecting a good part
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The output of the process measured by bull Cycle time bull Dimensional data bull Number of defects and others
Observed Variation
Process Variation
Measurement System
Variation
Reproducibility
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Accuracy (Central Location)
OBSERVED VARIATION
Calibration addresses accuracy
Measurement System Analysis (MSA)
MEASUREMENT SYSTEM ERRORS
Accuracy difference between the observed measurement and the actual measurement
Precision variation that occurs when measuring the same part with the same instrument
MEASUREMENT SYSTEM ERROR
Precise but not
accurate
Accurate but not
precise
Not accurate or
precise
Accurate and
precise
ACCURACY OF MEASUREMENT
Broken down into three components
aStability
The consistency of measurements over time
bBias
A measure of the amount of partiality in the system
cLinearity
A measure of the bias values through the expected
range of measurements
OBSERVED VARIATION
Observed Variation
Process Variation
Measurement System
Variation
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Reproducibility
Accuracy (Central Location)
Calibration Addresses Accuracy
Letrsquos take a closer look at Precision
Measurement System Analysis (MSA)
Measurement System Analysis (MSA)
Error in Resolution The inability to detect small changes
Possible Cause
Wrong measurement device selected - divisions on scale not fine enough to detect changes
Resolution
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Repeatability The inability to get the same answer from repeated measurements made of the same item under absolutely identical conditions
Possible Cause
Lack of standard operating procedures (SOP) lack of training measuring system variablilty
Repeatability
Equipment Variation
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Reproducibility The inability to get the same answer from repeated measurements made under various conditions from different inspectors
Possible Cause
Lack of SOP lack of training
Reproducibility
Appraiser Variation
VARIABLE MSA ndash GAGE RampR STUDY
bull Gage RampR is the combined estimate of
measurement system Repeatability and
Reproducibility
bull Typically a 3-person study is performed Each person randomly measures 10 marked parts per trial
Each person can perform up to 3 trials
bull There are 3 key indicators EV or Equipment Variation
AV or Appraiser Variation
Overall GRR
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
A
B
What does a very good Cpk do for us
This process is producing good units with a good safety margin
Note that when Cpk = 2 our process mean is 6 standard deviations from
the nearest spec so we say it has ldquo6 Sigma Capabilityrdquo
Specification
Limit
Specification
Limit
This Cpk is
about 2
Very good
Mean
58
A
B
What does a problem Cpk look like
This process is in danger of producing some defects
It is too close to the specification limits
(Remember the bell curve tail goes further than Bhellip hellipwe only show the bell to 3-sigma to make it easier to draw)
Specification
Limit
Specification
Limit
This Cpk is just
slightly greater
than 1 Not good
59
A
B
What does a very bad Cpk look like
A significant part of the ldquotailrdquo is hanging out beyond the spec limits
This process is producing scrap rework and customer rejects
Notice that if distance ldquoArdquo approaches zerohellip
hellipthe Cpk would approach zero andhellip
hellipthe process would become 50 defective
Specification
Limit
Specification
Limit
This Cpk is less
than 1 We desire
a minimum of 133
and ultimately we
want 2 or more
60
-
Q amp A
61
MEASUREMENT SYSTEM ANALYSIS (MSA)
An MSA is a statistical tool used to determine if a measurement system is capable of precise measurement
What is It
Objective or Purpose
bull To determine how much error is in the measurement due to the measurement process itself
bull Quantifies the variability added by the measurement system
bull Applicable to attribute data and variable data
When to Use It
bull On the critical inputs and outputs prior to collecting data for analysis
bull For any new or modified process in order to ensure the quality of the data
Measurement System Analysis is an analysis of the measurement process not an analysis of the people
IMPORTANT
Who Should be Involved
Everyone that measures and makes decisions about these measurements should be involved in the MSA
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The observed variation in process output measurements is not simply the variation in the process itself it is the variation in the process plus the variation in measurement that results from an inadequate measurement system
Conducting an MSA reduces the likelihood of passing a bad part or rejecting a good part
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The output of the process measured by bull Cycle time bull Dimensional data bull Number of defects and others
Observed Variation
Process Variation
Measurement System
Variation
Reproducibility
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Accuracy (Central Location)
OBSERVED VARIATION
Calibration addresses accuracy
Measurement System Analysis (MSA)
MEASUREMENT SYSTEM ERRORS
Accuracy difference between the observed measurement and the actual measurement
Precision variation that occurs when measuring the same part with the same instrument
MEASUREMENT SYSTEM ERROR
Precise but not
accurate
Accurate but not
precise
Not accurate or
precise
Accurate and
precise
ACCURACY OF MEASUREMENT
Broken down into three components
aStability
The consistency of measurements over time
bBias
A measure of the amount of partiality in the system
cLinearity
A measure of the bias values through the expected
range of measurements
OBSERVED VARIATION
Observed Variation
Process Variation
Measurement System
Variation
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Reproducibility
Accuracy (Central Location)
Calibration Addresses Accuracy
Letrsquos take a closer look at Precision
Measurement System Analysis (MSA)
Measurement System Analysis (MSA)
Error in Resolution The inability to detect small changes
Possible Cause
Wrong measurement device selected - divisions on scale not fine enough to detect changes
Resolution
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Repeatability The inability to get the same answer from repeated measurements made of the same item under absolutely identical conditions
Possible Cause
Lack of standard operating procedures (SOP) lack of training measuring system variablilty
Repeatability
Equipment Variation
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Reproducibility The inability to get the same answer from repeated measurements made under various conditions from different inspectors
Possible Cause
Lack of SOP lack of training
Reproducibility
Appraiser Variation
VARIABLE MSA ndash GAGE RampR STUDY
bull Gage RampR is the combined estimate of
measurement system Repeatability and
Reproducibility
bull Typically a 3-person study is performed Each person randomly measures 10 marked parts per trial
Each person can perform up to 3 trials
bull There are 3 key indicators EV or Equipment Variation
AV or Appraiser Variation
Overall GRR
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
A
B
What does a problem Cpk look like
This process is in danger of producing some defects
It is too close to the specification limits
(Remember the bell curve tail goes further than Bhellip hellipwe only show the bell to 3-sigma to make it easier to draw)
Specification
Limit
Specification
Limit
This Cpk is just
slightly greater
than 1 Not good
59
A
B
What does a very bad Cpk look like
A significant part of the ldquotailrdquo is hanging out beyond the spec limits
This process is producing scrap rework and customer rejects
Notice that if distance ldquoArdquo approaches zerohellip
hellipthe Cpk would approach zero andhellip
hellipthe process would become 50 defective
Specification
Limit
Specification
Limit
This Cpk is less
than 1 We desire
a minimum of 133
and ultimately we
want 2 or more
60
-
Q amp A
61
MEASUREMENT SYSTEM ANALYSIS (MSA)
An MSA is a statistical tool used to determine if a measurement system is capable of precise measurement
What is It
Objective or Purpose
bull To determine how much error is in the measurement due to the measurement process itself
bull Quantifies the variability added by the measurement system
bull Applicable to attribute data and variable data
When to Use It
bull On the critical inputs and outputs prior to collecting data for analysis
bull For any new or modified process in order to ensure the quality of the data
Measurement System Analysis is an analysis of the measurement process not an analysis of the people
IMPORTANT
Who Should be Involved
Everyone that measures and makes decisions about these measurements should be involved in the MSA
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The observed variation in process output measurements is not simply the variation in the process itself it is the variation in the process plus the variation in measurement that results from an inadequate measurement system
Conducting an MSA reduces the likelihood of passing a bad part or rejecting a good part
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The output of the process measured by bull Cycle time bull Dimensional data bull Number of defects and others
Observed Variation
Process Variation
Measurement System
Variation
Reproducibility
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Accuracy (Central Location)
OBSERVED VARIATION
Calibration addresses accuracy
Measurement System Analysis (MSA)
MEASUREMENT SYSTEM ERRORS
Accuracy difference between the observed measurement and the actual measurement
Precision variation that occurs when measuring the same part with the same instrument
MEASUREMENT SYSTEM ERROR
Precise but not
accurate
Accurate but not
precise
Not accurate or
precise
Accurate and
precise
ACCURACY OF MEASUREMENT
Broken down into three components
aStability
The consistency of measurements over time
bBias
A measure of the amount of partiality in the system
cLinearity
A measure of the bias values through the expected
range of measurements
OBSERVED VARIATION
Observed Variation
Process Variation
Measurement System
Variation
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Reproducibility
Accuracy (Central Location)
Calibration Addresses Accuracy
Letrsquos take a closer look at Precision
Measurement System Analysis (MSA)
Measurement System Analysis (MSA)
Error in Resolution The inability to detect small changes
Possible Cause
Wrong measurement device selected - divisions on scale not fine enough to detect changes
Resolution
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Repeatability The inability to get the same answer from repeated measurements made of the same item under absolutely identical conditions
Possible Cause
Lack of standard operating procedures (SOP) lack of training measuring system variablilty
Repeatability
Equipment Variation
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Reproducibility The inability to get the same answer from repeated measurements made under various conditions from different inspectors
Possible Cause
Lack of SOP lack of training
Reproducibility
Appraiser Variation
VARIABLE MSA ndash GAGE RampR STUDY
bull Gage RampR is the combined estimate of
measurement system Repeatability and
Reproducibility
bull Typically a 3-person study is performed Each person randomly measures 10 marked parts per trial
Each person can perform up to 3 trials
bull There are 3 key indicators EV or Equipment Variation
AV or Appraiser Variation
Overall GRR
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
A
B
What does a very bad Cpk look like
A significant part of the ldquotailrdquo is hanging out beyond the spec limits
This process is producing scrap rework and customer rejects
Notice that if distance ldquoArdquo approaches zerohellip
hellipthe Cpk would approach zero andhellip
hellipthe process would become 50 defective
Specification
Limit
Specification
Limit
This Cpk is less
than 1 We desire
a minimum of 133
and ultimately we
want 2 or more
60
-
Q amp A
61
MEASUREMENT SYSTEM ANALYSIS (MSA)
An MSA is a statistical tool used to determine if a measurement system is capable of precise measurement
What is It
Objective or Purpose
bull To determine how much error is in the measurement due to the measurement process itself
bull Quantifies the variability added by the measurement system
bull Applicable to attribute data and variable data
When to Use It
bull On the critical inputs and outputs prior to collecting data for analysis
bull For any new or modified process in order to ensure the quality of the data
Measurement System Analysis is an analysis of the measurement process not an analysis of the people
IMPORTANT
Who Should be Involved
Everyone that measures and makes decisions about these measurements should be involved in the MSA
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The observed variation in process output measurements is not simply the variation in the process itself it is the variation in the process plus the variation in measurement that results from an inadequate measurement system
Conducting an MSA reduces the likelihood of passing a bad part or rejecting a good part
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The output of the process measured by bull Cycle time bull Dimensional data bull Number of defects and others
Observed Variation
Process Variation
Measurement System
Variation
Reproducibility
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Accuracy (Central Location)
OBSERVED VARIATION
Calibration addresses accuracy
Measurement System Analysis (MSA)
MEASUREMENT SYSTEM ERRORS
Accuracy difference between the observed measurement and the actual measurement
Precision variation that occurs when measuring the same part with the same instrument
MEASUREMENT SYSTEM ERROR
Precise but not
accurate
Accurate but not
precise
Not accurate or
precise
Accurate and
precise
ACCURACY OF MEASUREMENT
Broken down into three components
aStability
The consistency of measurements over time
bBias
A measure of the amount of partiality in the system
cLinearity
A measure of the bias values through the expected
range of measurements
OBSERVED VARIATION
Observed Variation
Process Variation
Measurement System
Variation
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Reproducibility
Accuracy (Central Location)
Calibration Addresses Accuracy
Letrsquos take a closer look at Precision
Measurement System Analysis (MSA)
Measurement System Analysis (MSA)
Error in Resolution The inability to detect small changes
Possible Cause
Wrong measurement device selected - divisions on scale not fine enough to detect changes
Resolution
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Repeatability The inability to get the same answer from repeated measurements made of the same item under absolutely identical conditions
Possible Cause
Lack of standard operating procedures (SOP) lack of training measuring system variablilty
Repeatability
Equipment Variation
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Reproducibility The inability to get the same answer from repeated measurements made under various conditions from different inspectors
Possible Cause
Lack of SOP lack of training
Reproducibility
Appraiser Variation
VARIABLE MSA ndash GAGE RampR STUDY
bull Gage RampR is the combined estimate of
measurement system Repeatability and
Reproducibility
bull Typically a 3-person study is performed Each person randomly measures 10 marked parts per trial
Each person can perform up to 3 trials
bull There are 3 key indicators EV or Equipment Variation
AV or Appraiser Variation
Overall GRR
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
-
Q amp A
61
MEASUREMENT SYSTEM ANALYSIS (MSA)
An MSA is a statistical tool used to determine if a measurement system is capable of precise measurement
What is It
Objective or Purpose
bull To determine how much error is in the measurement due to the measurement process itself
bull Quantifies the variability added by the measurement system
bull Applicable to attribute data and variable data
When to Use It
bull On the critical inputs and outputs prior to collecting data for analysis
bull For any new or modified process in order to ensure the quality of the data
Measurement System Analysis is an analysis of the measurement process not an analysis of the people
IMPORTANT
Who Should be Involved
Everyone that measures and makes decisions about these measurements should be involved in the MSA
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The observed variation in process output measurements is not simply the variation in the process itself it is the variation in the process plus the variation in measurement that results from an inadequate measurement system
Conducting an MSA reduces the likelihood of passing a bad part or rejecting a good part
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The output of the process measured by bull Cycle time bull Dimensional data bull Number of defects and others
Observed Variation
Process Variation
Measurement System
Variation
Reproducibility
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Accuracy (Central Location)
OBSERVED VARIATION
Calibration addresses accuracy
Measurement System Analysis (MSA)
MEASUREMENT SYSTEM ERRORS
Accuracy difference between the observed measurement and the actual measurement
Precision variation that occurs when measuring the same part with the same instrument
MEASUREMENT SYSTEM ERROR
Precise but not
accurate
Accurate but not
precise
Not accurate or
precise
Accurate and
precise
ACCURACY OF MEASUREMENT
Broken down into three components
aStability
The consistency of measurements over time
bBias
A measure of the amount of partiality in the system
cLinearity
A measure of the bias values through the expected
range of measurements
OBSERVED VARIATION
Observed Variation
Process Variation
Measurement System
Variation
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Reproducibility
Accuracy (Central Location)
Calibration Addresses Accuracy
Letrsquos take a closer look at Precision
Measurement System Analysis (MSA)
Measurement System Analysis (MSA)
Error in Resolution The inability to detect small changes
Possible Cause
Wrong measurement device selected - divisions on scale not fine enough to detect changes
Resolution
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Repeatability The inability to get the same answer from repeated measurements made of the same item under absolutely identical conditions
Possible Cause
Lack of standard operating procedures (SOP) lack of training measuring system variablilty
Repeatability
Equipment Variation
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Reproducibility The inability to get the same answer from repeated measurements made under various conditions from different inspectors
Possible Cause
Lack of SOP lack of training
Reproducibility
Appraiser Variation
VARIABLE MSA ndash GAGE RampR STUDY
bull Gage RampR is the combined estimate of
measurement system Repeatability and
Reproducibility
bull Typically a 3-person study is performed Each person randomly measures 10 marked parts per trial
Each person can perform up to 3 trials
bull There are 3 key indicators EV or Equipment Variation
AV or Appraiser Variation
Overall GRR
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
MEASUREMENT SYSTEM ANALYSIS (MSA)
An MSA is a statistical tool used to determine if a measurement system is capable of precise measurement
What is It
Objective or Purpose
bull To determine how much error is in the measurement due to the measurement process itself
bull Quantifies the variability added by the measurement system
bull Applicable to attribute data and variable data
When to Use It
bull On the critical inputs and outputs prior to collecting data for analysis
bull For any new or modified process in order to ensure the quality of the data
Measurement System Analysis is an analysis of the measurement process not an analysis of the people
IMPORTANT
Who Should be Involved
Everyone that measures and makes decisions about these measurements should be involved in the MSA
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The observed variation in process output measurements is not simply the variation in the process itself it is the variation in the process plus the variation in measurement that results from an inadequate measurement system
Conducting an MSA reduces the likelihood of passing a bad part or rejecting a good part
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The output of the process measured by bull Cycle time bull Dimensional data bull Number of defects and others
Observed Variation
Process Variation
Measurement System
Variation
Reproducibility
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Accuracy (Central Location)
OBSERVED VARIATION
Calibration addresses accuracy
Measurement System Analysis (MSA)
MEASUREMENT SYSTEM ERRORS
Accuracy difference between the observed measurement and the actual measurement
Precision variation that occurs when measuring the same part with the same instrument
MEASUREMENT SYSTEM ERROR
Precise but not
accurate
Accurate but not
precise
Not accurate or
precise
Accurate and
precise
ACCURACY OF MEASUREMENT
Broken down into three components
aStability
The consistency of measurements over time
bBias
A measure of the amount of partiality in the system
cLinearity
A measure of the bias values through the expected
range of measurements
OBSERVED VARIATION
Observed Variation
Process Variation
Measurement System
Variation
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Reproducibility
Accuracy (Central Location)
Calibration Addresses Accuracy
Letrsquos take a closer look at Precision
Measurement System Analysis (MSA)
Measurement System Analysis (MSA)
Error in Resolution The inability to detect small changes
Possible Cause
Wrong measurement device selected - divisions on scale not fine enough to detect changes
Resolution
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Repeatability The inability to get the same answer from repeated measurements made of the same item under absolutely identical conditions
Possible Cause
Lack of standard operating procedures (SOP) lack of training measuring system variablilty
Repeatability
Equipment Variation
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Reproducibility The inability to get the same answer from repeated measurements made under various conditions from different inspectors
Possible Cause
Lack of SOP lack of training
Reproducibility
Appraiser Variation
VARIABLE MSA ndash GAGE RampR STUDY
bull Gage RampR is the combined estimate of
measurement system Repeatability and
Reproducibility
bull Typically a 3-person study is performed Each person randomly measures 10 marked parts per trial
Each person can perform up to 3 trials
bull There are 3 key indicators EV or Equipment Variation
AV or Appraiser Variation
Overall GRR
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The observed variation in process output measurements is not simply the variation in the process itself it is the variation in the process plus the variation in measurement that results from an inadequate measurement system
Conducting an MSA reduces the likelihood of passing a bad part or rejecting a good part
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The output of the process measured by bull Cycle time bull Dimensional data bull Number of defects and others
Observed Variation
Process Variation
Measurement System
Variation
Reproducibility
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Accuracy (Central Location)
OBSERVED VARIATION
Calibration addresses accuracy
Measurement System Analysis (MSA)
MEASUREMENT SYSTEM ERRORS
Accuracy difference between the observed measurement and the actual measurement
Precision variation that occurs when measuring the same part with the same instrument
MEASUREMENT SYSTEM ERROR
Precise but not
accurate
Accurate but not
precise
Not accurate or
precise
Accurate and
precise
ACCURACY OF MEASUREMENT
Broken down into three components
aStability
The consistency of measurements over time
bBias
A measure of the amount of partiality in the system
cLinearity
A measure of the bias values through the expected
range of measurements
OBSERVED VARIATION
Observed Variation
Process Variation
Measurement System
Variation
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Reproducibility
Accuracy (Central Location)
Calibration Addresses Accuracy
Letrsquos take a closer look at Precision
Measurement System Analysis (MSA)
Measurement System Analysis (MSA)
Error in Resolution The inability to detect small changes
Possible Cause
Wrong measurement device selected - divisions on scale not fine enough to detect changes
Resolution
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Repeatability The inability to get the same answer from repeated measurements made of the same item under absolutely identical conditions
Possible Cause
Lack of standard operating procedures (SOP) lack of training measuring system variablilty
Repeatability
Equipment Variation
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Reproducibility The inability to get the same answer from repeated measurements made under various conditions from different inspectors
Possible Cause
Lack of SOP lack of training
Reproducibility
Appraiser Variation
VARIABLE MSA ndash GAGE RampR STUDY
bull Gage RampR is the combined estimate of
measurement system Repeatability and
Reproducibility
bull Typically a 3-person study is performed Each person randomly measures 10 marked parts per trial
Each person can perform up to 3 trials
bull There are 3 key indicators EV or Equipment Variation
AV or Appraiser Variation
Overall GRR
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
MEASUREMENT SYSTEM ANALYSIS (MSA)
Process Variation
Measurement System
Variation
Observed Variation
The output of the process measured by bull Cycle time bull Dimensional data bull Number of defects and others
Observed Variation
Process Variation
Measurement System
Variation
Reproducibility
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Accuracy (Central Location)
OBSERVED VARIATION
Calibration addresses accuracy
Measurement System Analysis (MSA)
MEASUREMENT SYSTEM ERRORS
Accuracy difference between the observed measurement and the actual measurement
Precision variation that occurs when measuring the same part with the same instrument
MEASUREMENT SYSTEM ERROR
Precise but not
accurate
Accurate but not
precise
Not accurate or
precise
Accurate and
precise
ACCURACY OF MEASUREMENT
Broken down into three components
aStability
The consistency of measurements over time
bBias
A measure of the amount of partiality in the system
cLinearity
A measure of the bias values through the expected
range of measurements
OBSERVED VARIATION
Observed Variation
Process Variation
Measurement System
Variation
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Reproducibility
Accuracy (Central Location)
Calibration Addresses Accuracy
Letrsquos take a closer look at Precision
Measurement System Analysis (MSA)
Measurement System Analysis (MSA)
Error in Resolution The inability to detect small changes
Possible Cause
Wrong measurement device selected - divisions on scale not fine enough to detect changes
Resolution
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Repeatability The inability to get the same answer from repeated measurements made of the same item under absolutely identical conditions
Possible Cause
Lack of standard operating procedures (SOP) lack of training measuring system variablilty
Repeatability
Equipment Variation
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Reproducibility The inability to get the same answer from repeated measurements made under various conditions from different inspectors
Possible Cause
Lack of SOP lack of training
Reproducibility
Appraiser Variation
VARIABLE MSA ndash GAGE RampR STUDY
bull Gage RampR is the combined estimate of
measurement system Repeatability and
Reproducibility
bull Typically a 3-person study is performed Each person randomly measures 10 marked parts per trial
Each person can perform up to 3 trials
bull There are 3 key indicators EV or Equipment Variation
AV or Appraiser Variation
Overall GRR
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
Observed Variation
Process Variation
Measurement System
Variation
Reproducibility
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Accuracy (Central Location)
OBSERVED VARIATION
Calibration addresses accuracy
Measurement System Analysis (MSA)
MEASUREMENT SYSTEM ERRORS
Accuracy difference between the observed measurement and the actual measurement
Precision variation that occurs when measuring the same part with the same instrument
MEASUREMENT SYSTEM ERROR
Precise but not
accurate
Accurate but not
precise
Not accurate or
precise
Accurate and
precise
ACCURACY OF MEASUREMENT
Broken down into three components
aStability
The consistency of measurements over time
bBias
A measure of the amount of partiality in the system
cLinearity
A measure of the bias values through the expected
range of measurements
OBSERVED VARIATION
Observed Variation
Process Variation
Measurement System
Variation
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Reproducibility
Accuracy (Central Location)
Calibration Addresses Accuracy
Letrsquos take a closer look at Precision
Measurement System Analysis (MSA)
Measurement System Analysis (MSA)
Error in Resolution The inability to detect small changes
Possible Cause
Wrong measurement device selected - divisions on scale not fine enough to detect changes
Resolution
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Repeatability The inability to get the same answer from repeated measurements made of the same item under absolutely identical conditions
Possible Cause
Lack of standard operating procedures (SOP) lack of training measuring system variablilty
Repeatability
Equipment Variation
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Reproducibility The inability to get the same answer from repeated measurements made under various conditions from different inspectors
Possible Cause
Lack of SOP lack of training
Reproducibility
Appraiser Variation
VARIABLE MSA ndash GAGE RampR STUDY
bull Gage RampR is the combined estimate of
measurement system Repeatability and
Reproducibility
bull Typically a 3-person study is performed Each person randomly measures 10 marked parts per trial
Each person can perform up to 3 trials
bull There are 3 key indicators EV or Equipment Variation
AV or Appraiser Variation
Overall GRR
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
MEASUREMENT SYSTEM ERRORS
Accuracy difference between the observed measurement and the actual measurement
Precision variation that occurs when measuring the same part with the same instrument
MEASUREMENT SYSTEM ERROR
Precise but not
accurate
Accurate but not
precise
Not accurate or
precise
Accurate and
precise
ACCURACY OF MEASUREMENT
Broken down into three components
aStability
The consistency of measurements over time
bBias
A measure of the amount of partiality in the system
cLinearity
A measure of the bias values through the expected
range of measurements
OBSERVED VARIATION
Observed Variation
Process Variation
Measurement System
Variation
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Reproducibility
Accuracy (Central Location)
Calibration Addresses Accuracy
Letrsquos take a closer look at Precision
Measurement System Analysis (MSA)
Measurement System Analysis (MSA)
Error in Resolution The inability to detect small changes
Possible Cause
Wrong measurement device selected - divisions on scale not fine enough to detect changes
Resolution
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Repeatability The inability to get the same answer from repeated measurements made of the same item under absolutely identical conditions
Possible Cause
Lack of standard operating procedures (SOP) lack of training measuring system variablilty
Repeatability
Equipment Variation
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Reproducibility The inability to get the same answer from repeated measurements made under various conditions from different inspectors
Possible Cause
Lack of SOP lack of training
Reproducibility
Appraiser Variation
VARIABLE MSA ndash GAGE RampR STUDY
bull Gage RampR is the combined estimate of
measurement system Repeatability and
Reproducibility
bull Typically a 3-person study is performed Each person randomly measures 10 marked parts per trial
Each person can perform up to 3 trials
bull There are 3 key indicators EV or Equipment Variation
AV or Appraiser Variation
Overall GRR
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
MEASUREMENT SYSTEM ERROR
Precise but not
accurate
Accurate but not
precise
Not accurate or
precise
Accurate and
precise
ACCURACY OF MEASUREMENT
Broken down into three components
aStability
The consistency of measurements over time
bBias
A measure of the amount of partiality in the system
cLinearity
A measure of the bias values through the expected
range of measurements
OBSERVED VARIATION
Observed Variation
Process Variation
Measurement System
Variation
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Reproducibility
Accuracy (Central Location)
Calibration Addresses Accuracy
Letrsquos take a closer look at Precision
Measurement System Analysis (MSA)
Measurement System Analysis (MSA)
Error in Resolution The inability to detect small changes
Possible Cause
Wrong measurement device selected - divisions on scale not fine enough to detect changes
Resolution
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Repeatability The inability to get the same answer from repeated measurements made of the same item under absolutely identical conditions
Possible Cause
Lack of standard operating procedures (SOP) lack of training measuring system variablilty
Repeatability
Equipment Variation
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Reproducibility The inability to get the same answer from repeated measurements made under various conditions from different inspectors
Possible Cause
Lack of SOP lack of training
Reproducibility
Appraiser Variation
VARIABLE MSA ndash GAGE RampR STUDY
bull Gage RampR is the combined estimate of
measurement system Repeatability and
Reproducibility
bull Typically a 3-person study is performed Each person randomly measures 10 marked parts per trial
Each person can perform up to 3 trials
bull There are 3 key indicators EV or Equipment Variation
AV or Appraiser Variation
Overall GRR
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
ACCURACY OF MEASUREMENT
Broken down into three components
aStability
The consistency of measurements over time
bBias
A measure of the amount of partiality in the system
cLinearity
A measure of the bias values through the expected
range of measurements
OBSERVED VARIATION
Observed Variation
Process Variation
Measurement System
Variation
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Reproducibility
Accuracy (Central Location)
Calibration Addresses Accuracy
Letrsquos take a closer look at Precision
Measurement System Analysis (MSA)
Measurement System Analysis (MSA)
Error in Resolution The inability to detect small changes
Possible Cause
Wrong measurement device selected - divisions on scale not fine enough to detect changes
Resolution
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Repeatability The inability to get the same answer from repeated measurements made of the same item under absolutely identical conditions
Possible Cause
Lack of standard operating procedures (SOP) lack of training measuring system variablilty
Repeatability
Equipment Variation
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Reproducibility The inability to get the same answer from repeated measurements made under various conditions from different inspectors
Possible Cause
Lack of SOP lack of training
Reproducibility
Appraiser Variation
VARIABLE MSA ndash GAGE RampR STUDY
bull Gage RampR is the combined estimate of
measurement system Repeatability and
Reproducibility
bull Typically a 3-person study is performed Each person randomly measures 10 marked parts per trial
Each person can perform up to 3 trials
bull There are 3 key indicators EV or Equipment Variation
AV or Appraiser Variation
Overall GRR
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
OBSERVED VARIATION
Observed Variation
Process Variation
Measurement System
Variation
Precision (Variability)
Linearity
Bias
Stability
Resolution
Repeatability
Reproducibility
Accuracy (Central Location)
Calibration Addresses Accuracy
Letrsquos take a closer look at Precision
Measurement System Analysis (MSA)
Measurement System Analysis (MSA)
Error in Resolution The inability to detect small changes
Possible Cause
Wrong measurement device selected - divisions on scale not fine enough to detect changes
Resolution
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Repeatability The inability to get the same answer from repeated measurements made of the same item under absolutely identical conditions
Possible Cause
Lack of standard operating procedures (SOP) lack of training measuring system variablilty
Repeatability
Equipment Variation
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Reproducibility The inability to get the same answer from repeated measurements made under various conditions from different inspectors
Possible Cause
Lack of SOP lack of training
Reproducibility
Appraiser Variation
VARIABLE MSA ndash GAGE RampR STUDY
bull Gage RampR is the combined estimate of
measurement system Repeatability and
Reproducibility
bull Typically a 3-person study is performed Each person randomly measures 10 marked parts per trial
Each person can perform up to 3 trials
bull There are 3 key indicators EV or Equipment Variation
AV or Appraiser Variation
Overall GRR
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
Measurement System Analysis (MSA)
Error in Resolution The inability to detect small changes
Possible Cause
Wrong measurement device selected - divisions on scale not fine enough to detect changes
Resolution
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Repeatability The inability to get the same answer from repeated measurements made of the same item under absolutely identical conditions
Possible Cause
Lack of standard operating procedures (SOP) lack of training measuring system variablilty
Repeatability
Equipment Variation
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Reproducibility The inability to get the same answer from repeated measurements made under various conditions from different inspectors
Possible Cause
Lack of SOP lack of training
Reproducibility
Appraiser Variation
VARIABLE MSA ndash GAGE RampR STUDY
bull Gage RampR is the combined estimate of
measurement system Repeatability and
Reproducibility
bull Typically a 3-person study is performed Each person randomly measures 10 marked parts per trial
Each person can perform up to 3 trials
bull There are 3 key indicators EV or Equipment Variation
AV or Appraiser Variation
Overall GRR
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Repeatability The inability to get the same answer from repeated measurements made of the same item under absolutely identical conditions
Possible Cause
Lack of standard operating procedures (SOP) lack of training measuring system variablilty
Repeatability
Equipment Variation
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Reproducibility The inability to get the same answer from repeated measurements made under various conditions from different inspectors
Possible Cause
Lack of SOP lack of training
Reproducibility
Appraiser Variation
VARIABLE MSA ndash GAGE RampR STUDY
bull Gage RampR is the combined estimate of
measurement system Repeatability and
Reproducibility
bull Typically a 3-person study is performed Each person randomly measures 10 marked parts per trial
Each person can perform up to 3 trials
bull There are 3 key indicators EV or Equipment Variation
AV or Appraiser Variation
Overall GRR
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
MEASUREMENT SYSTEM ANALYSIS (MSA)
Error in Reproducibility The inability to get the same answer from repeated measurements made under various conditions from different inspectors
Possible Cause
Lack of SOP lack of training
Reproducibility
Appraiser Variation
VARIABLE MSA ndash GAGE RampR STUDY
bull Gage RampR is the combined estimate of
measurement system Repeatability and
Reproducibility
bull Typically a 3-person study is performed Each person randomly measures 10 marked parts per trial
Each person can perform up to 3 trials
bull There are 3 key indicators EV or Equipment Variation
AV or Appraiser Variation
Overall GRR
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
VARIABLE MSA ndash GAGE RampR STUDY
bull Gage RampR is the combined estimate of
measurement system Repeatability and
Reproducibility
bull Typically a 3-person study is performed Each person randomly measures 10 marked parts per trial
Each person can perform up to 3 trials
bull There are 3 key indicators EV or Equipment Variation
AV or Appraiser Variation
Overall GRR
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
1 Select 10 items that represent the full range of long-term process variation
2 Identify the appraisers
3 If appropriate calibrate the gage or verify that the last calibration date is valid
4 Open the Gage RampR worksheet in the PPAP Playbook to record data
5 Have each appraiser assess each part 3 times (trials ndash first in order second in reverse order third
random)
6 Input data into the Gage RampR worksheet
7 Enter the number of operators trials samples and specification limits
8 Analyze data in the Gage RampR worksheet
9 Assess MSA trust level
10 Take actions for improvement if necessary
VARIABLE MSA ndash GAGE RampR STEPS Step 1 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 2
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
STEPS 1 AND 2 VARIABLE MSA - GAGE RampR
Select 10 items that represent
the full range of long-term process
variation
Step 1
Identify the appraisers
ndash Should use individuals that actually do the process being tested
ndashCan also include other appraisers (supervisors etc)
ndash Should have a minimum of 3 appraisers
Step 2
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
STEPS 3 AND 4 VARIABLE MSA ndash GAGE RampR
If appropriate calibrate the gage
or verify that the last calibration
date is valid
Step 3
Enter the data Gage RampR worksheet
Step 4
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
STEP 5 VARIABLE MSA ndash GAGE RampR
Step 5 Have each appraiser assess each item 3 times
Each appraiser has to work independently
Items should be evaluated in random order
After each appraiser completes the first evaluation of
all items ndash repeat the process at least 2 more times
Do not let the appraisers see any of the data during
the test
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
STEPS 6 AND 7 VARIABLE MSA ndash GAGE RampR
Collect data into the Gage RampR
worksheet
Enter the number of operators trials
samples and specification limits in
same work sheet
Step 6
Step 7
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
STEPS 8 AND 9 VARIABLE MSA ndash GAGE RampR
Assess MSA Trust Level
ndash Red gt 30 (fail)
ndash Yellow 10-30 (marginal)
ndash Green lt 10 (pass)
Step 9
Step 8 Calculate amp Analyze data in the Gage RampR worksheet
Tolerance
10
30
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
STEP 10 VARIABLE MSA ndash GAGE RampR
If the Measurement System needs improvement
Brainstorm with the team for improvement solutions
Determine best ldquopractical solutionrdquo (may require some
experimentation)
Pilot the best solution (PDSA)
Implement best solution ndash train employees
Re-run the study to verify the improvement
Step 10
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
GAUGE R amp R FORMULAS
81
Repeatability - Equipment Variation (EV) = (R bar bar) X K1
Reproducibility ndash Appraiser Variation(AV) = Sqrt(X bar diff X K2)˄2-
(EV[( parts) X ( Trials)]
Repeatability amp Reproducibility (GRR) = Sqrt((EV˄2) +(AV˄2))
Part Variation (PV) = Rp X K3
Total Variation(TV) = Sqrt(GRR˄2) + (PV˄2)
Equipment Variation(EV) = 100(EVTV)
Appraiser Variation(AV) = 100(AVTV)
Gauge R amp R(GRR) = 100(GRRTV)
Part Variation(PV) = 100(PVTV)
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
SAMPLE EXCERCISE
Sample for Gauge R amp R
82
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
Important An MSA is an analysis of the process not an analysis of the people If
an MSA fails the process failed
A Variable MSA provides more analysis capability than an Attribute MSA For this
and other reasons always use variable data if possible
The involvement of people is the key to success
Involve the people that actually work the process
Involve the supervision
Involve the suppliers and customers of the process
An MSA primarily addresses precision with limited accuracy information
Tips and Lessons Learned
FINALLY
Thank You
84
FINALLY
Thank You
84