Business MomentBusiness Moment

Whether you think you can or whether you think you can't, you're right!

Henry Ford

Fundamentals of Statistical Fundamentals of Statistical Process Control.Process Control.

SPC

Statistical Process ControlStatistical Process Control

SPC is a tool for obtaining cost effective quality, achieved by process monitoring and forecasting techniques which are used to predict problems before they occur. (defect prevention)

ReliabilityReliability

Rework Insp.

Rework Corrective

Action

PreventionInspect

$ $

Quality

+-

Where should you spend your money?

Increased Reliability

Detection vs. PreventionDetection vs. PreventionManufacture

SPC

Ship

Inspect & Sort

Ship

Scrap or Rework

Prevent$

Manufacture

Feedback

Old methodNew Method

Elements of QualityElements of Quality

- Zero Defects (Implied or specified)- Conformance to Specification- Reliability (life & uptime)- Functionality (does what’s intended)- Price (competitive for performance)- Delivery (received on promise date)- Service and Support (incl. Warranty)

Normal VariationNormal VariationVariable DataVariable Data

68%95%

99.7%Six Sigma

.5.5 .5.5.5.5.5.5.5.5.5

.4

.4

.4

.4

.4

.4

.4

.4

.3

.3

.3

.3

.6

.6

.6

.6

.6

.6

.6

.6

.7

.7

.7

.7

.2 .8

X

-1-2-3 +3+2+1

Individual Measurements, the same values stack up.

Variable Data is data that can be measured.

Sample QuantitySample QuantitySample QuantitySample Quantity

-1 0 +2

3 -1 0 +2

3

-1 0 +2

53 -2 -1 0 +1 +2 +3

3 -2 -1 0 +1 +2+3

-1 0 +2

-1 0 +1

20

3 -2 -1 0 +1 +2 +3

0

3 -2 -1 0 +1 +2 +3

-2 -1 0+1 +2 -1 0+1+2 –1 0+1+2

3 -2 -1 0 +1 +2 +3

-2 -1 0 +1 +2

3 -2 -1 0 +1 +2 +3-2 -1 0 +1 +2

-1 0+1 –1 0+1+2

0

40

-1

23

102

xxxxxxxx

xxxxxxxxxxxxxxxx

xxxxxxxxxxxxxxxxxxxxxxxx

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

xxxxxxxxxxxxxxxxxxxx

x It takes approximately 30 samples to assure the normal bell shape.

Any MeasurementAny Measurement!!

Range height 76-60 = 16 in. Range of weight could be 300-60 = 240 lb

Mean (Center) height = 68 in. Mean weight = 180 lbs

Increment of MeasurementIncrement of Measurement

Fewer points make bell shape

Takes more points to define bell shape.

.005 range per block

.001

.001

.002

.005

.016

.019

.018

.017

.016

.018

.017

.0# .00#

HistogramHistogram

4.5 to 5.5 5.5 to 6.5 6.5 to 7.5

Process ControlProcess ControlA process is “In Control” if products vary CONSISTENTLY within expected limits over TIME. Normal expectations when displayed by frequency of occurrence will present a curve or distribution showing a central peak and tapering off smoothly to tails on either side.

.5.5 .5.5.5.5.5.5.5.5.5

.4

.4

.4

.4

.4

.4

.4

.4

.3

.3

.3

.3

.6

.6

.6

.6

.6

.6

.6

.6

.7

.7

.7

.7

.2 .8

When the normal distribution exits the process is operating consistently and we can predict the process behavior.

Controlling a ProcessControlling a Process

2. Get the Process to a normal distribution. (Remove assignable causes) You don’t want to control a broken process.

1. To control a process means to keep the bell shape normal.

3. Monitor the process property at an interval that can detect deterioration of the property and allow correction before rejections.

Example: If the property was effected by a belt that wears over time, checking once a week may be adequate.

If the property were to use a batch of epoxy in the working range before it cures to much, checking every 15 minutes would be appropriate. (The time interval is called “Frequency”)

4. Take corrective action before defects are produced.

Assignable CausesAssignable CausesEasy to identify and correct. (low cost)

What is poor Quality?What is poor Quality?Not meeting customer expectations, implied or specified!

B A

Customer Dis-satisfactionCustomer Dis-satisfaction

TargetLower Spec Upper Spec

A = more variation on target? or B = less variation off target?

Reject No Question Perfection – Not Required

What causes defects? 6 M’sWhat causes defects? 6 M’sMan (associated operator error)

Machine (improper, misadjusted or broken)

Material (wrong or defective)

Measurement (wrong, bad or misread instrument)

Method (improper, unclear or incomplete)

Mother Nature (environment – temp – moisture …)

Good or Bad?Good or Bad?

6

6Customer Specification

Bad (Out of Spec.)

The Bell shape has nothing to do with good/bad only Normal.

LCL

LCL

UCL

UCL

When do you have rejects?When do you have rejects?

When Specification Limits are imposed. (Customer or Company Spec.)

CapabilityCapability

USL

xxxxxxxx

xxxxxxxxxxxxxxxx

xxxxxxxxxxxxxxxxxxxxxxxx

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

LCL UCLLSL

LSL USL

Capable

Not Capable

6

CP

Specification Limits Control

limits

Precise and AccuratePrecise and Accurate

Precise and Accurate

Not Precise and Not AccurateAccurate and not Precise

Precise and Not Accurate

Capability Improvement Capability Improvement Variation ReductionVariation Reduction

CapabilityCapability

xxxxxxxx

xxxxxxxxxxxxxxxx

xxxxxxxxxxxxxxxxxxxxxxxx

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

xxxxxxxx

xxxxxxxxxxxxxxxx

xxxxxxxxxxx

xxxxxxxxxxxxxxxxxxxxxxxxxx

xxxxxxxxxxxxxxxxx

Six Sigma

Normal Shift

CPk

USL

Not Capable Capable

Avg.

USL

Avg-USL/3/2 Or LSL-Avg/ 3/2

Cpk=min

Variation of the Mean

Two Distributions Working TogetherTwo Distributions Working Together

xxxxxxxx

xxxxxxxxxxxxxxxx

xxxxxxxxxxxxxxxxxxxxxxxx

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

xxxxxxxx

xxxxxxxxxxxxxxxx

xxxxxxxxxxxxxxxxxxxxxxxx

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

Bimodal

Six Sigma

(Movement: right, left or up, down or clockwise, counterclockwise …) (mixed materials, different lots of material, different operators…)

(If parts tighter tolerance parts were selected out it would look like this.)

Control Limits, the six sigma pointsControl Limits, the six sigma points

6 sigma

Mean (Average)

LCL UCL

+3- 3

Making a time related distribution.Making a time related distribution.Display the measurements in the order taken.

Each point is an average from the samples measured (5 smpls)

Add Control Lines to chartsAdd Control Lines to charts

6 sigma

Mean

(Average)

LC

LU

CL

+3

- 3

Xbar and Range ChartsXbar and Range ChartsXbar = X = The average of measured samples (5)Range = R = Highest reading – Lowest reading in sample (5)

Plotting Procedure

1. Take five measurements / data points, noting any decimal points required.

2. If you are using the current date and time skip step 3.

3. Enter your earlier date and time in military format 10/18/03 14:15 in the Override Date/Time cell

4. Enter your data into the cells provided. Sample 1 2 3 4 5 (Yellow cells)

(Note: Click on the yellow Cell under the number 1 to start entering data, use the Tab key to move to the next cell.)

5. On the last entry use the down arrow to enter and proceed to the Initials cell (otherwise click the Initials cell). Enter your Initials, Press Tab.

6. Press the "plot button" in the lower right corner and observe that your data point has been plotted.

7. If there appears to be an error in the data, you can click on the defective data and reenter it. Press Tab, then click the Replot Button.

8. Once the point is correctly plotted, Observe if any Run Rules have been violated. If not, enter "none" in the action cell, then click the "Tab then Action Button." (lower right corner). Otherwise, take and log the corrective action taken.

9. Observe that the data cells are empty, indicating a successful transaction. The lower scroll pane (two rows at the bottom of screen) can be used to observe the calculations and action entered. (Just click the down scroll arrow until the last row is displayed. (80 rows maximum can be entered.)

Run Rules

1. Any point that crosses the upper or lower control limit on the XBar Chart or the upper control limit on the R Chart.

2. 7 points in a row on one side of the center line on the Bar Chart.

3. 7 points in a continuing upward or downward direction on the Bar Chart or R - Range (lower) chart (Trend).

4. 7 points in a row at the upper and lower extremes (no points on or near the centerline) Bar Chart.

5. 7 points in a row clustered closely around the center line on the X Bar Chart (Capture improvement or speed up the process).

6. 7 points in a row clustered near bottom of R Chart or trending toward bottom (Capture improvement or speed up the process)

Run Rules Run Rules (normal no action required)(normal no action required)Any point that crosses the upper or lower control limit on the Xbar Chart or the upper control limit on the R chart.

Xbar (upper chart)

Range – R (lower chart)

* Note random points, some near control lines some near center.

Run Rules Run Rules (when to take action)(when to take action)

Any point that crosses the upper or lower control limit on the Xbar Chart or the upper control limit on the R chart.

Xbar (upper chart)

Range – R (lower chart)

* Check for possible bad measurement or data entry error.

Run Rules Run Rules (when to take action - Run) (when to take action - Run)

7 points in a row on one side of the center line on the upper chart.

Xbar (upper chart)

Or

*Check material, lot, operator, machine adjustment…

Run Rules Run Rules (when to take action - trends)(when to take action - trends)

Xbar (upper chart)

Or

7 points in a continuing downward or upward direction on X chart

* Check machine wear, material, method or operator fatigue…

Run Rule Run Rule (when to take action - trends)(when to take action - trends)

Range R (lower chart)

Or

7 points in a continuing downward or upward direction on R chart

Improving – capture or speed up

Getting Worse - correct

* Check machine wear, material, method or operator fatigue…

Run Rule Run Rule (clustered points)(clustered points)

7 points in a row clustered around the center line on the Xbar chart or clustered around zero (bottom line) on the R Range chart

Xbar (upper chart)

Range – R (lower chart)

Improved – capture or speed up

Improved – capture or speed up

“Over controlled” If bell was normal points would be near the edges.

Run Rules Run Rules (when to take action – Unusual pattern)(when to take action – Unusual pattern)

Xbar (upper chart)

No points near the center (possibly bimodal)

*Two lots of material, two operators, selected parts removed…

Attribute DataAttribute DataNon-measurable data

Good, Bad; Pass, Fail; True, False; Go, NoGo; Present, Missing…

Charts: P (Percent Defective), NP (Number Defective) C (Defects per unit), U (Defects per Subgroup)

Simple if sample size is constant and equated easily to 100. Ex: Number defective from sample 50 multiply by 2, 25x4, 10x10, 5x20, 2x50 EXAMPLE: 5 bad in sample of 25 (5x4) =20% The software will do the math but keeping a fixed sample size is preferred.

Fixed sample size will keep the control lines straight and understood.

Plotting Procedure

1. Count out the sample size and note the number defective.

2. If you are using the current date and time skip step 3.

3. Enter your earlier date and time in military format 10/18/03 14:15 in the Override Date/Time cell

4. Enter your data into the cells provided. Sample Size, Qty Defective (Yellow cells)

(Note: Click on the yellow Cell to start entering data, use the Tab key and or arrow keys to move to the next yellow cell.)

5. On the last entry use the arrow keys to enter and procede to the Initials cell (otherwise click the Initials cell). Enter your Initials, Press Tab.

6. Press the "plot button" in the lower right corner and observe that your data point has been plotted.

7. If there appears to be an error in the data, you can click on the defective data and reenter it. Press Tab, then click the Replot Button.

8. Once the point is correctly plotted, Observe if any Run Rules have been violated. If not, enter "none" in the action cell, then click the "Tab then Action Button." (lower right corner). Otherwise, take and log the corrective action taken.

9. Observe that the data cells are empty, indicating a successful transaction. The lower scroll pane (two rows at the bottom of screen) can be used to observe the calculations and action entered. (Just click the down scroll arrow until the last row is displayed. (80 rows maximum can be entered.)

Run Rules

1. Any point that crosses the upper or lower control limit on the P Chart

2. 7 points in a row on one side of the center line.

3. 7 points in a continuing upward or downward direction on the P chart (Trend).

4. 7 points in a row at the upper and lower extremes (no points on or near the centerline)

5. 7 points in a row clustered near bottom of R Chart or trending toward bottom (Capture improvement or speed up the process)

The End