statistical process control (spc) chapter 6. mgmt 326 foundations of operations introduction...
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Statistical Process Control (SPC)
Chapter 6
MGMT 326
Foundations
of Operatio
nsIntroductio
n
Strategy
ManagingProjects
QualityAssuran
ce
Capacityand
Facilities
Planning& Control
Products &
Processes
ProductDesign
ProcessDesign
ManagingQuality
Statistical
ProcessControl
Just-in-Time & Lean Systems
Assuring Customer-Based Quality
Customer Requirements
Product Specifications
Process Specifications
Product launch
activities: Revise
periodically
Statistical Process Control:
Measure & monitor quality
Ongoingactivity
Statistical Process Control (SPC)
Meancharts
Rangecharts
and known
, unknown
CapableProcess
es
= target
= target
Variation
Basic SPC
Concepts
Objectives
First steps
Types ofMeasure
s
Attributes
Variables
SPC for Variabl
es
Variation in a Transformation Process
•Variation in inputs create variation in outputs• Variations in the transformation process create variation in outputs
Inputs• Facilities• Equipment• Materials• Energy
Transformation Process
OutputsGoods &Services
Variation in a Transformation Process
•Variation in inputs create variation in outputs• Variations in the transformation process create variation in outputs
Inputs• Facilities• Equipment• Materials• Energy
Transformation Process
OutputsGoods &Services
Customerrequiremen
tsare not met
Variation
All processes have variation. Common cause variation is random
variation that is always present in a process.
Assignable cause variation results from changes in the inputs or the process. The cause can and should be identified. Assignable cause variation shows that
the process or the inputs have changed, at least temporarily.
Objectives of Statistical Process Control (SPC)
Find out how much common cause variation the process has
Find out if there is assignable cause variation.
A process is in control if it has no assignable cause variation Being in control means that the process is
stable and behaving as it usually does.
First Steps in Statistical Process Control (SPC)
Measure characteristics of goods or services that are important to customers
Make a control chart for each characteristic The chart is used to determine whether the
process is in control
Types of Measures (1)Variable Measures
Continuous random variables Measure does not have to be a whole
number. Examples: time, weight, miles per
gallon, length, diameter
Types of Measures (2)Attribute Measures
Discrete random variables – finite number of possibilities Also called categorical variables The measure may depend on perception or
judgment. Different types of control charts are
used for variable and attribute measures
Examples of Attribute Measures
Good/bad evaluations Good or defective Correct or incorrect
Number of defects per unit Number of scratches on a table
Opinion surveys of quality Customer satisfaction surveys Teacher evaluations
SPC for VariablesThe Normal Distribution
= the population mean = the standard deviation for the population99.74% of the area under the normal curve is between - 3 and + 3
SPC for Variables The Central Limit Theorem
Samples are taken from a distribution with mean and standard deviation .k = the number of samplesn = the number of units in each sample
The sample means are normally distributed with mean and standard deviation
when k is large.
x n
Control Limits for the Sample Mean when and are known x is a variable, and samples of size n are
taken from the population containing x. Given: = 10, = 1, n = 4Then
A 99.7% confidence interval for is
1 10.5
24x n
x
x
( 3 , 3 ) 3 , 3x x n n
Control Limits for the Sample Mean when and are known (2)
The lower control limit for is
x
x
13 3 10 3
4xLCL
n
10 1.5 8.5
Control Limits for the Sample Mean when and are known (3)
The upper control limit for is
x
x
13 3 10 3
4xUCL
n
10 1.5 11.5
Control Limits for the Sample Mean when and are unknown
If the process is new or has been changed recently, we do not know and
Example 6.1, page 180 Given: 25 samples, 4 units in each
sample and are not given k = 25, n = 4
x
Control Limits for the Sample Mean when and are unknown (2)
1. Compute the mean for each sample. For example,
2. Compute
x
1
15.85 16.02 15.83 15.9315.91
4x
95.1525
75.398
25
94.15...00.1691.15
25
25
11
m
m
k
m
m x
k
xx
Control Limits for the Sample Mean when and are unknown (3)
For the ith sample, the sample range is Ri = (largest value in sample i )
- (smallest value in sample i )3. Compute Ri for every sample. For
example,
R1 = 16.02 – 15.83 = 0.19
x
Control Limits for the Sample Mean when and are unknown (4)
4. Compute , the average range
We will approximate by , whereA2 is a number that depends on the sample size n. We get A2 from Table 6.1, page 182
x
R
3x
2A R
29.025
17.7
25
30.0...27.019.01
k
RR
k
ii
Control Limits for the Sample Mean when and are unknown (5)
5. n = the number of units in each sample = 4.From Table 6.1, A2 = 0.73.
The same A2 is used
for every problemwith n = 4.
x
Factor for x-Chart
A2 D3 D42 1.88 0.00 3.273 1.02 0.00 2.574 0.73 0.00 2.285 0.58 0.00 2.116 0.48 0.00 2.007 0.42 0.08 1.928 0.37 0.14 1.869 0.34 0.18 1.8210 0.31 0.22 1.7811 0.29 0.26 1.7412 0.27 0.28 1.7213 0.25 0.31 1.6914 0.24 0.33 1.6715 0.22 0.35 1.65
Factors for R-ChartSample Size (n)
Control Limits for the Sample Mean when and are unknown (6)
6. The formula for the lower control limit is
7. The formula for the upper control limit is
x
2 15.95 0.73(0.29) 15.74LCL x A R
2 15.95 0.73(0.29) 16.16UCL x A R
Control Chart for x
The variation between LCL = 15.74 and UCL = 16.16is the common cause variation.
Common Cause andSpecial Cause Variation
The range between the LCL and UCL, inclusive, is the common cause variation for the process. When is in this range, the process is in control. When a process is in control, it is
predictable. Output from the process may or may not meet customer requirements.
When is outside control limits, the process is out of control and has special cause variation. The cause of the variation should be identified and eliminated.
x
x
Control Limits for R
1. From the table, get D3 and D4
for n = 4.
D3 = 0
D4 = 2.28
Factor for x-Chart
A2 D3 D42 1.88 0.00 3.273 1.02 0.00 2.574 0.73 0.00 2.285 0.58 0.00 2.116 0.48 0.00 2.007 0.42 0.08 1.928 0.37 0.14 1.869 0.34 0.18 1.8210 0.31 0.22 1.7811 0.29 0.26 1.7412 0.27 0.28 1.7213 0.25 0.31 1.6914 0.24 0.33 1.6715 0.22 0.35 1.65
Factors for R-ChartSample Size (n)
Control Limits for R (2)
2. The formula for the lower control limit is
2. The formula for the upper control limit is
3 0(0.29) 0LCL D R
66.0)29.0(28.24 RDUCL
fig_ex06_03
Statistical Process Control (SPC)
CapableProcess
es
= target
= target
Meancharts
Rangecharts
and known
, unknown
Variation
Basic SPC
Concepts
Objectives
First steps
Types ofMeasure
s
Attributes
Variables
SPC for Variabl
es
Capable Transformation Process
Capable Transformation
Process
Inputs• Facilities• Equipment• Materials• Energy
OutputsGoods &Servicesthat meet
specifications
a specification that meets customer requirements+ a capable process (meets specifications)= Satisfied customers and repeat business
Review of Specification Limits
The target for a process is the ideal value Example: if the amount of beverage in a bottle
should be 16 ounces, the target is 16 ounces Specification limits are the acceptable range of
values for a variable Example: the amount of beverage in a bottle must
be at least 15.8 ounces and no more than 16.2 ounces.
The allowable range is 15.8 – 16.2 ounces. Lower specification limit = 15.8 ounces or LSL = 15.8
ounces Upper specification limit = 16.2 ounces or USL = 16.2
ounces
Control Limits vs. Specification Limits
Control limits show the actual range of variation within a process What the process is doing
Specification limits show the acceptable common cause variation that will meet customer requirements. Specification limits show what the
process should do to meet customer requirements
Process is Capable: Control Limits are
within or on Specification Limits
UCL
LCL
X
Lower specification limit
Upper specification limit
Process is Not Capable: One or BothControl Limits are Outside Specification
Limits
UCL
LCL
X
Lower specification limit
Upper specification limit
Capability and Conformance Quality
A process is capable if It is in control and It consistently produces outputs that meet
specifications. This means that both control limits for the
mean must be within the specification limits A capable process produces outputs that have
conformance quality (outputs that meet specifications).
Process Capability Ratio
Use to determine whether the process is capable when = target.
If , the process is capable, If , the process is not
capable.
pC
pC
6p
USL LSLC
1pC
1pC
Example
Given: Boffo Beverages produces 16-ounce bottles of soft drinks. The mean ounces of beverage in Boffo's bottle is 16. The allowable range is 15.8 – 16.2. The standard deviation is 0.06. Find and determine whether the process is capable.
pC
pC
Given: = 16, = 0.06, target = 16LSL = 15.8, USL = 16.2
The process is capable.
Example (2)pC
16.2 15.81.11
6 6(0.06)p
USL LSLC
1pC
Process Capability Index Cpk
If Cpk > 1, the process is capable.
If Cpk < 1, the process is not capable.
We must use Cpk when does not equal the target.
smaller ,3 3pk
USL LSLC
Cpk Example
Given: Boffo Beverages produces 16-ounce bottles of soft drinks. The mean ounces of beverage in Boffo's bottle is 15.9. The allowable range is 15.8 – 16.2. The standard deviation is 0.06. Find and determine whether the process is capable.
pkC
Cpk Example (2)
Given: = 15.9, = 0.06, target = 16LSL = 15.8, USL = 16.2
Cpk < 1. Process is not capable.
smaller ,3 3pk
USL LSLC
16.2 15.9 15.9 15.8
smaller ,3(0.06) 3(0.06)
0.3 0.1, {1.67,0.56} 0.56
0.18 0.18smaller smaller
Statistical Process Control (SPC)
CapableProcess
es
= target
= target
Meancharts
Rangecharts
and known
Variation
Basic SPC
Concepts
Objectives
First steps
Types ofMeasure
s
Attributes
Variables
SPC for Variabl
es
, unknown