Measure Phase
Process Capability
Process Capability
Welcome to Measure
Process Discovery
Six Sigma Statistics
Measurement System Analysis
Process Capability
Continuous Capability
Concept of Stability
Attribute Capability
Wrap Up & Action Items
2
Understanding Process Capability
Process Capability:
•
The inherent ability of a process to meet the expectations of the
customer without any additional efforts.
•
Provides insight as to whether the process has a :
–
–
–
–
•
Centering Issue (relative to specification limits)
Variation Issue
A combination of Centering and Variation
Inappropriate specification limits
Allows for a baseline metric for improvement.
*Efforts: Time, Money, Manpower, Technology and Manipulation
3
Capability as a Statistical Problem
Our Statistical Problem: What is the probability of our
process producing a defect ?
Define a Practical
Problem
Create a
Statistical Problem
Correct the
Statistical Problem
Apply the Correction
to the Practical
Problem
4
Capability Analysis
The Y’s
(Outputs)
Y = f(X) (Process Function)
Verified
?
Op i
Op i + 1
Data for
Y1…Yn
X1
Y1
X2
Off-Line
Correction
Analysis
Scrap
Y2
X3
X4
Yes
X5
No
Correctable
Y3
10.16
10.11
10.16
10.05
10.11
10.33
10.05
10.44
10.33
9.86
10.44
10.07
9.86
10.29
10.07
10.36
10.29
10.36
Variation – “Voice of
the Process”
Frequency
The X’s
(Inputs)
9.87
10.16
9.99
9.87 10.11
10.12
9.99 10.05
10.43
10.12 10.33
10.21
10.43 10.44
10.01
10.21 9.86
10.15
10.01 10.07
10.44
10.15 10.29
10.03
10.44 10.36
10.33
10.03
10.15
10.33
10.15
9.80 9.90 10.0 10.1 10.2 10.3 10.4 10.5
?
Critical X(s):
Any variable(s)
which exerts an
undue influence on
the important
outputs (CTQ’s) of a
process
Capability Analysis Numerically
Compares the VOP to the VOC
Requirements – “Voice
of the Customer”
Data - VOP
10.16
10.11
10.05
10.33
10.44
9.86
10.07
10.29
10.36
9.87
9.99
10.12
10.43
10.21
10.01
10.15
10.44
10.03
10.33
10.15
USL = 10.44
LSL = 9.96
10.16
10.11
10.05
10.33
10.44
9.86
10.07
10.29
10.36
Defects
-6
-5
Defects
-4
-3
-2
-1
+1
+2
+3
+4
+5
+6
9.70 9.80 9.90 10.0 10.1 10.2 10.3 10.4 10.5 10.6
Percent Composition
5
Process Output Categories
Incapable
LSL
Average
Off target
LSL
USL
Average
Target
USL
Target
Capable and
on target
LSL
Average
USL
Target
6
Problem Solving Options – Shift the Mean
This involves finding the variables that will shift the process
over to the target. This is usually the easiest option.
LSL
USL
Shift
7
Problem Solving Options – Reduce Variation
This is typically not so easy to accomplish and occurs
often in Six Sigma projects.
LSL
USL
8
Problem Solving Options – Shift Mean & Reduce Variation
This occurs often in Six Sigma projects.
LSL
USL
Shift & Reduce
9
Problem Solving Options
Obviously this implies making them wider, not narrower.
Customers usually do not go for this option but if they
do…it’s the easiest!
LSL
USL
USL
Move Spec
10
Capability Studies
Capability Studies:
• Are intended to be regular, periodic, estimations of
a process’s ability to meet its requirements.
• Can be conducted on both Discrete and
Continuous Data.
• Are most meaningful when conducted on stable,
predictable processes.
• Are commonly reported as Sigma Level which is
optimal (short term) performance.
• Require a thorough understanding of the following:
–
–
–
–
–
Customer’s or business’s specification limits
Nature of long-term vs. short-term data
Mean and Standard Deviation of the process
Assessment of the Normality of the data (Continuous Data only)
Procedure for determining Sigma level
11
Steps to Capability
Select Output for
Improvement
#1
Verify Customer
Requirements
#2
Validate
Specification
Limits
#3
Collect Sample
Data
#4
Determine
Data Type
(LT or ST)
#5
Check data
for normality
#6
Calculate
Z-Score, PPM,
Yield, Capability
Cp, Cpk, Pp, Ppk
#7
12
Verifying the Specifications
Questions to consider:
• What is the source of the
specifications?
–
–
–
–
Customer requirements (VOC)
Business requirements (target, benchmark)
Compliance requirements (regulations)
Design requirements (blueprint, system)
• Are they current? Likely to
change?
• Are they understood and agreed
upon?
– Operational definitions
– Deployed to the work force
13
Data Collection
Capability Studies should include “all” observations (100% sampling) for a specified period.
Long-term data:
•Is collected across a broader inference
space.
•Monthly, quarterly; across multiple
shifts, machines, operators, etc
•Subject to both common and special
causes of variation.
•More representative of process
performance over a period of time.
•Typically consists of at least 100 – 200
data points.
Short-term data:
•Collected across a narrow
inference space.
•Daily, weekly; for one shift,
machine, operator, etc.
•Is potentially free of special cause
variation.
•Often reflects the optimal
performance level.
•Typically consists of 30 – 50 data
points.
Lot 1
Fill Quantity
Lot 5
Lot 3
Lot 2
Short-term studies
Lot 4
Long-term study
14
Baseline Performance
Process Baseline: The
average, long-term performance
level of a process when all input
variables are unconstrained.
Long-term
baseline
4
Short Term
Performance
`
3
2
1
LSL
TARGET
USL
15
Components of Variation
Even stable processes will drift and shift over time by as much as
1.5 Standard Deviations on the average.
Long Term
Overall Variation
Short Term
Between Group Variation
Short Term
Within Group Variation
16
Sum of the Squares Formulas
=
SS total
+
SS between
SS within
Precision
(short-term capability)
Shift
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
Time
x
17
Stability
A Stable Process is consistent over time. Time Series Plots and
Control Charts are the typical graphs used to determine stability.
At this point in the Measure Phase there is no reason to assume the
process is stable.
Time Series Plot of PC Data
70
PC Data
60
Tic toc…
tic toc…
50
40
30
1
48
96
144
192
240
Index
288
336
384
432
480
18
Measures of Capability
Hope
Cp and Pp
• What is Possible if your process is perfectly Centered
• The Best your process can be
• Process Potential (Entitlement)
Reality
Cpk and Ppk
• The Reality of your process performance
• How the process is actually running
• Process Capability relative to specification limits
19
Capability Formulas
Six times the sample
Standard Deviation
Sample Mean
Three times the sample
Standard Deviation
LSL – Lower specification limit
USL – Upper specification limit
20
MINITAB™ Example
Open worksheet “Camshaft.mtw”. Check for Normality: Stat > Basic Statistics > Normality.
By looking at the “P-values”
the data look to be Normal
since P is greater than .05
21
MINITAB™ Example
Create a Capability Analysis for both suppliers, assume long-term data.
Note the subgroup size for this example is 5.
LSL=598 USL=602
Stat > Quality Tools > Capability Analysis (Normal)
22
MINITAB™ Example
Process Capability of Supplier 1
LSL
USL
P rocess Data
LS L
598
Target
*
USL
602
S ample M ean
599.115
S ample N
100
S tDev (Within)
0.559239
S tDev (O v erall) 0.602583
Within
Ov erall
P otential (Within) C apability
Cp
1.19
C P L 0.66
C P U 1.72
C pk
0.66
O v erall C apability
Pp
PPL
PPU
P pk
C pm
1.11
0.62
1.60
0.62
*
597.75 598.50 599.25 600.00 600.75 601.50
O bserv ed P erformance
P P M < LS L 30000.00
PPM > USL
0.00
P P M Total
30000.00
E xp. Within P erformance
P P M < LS L 23088.05
PPM > USL
0.12
P P M Total
23088.18
E xp. O v erall P erformance
P P M < LS L
32130.26
PPM > USL
0.84
P P M Total
32131.10
23
MINITAB™ Example
Process Capability of Supplier 2
LSL
USL
P rocess Data
LS L
598
Target
*
USL
602
S ample M ean
600.061
S ample N
100
S tDev (Within)
1.00606
S tDev (O v erall) 1.14609
Within
Ov erall
P otential (Within) C apability
Cp
0.66
C P L 0.68
C P U 0.64
C pk
0.64
O v erall C apability
Pp
PPL
PPU
P pk
C pm
597
O bserv ed P erformance
P P M < LS L
40000.00
PPM > USL
60000.00
P P M Total
100000.00
598
599
E xp. Within P erformance
P P M < LS L
20251.30
P P M > U S L 26969.82
P P M Total
47221.11
600
601
602
0.58
0.60
0.56
0.56
*
603
E xp. O v erall P erformance
P P M < LS L
36065.24
P P M > U S L 45337.82
P P M Total
81403.06
24
MINITAB™ Example
MINITAB™ has a selection to calculate Benchmark Z’s or Sigma
levels along with the Cp and Pp statistics. By selecting these the
graph will display the “Sigma Level” of your process!
Stat>Quality Tools>Capability Analysis>Normal…>Options…Benchmark Z’s (sigma level)
25
MINITAB™ Example
Process Capability of Supplier 1
LSL
USL
P rocess Data
LS L
598
Target
*
USL
602
S ample M ean
599.115
S ample N
100
S tDev (Within)
0.559239
S tDev (O v erall) 0.602583
Within
Ov erall
P otential (Within) C apability
Z.Bench 1.99
Z.LS L
1.99
Z.U S L
5.16
C pk
0.66
O v erall C apability
Z.Bench
Z.LS L
Z.U S L
P pk
C pm
1.85
1.85
4.79
0.62
*
597.75 598.50 599.25 600.00 600.75 601.50
O bserv ed P erformance
P P M < LS L 30000.00
PPM > USL
0.00
P P M Total
30000.00
E xp. Within P erformance
P P M < LS L 23088.05
PPM > USL
0.12
P P M Total
23088.18
E xp. O v erall P erformance
P P M < LS L
32130.26
PPM > USL
0.84
P P M Total
32131.10
26
MINITAB™ Example
Process Capability of Supplier 2
LSL
USL
P rocess Data
LS L
598
Target
*
USL
602
S ample M ean
600.061
S ample N
100
S tDev (Within)
1.00606
S tDev (O v erall) 1.14609
Within
Ov erall
P otential (Within) C apability
Z.Bench 1.67
Z.LS L
2.05
Z.U S L
1.93
C pk
0.64
O v erall C apability
Z.Bench
Z.LS L
Z.U S L
P pk
C pm
597
O bserv ed P erformance
P P M < LS L
40000.00
PPM > USL
60000.00
P P M Total
100000.00
598
599
E xp. Within P erformance
P P M < LS L
20251.30
P P M > U S L 26969.82
P P M Total
47221.11
600
601
602
1.40
1.80
1.69
0.56
*
603
E xp. O v erall P erformance
P P M < LS L
36065.24
P P M > U S L 45337.82
P P M Total
81403.06
27
Example Short Term
With short-term data do one of the following:
Option 1
Enter “Subgroup size:” = total
number of samples
Option 2
Go to “Options”, turn off “Within
subgroup analysis”
Using data from Column “Bi modal” in the Minitab worksheet “GraphingData.mtw”
28
Continuous Variable Caveats
Capability indices assume Normally Distributed data.
Always perform a Normality test before assessing Capability.
29
Capability Steps
Select Output for
Improvement
#1
We can follow the steps for
calculating capability for
Continuous Data until we
reach the question about
data Normality…
Verify Customer
Requirements
#2
Validate
Specification
Limits
#3
Collect Sample
Data
#4
Determine
Data Type
(LT or ST)
#5
Check data
for Normality
#6
Calculate
Z-Score, PPM,
Yield, Capability
Cp, Cpk, Pp, Ppk
#7
30
Attribute Capability Steps
Select Output for
Improvement
#1
Notice the difference when
we come to step 5…
Verify Customer
Requirements
#2
Validate
Specification
Limits
#3
Collect Sample
Data
#4
Calculate
DPU
#5
Find Z-Score
#6
Convert Z-Score
to Cp & Cpk
#7
31
Z Scores
Z Score is a measure of the distance in Standard Deviations of a
sample from the Mean.
– Given an average of 50 with a Standard Deviation of 3 what is
the proportion beyond the upper spec limit of 54?
50
54
32
Z Table
33
Attribute Capability
Attribute data is always long-term in the shifted condition since it requires so
many samples to get a good estimate with reasonable confidence.
Short-term Capability is typically reported, so a shifting method will be
employed to estimate short-term Capability.
You Want to Estimate :
Your Data Is :
ZST
Short Term
Capability
ZLT
Long Term
Capability
ZST
Short Term
Capability
ZLT
Long Term
Capability
Subtract
1.5
Add
1.5
Sigma
Level
Short-Term
DPMO
Long-Term
DPMO
1
158655.3
691462.5
2
22750.1
308537.5
3
1350.0
66807.2
4
31.7
6209.7
5
0.3
232.7
6
0.0
3.4
34
Attribute Capability
By viewing these formulas you can see there is a relationship between them.
If we divide our Z short-term by 3 we can determine our Cpk and if we divide
our Z long-term by 3 we can determine our Ppk.
35
Attribute Capability Example
A customer service group is interested in estimating the Capability of
their call center.
A total of 20,000 calls came in during the month but 2,666 of them
“dropped” before they were answered (the caller hung up).
Results of the call center data set:
Samples = 20,000
Defects = 2,666
They hung up….!
36
Attribute Capability Example
1.
2.
3.
4.
Calculate DPU
Look up DPU value on the Z-Table
Find Z-Score
Convert Z Score to Cpk, Ppk
Example:
Look up ZLT
ZLT = 1.11
Convert ZLT to ZST = 1.11+1.5 = 2.61
37
Attribute Capability
1.
2.
3.
4.
Calculate DPU
Look up DPU value on the Z-Table
Find Z Score
Convert Z Score to Cpk, Ppk
Example:
Look up ZLT
ZLT = 1.11
Convert ZLT to ZST = 1.11+1.5 = 2.61
2
.87
38
Summary
At this point, you should be able to:
• Estimate Capability for Continuous Data
• Estimate Capability for Attribute Data
• Describe the impact of Non-normal Data
on the analysis presented in this module
for Continuous Capability
39
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