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Utilizing Process Capability Analyses and Gauge R&R Studies to
Improve Your Processes
ASQ 1106 Section MeetingApril 21, 2011
Kevin White, Eastman Chemical Company
Capability Metrics –Evaluation and Recommendations
ASQ 1106 Section MeetingApril 21, 2011
Kevin White, Eastman Chemical Company
Tonight’s agenda
3
Time Topic5:30 – 6:15pm Capability Metrics6:15 – 6:45pm Dinner6:45 – 7:30pm Gauge R&R (Measurement System) Metrics7:30 – 7:45pm Break7:45 – 8:30pm Effective Use of Capability and Gauge R&R Metrics
Presentation outline
Variation, short-term and long-termProcess Stability IndexProcess Capability IndicesProcess Performance IndicesNormality, data editing, sample size, one-sided specsLess common indices and six sigma metrics
4
Two types of variation
5
Common cause• Noise• Predictable• Routine• No assignable cause• Expected
Special cause• Signal• Not predictable• Exceptional• Assignable cause• Unusual
Control charts and control limits
6
The control chart is used to distinguish between common and special causesThe control limits represent the expected variation due to common cause
Stable versus unstable processes
7
A stable (in control) process is one in which the key process responses and product properties show no signs of special causesAn unstable (out of control) process exhibits both common and special causes
Visualizing variation in the “x-bar world”
8
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sure
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t Long-Term
Visualizing variation in the “individual world”
9
•• •• ••
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••••••Time
Short-Term
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sure
men
t
Long-Term
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sure
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t
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Time
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sure
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t Long-Term
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sure
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t
Long-Term
•
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Short-term versus long-term variation
10
Short-term (σST)• Represents the process
capability• Captures variation due to
common causes• Measures the variation
within subgroups or between successive values
• Used for calculating control chart limits
Long-term (σLT)• Represents the total
process variation• Captures variation due to
common and special causes
• Measures the variation in all the data
• Should not be used for calculating control chart limits
Short-term versus long-term variation
11
Short-term (σST) Long-term (σLT)
1
)(1
2
−
−∑=
n
xxn
ii
2dR
4cs
2dMR
Stability Index
12
For a stable process, you would expect values near 1For an unstable process, you would expect values > 1Rules of thumb• < 1.33 – good process stability• 1.33 - 1.67 – marginal process stability• > 1.67 – poor process stability
ST
LT Index Stability σσ=
How much data do I need?
13
Short-term and long-term standard deviations can be calculated on any dataset• 10 observations or 1000 observations• Over one week or over one year
A long-term standard deviation calculated using 10 observations collected over a one week period is not long-termThe amount of time covered is as important as the amount of data
Switching gears to process capability
14
When talking process stability, we were comparing the process variation to the control limitsWhen talking process capability, we will be comparing the process variation (and location) to the specification limitsSpecification limits or tolerance• Voice of the customer• Usually stated as a LSL and USL• Some cases will have only a LSL or USL (one-sided spec)
In other words…
15
Process capability index, Cp
16
Average not in formulaOnly considers short-term variabilityMust have both LSL and USL to calculateRules of thumb?
Cp =USL - LSL
6σST
LSL USL
What if Process is Off-Target?
17
Process capability index, Cpk
18
Still only considers short-term variabilityCan be used for one-sided specificationsIf on-target, Cp ≈ Cpk
LSL USL
Cpk =Min (USL - avg, avg - LSL)
3σST
Process performance index, Pp
19
Average not in formulaBut considers long-term variabilityMust have both LSL and USL to calculateIf stable, Cp ≈ Pp
Pp =USL - LSL
6σLT
LSL USL
Process performance index, Ppk
20
Considers average and long-term variabilityCan be used for one-sided specificationsCp ≈ Cpk ≈ Pp ≈ Ppk if on-target and stable
LSL USL
Ppk =Min (USL - avg, avg - LSL)
3σLT
Summary of indices
21
Cp is the best indicator of potential process capability because it assumes a stable and on-target processCpk is also an indicator of potential process capability if the process is stable. It does take into consideration if the process is off-target.Pp is an indicator of actual process performance if the process is on-target. It does take into account the long-term variability.Ppk is the best indicator of actual process performance because it considers the process average and long-term variability
Some additional interpretation of the indices
22
Cp / Pp = Stability IndexCpk / Ppk = Stability Index
3(Cp-Cpk) = The number of short-term standard deviations the average is from target3(Pp-Ppk) = The number of long-term standard deviations the average is from target
ST
LTLT
ST
LT
ST
P
P
σσ
LSLUSL6σ
6σLSLUSL
6σLSLUSL
6σLSLUSL
PC =
−×−=−
−
=
Interpretation – example #1
23
Cp = 1.64Cpk = 1.63Pp = 1.61Ppk = 1.60
Interpretation – example #2
24
Cp = 1.34Cpk = 0.67Pp = 1.36Ppk = 0.68
Interpretation – example #3
25
Cp = 1.32Cpk = 1.07Pp = 0.75Ppk = 0.62
Normality
26
The indices discussed assume the individual data points are from a normal distribution• Check normality – histogram or normal probability plot• If not normal, why?
Unstable processUp against a physical boundary (yield, impurities)Time oriented data like time between failures (exponential)
• If underlying process is truly non-normal, a data transformation may be appropriate
• Calculate indices after successful transformationBe sure to transform the specifications too
Data editing
27
If you have an unstable process, consider editing data to estimate the short-term variability• Involves editing of ranges or moving ranges• Do not edit more than 5-10% of the values• One possible edit – make a one-pass edit excluding ranges
above the UCL
Do not edit data when estimating the long-term standard deviation• One possible exception is to have a “blunder” edit
Use good judgment
Sample Size
28
These indices are statistics just like the average and standard deviation and have variation associated with their estimationCommon software packages will provide confidence intervals for these indicesA simulation was performed with underlying Pp = 1.51000 Pp’s calculated based on sample sizes of 10, 30, 50, 100
Sample size – simulation summary
29
Sample size 5th percentile 95th percentile10 1.10 2.5030 1.25 1.9050 1.28 1.81100 1.35 1.70
Six Sigma metrics (Sigma Level, PPM Defective)
30
A Sigma Level of 6 corresponds to 3.4 ppm defective• Like having a Cp=2 (short-term)• Even with 1.5σ shift, would only have 3.4 ppm defective
Tables available to convert ppm levels to Sigma levelsCommon software will also produce these calculations (Sigma Quality, Z.Bench, etc)• Need to be careful though, some incorporate 1.5σ shift, some
don’t
Less common indices
31
Cpm =USL - LSL
6 σST2 + (avg-tgt)2
Cr =6σST
USL - LSL=
Cp
1
K =Average - Target0.5(USL - LSL)
Summary
32
Cp, Cpk, Pp, Ppk very useful indices for:• understanding process performance• Guiding future improvement efforts
Need to consider normality, data editing, sample sizeOther similar indices and metrics exist
Questions?
Tonight’s agenda
34
Time Topic5:30 – 6:15pm Capability Metrics6:15 – 6:45pm Dinner6:45 – 7:30pm Gauge R&R (Measurement System) Metrics7:30 – 7:45pm Break7:45 – 8:30pm Effective Use of Capability and Gauge R&R Metrics
Gauge R&R Metrics –Evaluation and Recommendations
ASQ 1106 Section MeetingApril 21, 2011
Kevin White, Eastman Chemical Company
Tonight’s agenda
36
Time Topic5:30 – 6:15pm Capability Metrics6:15 – 6:45pm Dinner6:45 – 7:30pm Gauge R&R (Measurement System) Metrics7:30 – 7:45pm Break7:45 – 8:30pm Effective Use of Capability and Gauge R&R Metrics
Presentation outline
Introduction to…• Measurement systems analysis• Gauge repeatability and reproducibility (R&R) studies
Common gauge R&R metricsRelationships between the metrics
37
Issues with measurement systems
Bias (accuracy)LinearityStabilityPrecision (repeatability, reproducibility)
38
Precision
The focus of this presentation is on the precision aspect of measurement systems and the metrics often calculated from a gauge repeatability and reproducibility (GR&R) study• Repeatability – the variability from the gauge or test instrument
when used with the same operator or set-up to measure the same unit
• Reproducibility – the variability arising from different operators, set-ups, instruments, or time periods
39
Measurement systems analysis
Measurement Systems Analysis (MSA) occurs early in the Six Sigma DMAIC RoadmapThe Gauge R&R study is the primary tool taught to Belts• Quantify how much of the observed variability is real process
variation and how much is due to the measurement system• Isolate sources of variability in the measurement system
(repeatability and reproducibility)• Quantify amount of specification range consumed by the
measurement system
Overall, determine if measurement system is adequate for use in the broader project or application
40
Typical gauge R&R study
Ten (10) samplesThree (3) operatorsEach operator measures each sample three (3) times
41
Operator 1 Operator 2 Operator 3
Sample 1 2 3 1 2 3 1 2 3 1 11.0 10.8 11.0 … 2 11.4 11.3 11.5 … 3 10.2 10.3 10.3 … 4 11.4 11.5 11.4 … 5 10.0 10.2 10.1 … 6 M M M 7 8 9 10
The basic model
The total observed variation is equal to the real process variation plus the variation due to the measurement system
42
222msprocesstotal σσσ +=
22rpdrpt σσ +
Measurement system metrics
Some compare the measurement system variation to the total variation of the process• %GRR• Intraclass correlation coefficient (ρ)• ndc• DR
Some compare the measurement system variation to the specification limits• Precision-to-Tolerance Ratio (PTR)
43
%GRR
Addresses the "percent" of total variation taken up by the measurement system
Traditional guidelines state• <10% - Acceptable• 10 to 30% - May be acceptable• >30% - Not acceptable
44
100%GRR ×=total
ms
σσ
%GRR – a true percent of total variation?
Recall..
And…
A true percent would be…
45
222msprocesstotal σσσ +=
msprocesstotal σσσ +≠
100%MS 2
2
×=total
ms
σσ
%GRR versus %MS
46
0
10
20
30
40
50
60
70
80
90
100
%M
S
0 10 20 30 40 50 60 70 80 90 100%GRR
%GRR makes the measurement system appear
worse than reality
Intraclass correlation coefficient (ρ)
A traditional measure of association used to characterize the relative usefulness of a measurement systemProportion of variation due to process
Wheeler (EMP III)• First class monitors (>0.8)• Second class monitors (0.5 to 0.8)• Third class monitors (0.2 to 0.5)• Fourth class monitors (<0.2)
47
2
2
2
2
1total
ms
total
process
σσ
σσ
ρ −==
Number of distinct categories (ndc)
Number of non-overlapping 97% confidence intervals that will span the expected variationNumber of distinct categories a measurement system can readily indentify
Value should be truncated to the integer and ought to be greater than 5
48
ms
process
σσ
×= 41.1ndc
Discrimination Ratio (DR)
49
Very similar to ndcThe number of product categories which could be established within the natural process limits using these measurements (Wheeler, EMP 2nd Edition)
For simple measurements, should be > 4 (Wheeler)Improve measurement if < 2 (Wheeler)
1ndc1211D 2
2
2
R +=−=−+=
ms
total
σσ
ρρ
Relationships between metrics
50
100%GRR%MS
2
=
1%GRR
00141.1ndc2
−⎟⎟⎠
⎞⎜⎜⎝
⎛×=
2
100%GRR1 ⎟
⎠⎞
⎜⎝⎛−=ρ
1%
1002D2
R −⎟⎠⎞
⎜⎝⎛=
GRR
All of these metrics can be described as a function of %GRR
%GRR versus %MS and ICC
51
%M
S
ICC
%GRR versus ndc and DR
52
0123456789
10
ndc
/ DR
0 10 20 30 40 50 60 70 80 90 100%GRR
DR
ndc
Precision-to-Tolerance Ratio (PTR)
Addresses the percent of tolerance consumed by the measurement system
Normally, k=5.15 or k=6Traditional guidelines state• <10% - Acceptable• 10 to 30% - May be acceptable• >30% - Not acceptable
53
100Tolerance
kPTR ms ×= σ
Summary
54
There are many metrics that compare the measurement variation to the total variationBecause of their relationships, using more than one is redundantSome of the guidelines are a little contradictoryPTR is different because it compares the measurement variation to the tolerancePart of the next session is going to examine the relationship between Cp, %GRR, and PTR and propose new guidelines for the measurement system
Questions?
Tonight’s agenda
56
Time Topic5:30 – 6:15pm Capability Metrics6:15 – 6:45pm Dinner6:45 – 7:30pm Gauge R&R (Measurement System) Metrics7:30 – 7:45pm Break7:45 – 8:30pm Effective Use of Capability and Gauge R&R Metrics
Effective Use of Capability and Gauge R&R Metrics
ASQ 1106 Section MeetingApril 21, 2011
Kevin White, Eastman Chemical Company
Tonight’s agenda
58
Time Topic5:30 – 6:15pm Capability Metrics6:15 – 6:45pm Dinner6:45 – 7:30pm Gauge R&R (Measurement System) Metrics7:30 – 7:45pm Break7:45 – 8:30pm Effective Use of Capability and Gauge R&R Metrics
Presentation outline
Recommended set of process capability metrics with guidelinesApproach for using the capability metric guidelines to identify process improvement opportunitiesRecommended set of measurement system metrics with guidelinesRelationship between process capability and measurement system metricsTwo-dimensional guidelines for measurement system metrics
59
Index overload
60
PpPpk
Cpk
Cp
Stability IndexσLT
σST
LSLUSL
ppmCpm
Cr
K
%GRR
%MS
ndc
DRPTR
ρ
The goal
61
The goal is to have processes that are:• Stable (in-control)• On-target• Within specifications• With adequate (capable)
measurement systems
Which indices can help us assess our performance against this goal?
LSL USL
Ppk – assessing actual performance (start here)
62
Ppk is the best indicator of actual process performance because it considers the process average and long-term variability
LTpk 3
LSL)x,xmin(USLPσ
−−=
Ppk guidelines
63
RED
YELLOW
GREEN
POOR
MARGINAL
ADEQUATE
Ppk
1.0
1.5
Stability index – assessing stability
64
Look at ratio of long-term variability to short-term variability
Note stability index is also same as Cp/Pp or Cpk/Ppk
ST
LT Index Stability σσ=
Stability index guidelines
65
RED
YELLOW
GREEN
POOR
MARGINAL
ADEQUATE
StabilityIndex
1.67
1.33
Target index – assessing ability to hit target
66
The target index is defined as the number of short-term standard deviations the process average is from the target
Note this is the same as 3*(Cp-Cpk)
ST
TxIndex Target
σ−
=
Target index guidelines
67
RED
YELLOW
GREEN
POOR
MARGINAL
ADEQUATE
TargetIndex
1.0
0.5
Cp – assessing potential performance
68
Cp is the best indicator of potential process capability because it assumes a stable and on-target process
STp 6
LSLUSLCσ−=
Cp guidelines
69
RED
YELLOW
GREEN
POOR
MARGINAL
ADEQUATE
Cp
1.0
1.5
Using the indices (flowchart)
70
PpkActual
Performance
Adequate
Marginalor Poor
Likely,do nothing
CpCommon cause
too large?
Target IndexOff target?
Stability Indexunstable?
Improve Stability(special causes)
Yes
Work on Level(Average)Yes
Improve Capability(common cause)
Yes
Routine Reporting
71
It is recommended that a routine report or scorecard (monthly, quarterly, bi-annual) be created that shows this information for all key processes and responsesWith some simple color coding, it can easily help identify improvement opportunities• What to work on• And the type of effort that it will involve
Example scorecard #1
72
1st Quarter 2010Process 1 Ppk Cp Stability Index Target Index
Response 1 1.67 1.67 1.00 0.00Response 2 2.78 8.33 3.00 0.00Response 3 0.95 1.33 1.40 0.00Response 4 0.33 1.67 2.55 2.50Response 5 1.59 2.38 1.00 2.38
Process 2 Ppk Cp Stability Index Target IndexResponse 1 1.11 1.11 1.00 0.00Response 2 2.08 2.78 1.33 0.00Response 3 0.62 1.33 1.40 1.40
Example scorecard #2
73
Process XYZ, Response ABCQtr/Yr Ppk Cp Stability Index Target Index
3Q 2008 1.52 3.09 1.91 0.564Q 2008 1.63 2.82 1.66 0.341Q 2009 1.45 3.09 2.04 0.372Q 2009 1.65 3.40 2.02 0.203Q 2009 1.75 3.21 1.83 0.004Q 2009 1.61 2.92 1.67 0.701Q 2010 1.49 3.03 1.91 0.55
Plots of indices over time can also be useful
Improving unstable processes
74
Involves finding and fixing special causesControl charts used in conjunction with control strategiesPotential special causes• Lack of standardization• Lack of consistent process conditions
Uncontrolled process variablesUnknown process variablesEquipment malfunctions
• Unstable measurement system• Changes in process inputs• Management intervention
Improving off-target processes
75
Actions based on:• Process understanding• Engineering theory• Design of Experiments• EVOP Experiments
Potential fixes• Raw material quality level• Change in operating conditions• Modify or change equipment• Improved measurement accuracy
USLLSL
Improving (reducing) common cause variation
76
Actions based on:• Process understanding• Engineering theory• Process variation studies• Design of Experiments• Measurement systems analysis• Stratification
Potential fixes• Improved measurement precision• Standardization• Engineering process control (EPC)• Change in operating conditions
USLLSL
What about the measurement system?
77
Does the measurement system need to be improved…• When the process is unstable?
So long as the measurement system is stable and you’re able to see instability in the process, work on the process instability
• When the process is off-target?Possibly, it may be hard to detect improvements if there is large amount of measurement variabilityReplicate testing to reduce measurement variation is also something to consider
• When the common cause variability is too large?Very possibleWill depend on the measurement system metrics
Measurement system metrics
78
%GRR• Compares the measurement system variation to the total
variation
PTR (Precision-to-Tolerance Ratio)• Compares the measurement system variation to the specification
range (tolerance)
Other metrics exist, but as you saw in the previous session, they are very related
100%GRR ×=total
ms
σσ
100Tolerance
kPTR ms ×= σ
Measurement system metric guidelines
79
RED
YELLOW
GREEN
POOR
MARGINAL
ADEQUATE
%GRR PTR
30% 30%
10% 10%
One problem with %GRR
80
%GRR looks at a ratio of standard deviations (measurement/total)Since standard deviations are not additive, %GRR is not a true percent of the total variationGuidelines may not be realistic for some measurement systems
0
10
20
30
40
50
60
70
80
90
100
%M
S
0 10 20 30 40 50 60 70 80 90 100%GRR
Percent Cp improvement with measurement improvement
81
Plot shows %improvement in Cp for
given %reductions in the measurement standard deviation
Relationship between capability and measurement system metrics
82
%GRR PTR Cp
σmsX X
σSTX X
Tolerance X X
If you know two of the metrics, then you can figure out the third without knowing the individual components.
Graphical depiction of relationship
83
0
10
20
30
40
50
60
70
80
90
100
P/T
Rat
io
0 10 20 30 40 50 60 70 80 90 100% Gage R&R
Cp=1.0
Cp=0.5
Cp=2.0
Cp=1.5
%GRR
PTR
Note: k=5.15 in PTR
calculation
Applying the measurement metric guidelines
84
0
10
20
30
40
50
60
70
80
90
100
P/T
Rat
io
0 10 20 30 40 50 60 70 80 90 100% Gage R&R
Cp=1.0
Cp=0.5
Cp=2.0
Cp=1.5
%GRR
PTR
Two-dimensional guidelines
85
0
10
20
30
40
50
60
70
80
90
100P
/T R
atio
0 10 20 30 40 50 60 70 80 90 100% Gage R&R
Cp=1.0
Cp=0.5
Cp=2.0
Cp=1.5
Sigma Level > 6
Improving process variation will help,but the measurement systemwill still need to be improved
(BOTH)
Meas. sys. is adequate,focus on process(PROCESS)
Focus on process variation first,measurement system may become
limiting after some level ofprocess variation improvement
(PROCESS)
The measurementsystem is primary
limitation on furtherprocess capability
Improvement(TEST)
Work on bothprocess andmeas. sys.
(BOTH)
%GRR
PTR
Example
86
0
10
20
30
40
50
60
70
80
90
100P
/T R
atio
0 10 20 30 40 50 60 70 80 90 100% Gage R&R
Cp=1.0
Cp=0.5
Cp=2.0
Cp=1.5
%GRR
PTR
Summary Comments
87
A limited number of metrics are all you need and will indicate process improvement opportunities• Process instability• Off-target• Excessive common cause variation• Inadequate measurement system
If you prefer another metric, you can probably substitute for one of the ones shown• Example: use ndc instead of %GRR
May want to tweak the guidelines (rules of thumb) for your specific industry
Questions?