measure for six sigma and beyond… · ©tom pearson consulting 2006 slide #2 tom pearson...
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IndyASQ WorkshopSeptember 12, 2007
Measure for Six Sigma and Beyond…
©Tom Pearson Consulting 2006 Slide #2
Tom PearsonTom Pearson317317--507507--53585358
[email protected]@insightbb.com
n MS ORn Old #76n Golf Guy
n Innovatorn Dog Lover
n Tomorrowistn Entrepreneur
n Author / Speakern Systems Scientist
n Measurement Scientistn Six Sigma Master Black Belt
n Dilbert / Pointy-Haired Boss / Dogbertn ASQ Fellow, Past Chair MQD and Section 903
Introductions…
©Tom Pearson Consulting 2006 Slide #3
““Measure for Six Sigma and BeyondMeasure for Six Sigma and Beyond…”…”
n Measure is more than just a step in SixSigma's DMAIC method.
n Good measurements are basic buildingblocks of good information.
n Good measurements are critical for gooddecision making.
n This workshop will investigate the keyelements of good measurement systems.
©Tom Pearson Consulting 2006 Slide #4
Measurement and Statistics
n Measurements have a long and rich …relationship with statistical sciences.
n Metrology (measurement science) is thestudy of measurement error (uncertainty).It is essentially a statistical pursuit.
n Were there no uncertainty, there would bevery little science in measurement science.
Philip Stein, “Statistical Issues in Measurement”,ASQ Statistics Division Special Publication (July 2002)
©Tom Pearson Consulting 2006 Slide #5
What to Measure…
All Possible Input Xs
ProcessMapping
FishboneDiagrams
X-YMatrices
FMEA
Critical Few Xs
DataMining
HypothesisTesting
Design ofExperiments
©Tom Pearson Consulting 2006 Slide #6
Types of Data
n Variable or Continuousn Quantitative – a scale that can take an infinite
number of values along it’s length, with orwithout end points (e.g., temperature,pressure), or with an absolute zero point (e.g.,height, weight).
n Attribute or Discreten Qualitative
• Count or percentage• Binomial• Nominal• Ordinal
Tonight’s Focus
©Tom Pearson Consulting 2006 Slide #7
Class Attribute Data
n Ordinaln Categorical variables that have three or more
possible levels with natural ordering.n Distance between the levels is unknown
• I.e., poor, fair, excellent, or Olympic scoring.
n Can be attribute or discrete variable data.
n Nominaln Categorical variables that have two or more
possible mutually exclusive levels with nonatural ordering (e.g., sex, race).
n Typically attribute data.
© Joe Swartz 2005
©Tom Pearson Consulting 2006 Slide #8
Critical Six Sigma questions…
n What is the Voice of the Customer?n What to Measure: Cost, Quality, Features, Availability
n What is the Voice of the Process?n Center, Spread, Shape, Stability (Control)
n Does our process meet customer needs?n Compliance, Process Capability, Opportunities?
n Can we make it better?n Continuous Improvement, Breakthrough, Innovation.
©Tom Pearson Consulting 2006 Slide #9
CTQ
<6
>0
Specifications
Observation5045403530252015105
7.5
5.0
2.5
0.0
5045403530252015105
6.0
4.5
3.0
1.5
0.0
6
6
6
6
1
I-MR Chart of DefectsLab Test Requested IMR Chart
VOPVoice Of the Process
VOCVoice Of the Customer
Note the Process•Center•Shape•Spread•Stability
Example:
©Tom Pearson Consulting 2006 Slide #10
Consider the Shape, Center, and Spread…
©Tom Pearson Consulting 2006 Slide #11
What about Stability?
p=0.0013
p=(.02485)2
=.00062
P=(0.5)8
=0.0039
68%p=0.68
©Tom Pearson Consulting 2006 Slide #12
5045403530252015105
6
6
6
6
Hearing the VOP…
68%
12
1426
Lab Test Requested IMR Chart
©Tom Pearson Consulting 2006 Slide #13
Does it meet customer needs (VOC)?
6543210-1
LSL Target USLProcess Data
Sample N 52StDev (Within) 1.35586StDev (O v erall) 1.68261
LSL 0.10000Target 3.00000USL 5.90000Sample Mean 2.51923
Potential (Within) C apability
C C pk 0.71
O verall C apability
Pp 0.57PPL 0.48PPU 0.67Ppk
C p
0.48C pm 0.55
0.71C PL 0.59C PU 0.83C pk 0.59
O bserv ed PerformancePPM < LSL 115384.62PPM > USL 57692.31PPM Total 173076.92
Exp. Within PerformancePPM < LSL 37189.44PPM > USL 6325.47PPM Total 43514.90
Exp. O v erall PerformancePPM < LSL 75247.13PPM > USL 22255.54PPM Total 97502.67
WithinOverall
Process Capability of DefectsLab Test Process Capability
©Tom Pearson Consulting 2006 Slide #14
VOP helps us plan future operations…
Defects
Perc
ent
76543210-1-2
99
95
90
80
70
60504030
20
10
5
1 0.37
3
10
4.66
5
90
Mean
<0.005
2.519StDev 1.674N 52AD 1.365P-Value
Probability Plot of DefectsNormal
Lab Test Probability Plot
©Tom Pearson Consulting 2006 Slide #15
Team
Def
ects
87654321
6
5
4
3
2
1
0
Boxplot of Defects vs Team
Method
Def
ects
4321
6
5
4
3
2
1
0
Boxplot of Defects vs Method
Trial
Def
ects
13121110987654321
6
5
4
3
2
1
0
Boxplot of Defects vs Trial
VOP helps us find improvement opportunities
©Tom Pearson Consulting 2006 Slide #16
Measurement Systems Analysis
MSA insures:n Good correlationn Adequate discriminationn In statistical controln Measurement uncertainty small:n Compared to process variationn Compared to specification limits
©Tom Pearson Consulting 2006 Slide #17
Measurment Variation…
Target
σ2measuring system
= σ2operator
+ σ2measurement device
+ σ2environment
σ2total = σ2
process + σ2measurement system
Spec
©Tom Pearson Consulting 2006 Slide #18
Measurment Variation with Bias…
Target
σ2total = σ2
process + σ2measurement system
Spec
Note: The observed mean isthe average of the processmean and the measurementsystem mean.
©Tom Pearson Consulting 2006 Slide #19
Sources of Measurement Uncertainty…
n Measurement Accuracyn How closely the average measured value agrees with
the “true” value.n Average Measurement – True Value = Bias
MoreAccurate
LessAccurate
TrueValue
TrueValue
©Tom Pearson Consulting 2006 Slide #20
Sources of Measurement Uncertainty
n Measurement Precisionn How closely repeated measurements agree with each
other.n Compensate for Poor Precision by
• Better Measuring Device• Better Measurement Method• Averaging repeat measurements…
Less PreciseMore Precise
©Tom Pearson Consulting 2006 Slide #21
Sources of Measurement Uncertainty…
n Measurement Resolutionn Minimum of 10 increments within the specification.n At least 5 increments within the SPC Range Chart.n Increase Resolution, Normality, (and Cost) by
averaging repeated measurements.
Less Precise Averages of 4 Readings have½ the variation of individuals.
Remember: 2xbar = 2
x
©Tom Pearson Consulting 2006 Slide #22
How Good is Good Enough?n If 2
measure/ 2observed is less than or equal to 0.1:
n Good Measurement Systemn Use as is, look for ways to simplify or reduce expense
n If 2measure/ 2
observed is between 0.1 and 0.3:n Marginal Measurement System… use with caution.n Improve the measurement system by training
operators, standardizing procedures, using statistics,investigating new methods and equipment.
n If 2measure/ 2
observed is 0.3 or greater:n Unacceptable Measurement Systemn Do not use for critical decisionsn Correct ASAP.
©Tom Pearson Consulting 2006 Slide #23
Example: Needs improved or replaced.
Target
σ2measure = 9
σ2observed = 25
σ2meas/σ2
obs = .36 > .3
©Tom Pearson Consulting 2006 Slide #24
Measurement System Errors
n Precision (Gage R&R)n Repeatability
• The variation between successive measurements ofsame product or service, same characteristic, bysame person, using same measurement device
n Reproducibility• Variation in appraisers
n Additional Factors?• Environment• Equipment• Other
n Determine via Designed Experiments…
©Tom Pearson Consulting 2006 Slide #25
Questions?