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…

mailto:[email protected]

mailto:[email protected]


““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.


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)


What to Measure…

All Possible Input Xs

ProcessMapping

FishboneDiagrams

X-YMatrices

FMEA

Critical Few Xs

DataMining

HypothesisTesting

Design ofExperiments


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


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


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.


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:


Consider the Shape, Center, and Spread…


What about Stability?

p=0.0013

p=(.02485)2

=.00062

P=(0.5)8

=0.0039

68%p=0.68


5045403530252015105

6

6

6

6

Hearing the VOP…

68%

12

1426

Lab Test Requested IMR Chart


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


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


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


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


Measurment Variation…

Target

σ2measuring system

= σ2operator

+ σ2measurement device

+ σ2environment

σ2total = σ2

process + σ2measurement system

Spec


Measurment Variation with Bias…

Target

σ2total = σ2

process + σ2measurement system

Spec

Note: The observed mean isthe average of the processmean and the measurementsystem mean.


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


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


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


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.


Example: Needs improved or replaced.

Target

σ2measure = 9

σ2observed = 25

σ2meas/σ2

obs = .36 > .3


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…


Questions?

measure for six sigma and beyond… · ©tom pearson consulting 2006 slide #2 tom pearson...

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