six sigma metrics, confusion & resolutions - breyfogle

8/13/2019 Six Sigma Metrics, Confusion & Resolutions - Breyfogle

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2001 by Smarter Solutions, Inc., All rights reserved.

Forrest W. Breyfogle III

Smarter Solutions, Inc.

Austin, Texaswww.smartersolutions.com

References Implementing Six Sigma, Forrest W. Breyfogle III, Wiley, 1999

Managing Six Sigma, Forrest W. Breyfogle III, James M. Cupello, Becki Meadows, Wiley, 2001

Bottom-Line Success with Six Sigma, Forrest W. Breyfogle III and Becki Meadows, Quality

Progress, May 2001


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The metrics of Six Sigma can be useful or they can bedeceiving For example, equations to determine process capability indices are

basically very simple; however, these equations are very sensitiveto the standard deviation input

This presentation address the confusion and deception thatoften accompanies Six Sigma process capability metrics,

along with a strategy that can improve the communication ofprocess capability issues.


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Process capability/performance studies assess a processrelative to specification criteria

Statisticians often challenge how well commonly used capabilityindices do this

Customers often request these indices when communicating withtheir suppliers

Customers also might set process capability/performance targetsand then ask its suppliers for to meet these targets


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6

LSL-USL=pC

=

3

LSL,

3

-USLminpkC

Process capability indices Cp

and Cpk

can be expressed as


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6

LSL-USL=pC

x

f(x)

Cp=1.33

Cp=1.67

Lower

Specification

Limit (LSL)

Upper

Specification

Limit (USL)

Cp=2.00

Cp=1.00

Cp compares the spread of our data to the width of the

specification limits

Process variabilityProcess variability

Width of specification limitsWidth of specification limits


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x

f(x)

Cpk=1.33

Cpk=1.67

Lower

Specification

Limit (LSL)

Upper

Specification

Limit (USL)

Cpk=2.00

Cpk=1.00

Cpk

calculations are made relative to closest specificationlimit (LSL line shifted left)

=

3LSL,

3-USLminpkC


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Consider how one should

determine the standarddeviation of a process in orderto estimate a processcapability index

There are differences ofopinion on how this shouldbe done

The question: Should

we focus on overall variability or within subgroup variability

Average within

standard deviation

Average within

standard deviation


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Process Capability: The 6

range of a process inherentvariation, for statistically stable processes only where is usually estimated by R-bar/d2

Cp: This is the capability index which is defined as thetolerance width divided by the Process Capability, irrespectiveof process centering

Cpk: This is the capability index which accounts for processcenteringIt relates the scaled distance between the process mean and

the closest specification limit to half the total process spread

AIAG DefinitionsAIAG Definitions


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Process Performance: The 6 range of a process total variation, where is usually estimated by s, the sample standard deviation

Pp: This is the performance index which is defined as thetolerance width divided by the process performance, irrespectiveof process centering Typically, this is expressed as the tolerance width divided by six times the

sample standard deviation It should only be used to compare to or with CpandCpk and to measure

and prioritize improvement over time

Ppk: This is the performance index which accounts for processcentering It should only be used to compare to or with Cp andCpk and to measure

and prioritize improvement over time

AIAG DefinitionsAIAG Definitions


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Long-term variability

Short-term variability

if x-bar and R chart:

if XmR chart:

=

=

n

i

i

n

xx

1

2

1

)(

2

d

R=

128.1

2

RM

d

RM==


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Not all statistical software programs will give the same

answer for process capability calculations Minitab calculations for process capability depend upon the order

the data is entered

The equations described are for normally distributed data Computer programs can often address situations where data are

not from a normal distribution; however, this is often not done inpractice

Sample size and confidence intervals are not typicallyaddressed.


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Since most people try to visualize the ppm rate impact fromany reported process capability index, we suggest reporting only a long-term ppm rate directly using

transformations as needed

We also do not recommend converting ppm rates to SigmaQuality Levels

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