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Chapter 7Is the Six Sigma statistical modeltechnically sound?

When I use a word, Humpty Dumpty said, in a rather scornful tone

it means just what I choose it to mean neither more nor less.

The question is, said Alice, whether you can make words mean

so many different things. The question is, said

Humpty Dumpty, which is to

be master thats allThrough the looking glass, Lewis Carroll

Overview

Purists challenge the statistical component of the Six Sigma model on the

grounds that it is, at worst, fundamentally flawed and, at best, based on very

tenuous grounds. There are a number of reasons for this. The critique and

response to the critique given in this chapter are prompted by four constructive

and positive considerations:

to place potential users in a better position to deal with technical queries on

the standard Six Sigma statistical model as they arise; to point out frailties in the conventional or original Six Sigma statistical

model and to propose more appropriate metrics where required by a partic-

ular situation;

to indicate the probable marketing reasons for the model that has given the

initiative its name; and

to put this matter of model frailty into proper perspective in relation to the

merits of the overall Six Sigma business initiative.

There are five very controversial aspects of the Six Sigma statistical modelthat are criticized, cause confusion, and hence prompt discussion and

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Is the Six Sigma statistical model technically sound? 209

resolution:

1 the different use of the universally accepted term denoting standard deviation,

the Greek term sigma;

2 the method of the linking of 6 Sigma to a claimed world-class performance

standard of 3.4 defects per million opportunities;

3 the claim that 3.4 defects per million opportunities represent world-class

performance;4 the use of the term defects when non-conformities or undesirable events is

intended;

5 the multiple meaning of the term opportunity.

Let us deal head-on with the most significant criticisms of the Six Sigma

model. The critique and response in the body of this chapter are dealt with in as

non-statistical a manner as possible. A more statistical approach, to justify the

conclusions drawn is given in the Chapter 8. These criticisms are dealt with either

by explaining and justifying the rationale, advising in interpretation and appli-

cation, and/or proposing alternative approaches in particular circumstances.

Sigma versus sigma

Criticism

The originators of the Six Sigma initiative use a unit of measurement, a Sigma, to

measure performance, the higher the value of Sigma the better the performance.

For example, a 6 Sigma process is rated better than a 5 Sigma one. This meaning

contrasts with the standard statistical meaning and usage of the term, sigma. The

symbol, sigma, a Greek letter symbolizing a statistical measure of variation, termed

the standard deviation is in universal use. The lower the value of the standard devi-

ation, sigma, the less the variation present and the better the performance of a

characteristic. The opposing meanings inevitably cause confusion. This confusioncan be compounded as the internationally accepted standard sigma provides the

derivation of the Sigma metric used in Six Sigma projects and also the relationship

between non-conformities per million opportunities and the Six Sigma, Sigma.

Throughout this book, to distinguish between the two uses of the term the

Six Sigma Sigma is represented by an upper case initial letter thus, Sigma.

The standardized conventional use of the term is represented wholly in lower

case italic, thus sigma.

Response to criticism

An advantage of the Sigma measure is its simplicity and practicality. This appeals

to all those who do not wish to get too embroiled in statistical niceties but

just want a simple readily understandable scale of performance measurement.



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The fact that 6 Sigma denotes something better than 5 Sigma and that

5 Sigma is better than 4 Sigma, and so on makes good practical sense to them

and they are quite prepared to run with it.

Others, who are already actively engaged in the application of statistical

process control, will readily understand the use of Sigmas in a different way to

sigmasbut may feel uncomfortable and uneasy with both the frailty of the under-

lying concept and the outcome. This is because an alternative soundly basedapproach is available with the use of the internationally defined measured data

process capability indices such as Cp. A Cp of 3 indicates less variation than a Cp

of 2, and so on. Such measures require the pre-establishment of both process

stability and a knowledge of the underlying pattern of variation.

Linkage of Sigma value to defect rate

Criticism

The value of Sigma is linked to a defects per million opportunities value in a

pseudo-statistical manner in two ways. Two gross assumptions are made.

1 The pattern of variation of the characteristic is symmetrical and bell shaped.

This pattern is termed normal or Gaussian distribution by statisticians.

2 A drift in one, unspecified, direction of the value of a characteristic amounting

to 1.5 standard deviations.

Response to criticism 1

It should be noted that the use of the term normal here is not that of usual but

rather just a statistical name given to a particular distribution. In the technical

sense it is quite appropriate to state, quite categorically, that: in diagnostic

activities leading to process improvement and in the estimation of process per-

formance normality of data should never be assumed. An erroneous assumptionof normality can, and undoubtably will, lead to false trails and take one up the

garden path in Six Sigma project-improvement activities.

Having said this, we need to recognize that a lot of people throughout the

world do and have being doing so, very successfully in the control of processes,

for a great many years. Walter Shewhart (Shewhart, W. A., 1931) introduced sta-

tistical quality control charts for both measured and attribute data. Standard

action control limits on such charts are set, quite simply, at 3 sigma (standard

deviations) of the measure plotted. This is so for both measured and attribute

characteristics. The assumption is that the data are normal when it is patently

not for range and standard deviation charts and frequently not for measured

individuals and attribute ones. Such procedures are, in general, used throughout

the world, and are specified by the International Standards Organization (ISO)

and the British Standards Institution in various standards. Examples are

210 Six Sigma: Continual Improvement for Businesses



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