Chapter 4

Statistical Models

All models are wrong, but some are useful. (Box, (1999), p. 23)


Control charts are versatile statistical tools with a role to play in all four of the measure, analyse, improve and control phases of Six Sigma projects. In order to develop control charts from run charts, some understanding of statistical models for both discrete and continuous random variables is required, in particular of the normal or Gaussian statistical model. The normal distribution is also fundamental in understanding of the concept of sigma quality level referred to earlier in Section 1.1. Brief reference will also be made to the multivariate normal distribution. An understanding of statistical models in turn necessitates some fundamental knowledge of probability.

Finally, knowledge of the statistical properties of sums of independent random variables yields important results concerning means and proportions – results that are vital for the assessment of whether or not changes made during the improve phase of a Six Sigma project have been effective, for an appreciation of the way in which the various sources of errors in measurement processes contribute to the overall measurement error, and for an understanding of the construction of control charts.

Unlike other chapters, this one includes a number of exercises at various points, some of which do not require the use of Minitab. They are included to help the reader understand the topics of probability and statistical models ...

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