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Statistics for Process Control Engineers by Myke King

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12Selected Distributions

We have seen that it is a common error to assume that data are normally distributed. This can even be done unknowingly. The control engineer may not appreciate that a statistical formula being applied was derived from the PDF or CDF of the normal distribution. This can result in seriously erroneous conclusions, of which there are many examples. They include proceeding with an improved control project that appears to be economically attractive when, in fact, it is not. Another is deducing an inferential property is reliable when, in fact, including it in a control scheme actually worsens control of the property.

There are many reasons why process data may not be normally distributed. One of the aims of this book is to highlight this issue and present a wide range of alternative choices for the prior distribution. This chapter focusses on those that are more commonly presented in textbooks. They represent a small fraction of many hundred published. In some cases their popularity is justified; they work well for the purpose for which they were developed. However, popularity is rarely a reliable measure of effectiveness. Take, as an example, the Ziegler–Nichols controller tuning method. It is almost universally included in university courses on process control, despite it now being virtually useless as a tuning method. Of the dozens of other published methods, perhaps one or two are effective and these are among the least well known. The same is true of ...

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