Statistics for Process Control Engineers

9Fitting a Distribution

The process control engineer is likely to be familiar with the uniform and normal distributions, and perhaps one or two others, but these form only part of a bewildering array of over 250 published. Very few documented PDF have a solid engineering basis. Primarily they were developed empirically and justified on the basis that they fit published datasets better than their predecessors. Indeed the approach we take in this book is to select the most appropriate distribution for each dataset – irrespective of the purpose for which the distribution might originally have been developed. Indeed, the control engineer has little choice in adopting this approach. Development of distributions has been largely focussed on pharmaceutical, meteorological and demographic studies. More recently, new techniques have been developed for analysis of financial investments. But there are none that are specifically designed for the process industry.

We will see that each PDF (or PMF), CDF and QF includes at least one parameter that affects its shape. For example, we have seen that the shape of a normal distribution is defined by its mean (μ) and standard deviation (σ). Presented with a dataset we choose a CDF (or PDF or QF) that should describe its distribution and then estimate the shape parameters based on the observed distribution. This is known as the Bayesian approach and, as defined earlier, the chosen function is known as the prior distribution.

The approach an engineer ...