Statistics for Process Control Engineers

1Introduction

Statistical methods have a very wide range of applications. They are commonplace in demographic, medical and meteorological studies, along with more recent extension into financial investments. Research into new techniques incurs little cost and, nowadays, large quantities of data are readily available. The academic world takes advantage of this and is prolific in publishing new techniques. The net result is that there are many hundreds of techniques, the vast majority of which offer negligible improvement for the process industry over those previously published. Further, the level of mathematics now involved in many methods puts them well beyond the understanding of most control engineers. This quotation from Henri Poincaré, although over 100 years old and directed at a different branch of mathematics, sums up the situation well.

In former times when one invented a new function it was for a practical purpose; today one invents them purposely to show up defects in the reasoning of our fathers and one will deduce from them only that.

The reader will probably be familiar with some of the more commonly used statistical distributions – such as those described as uniform or normal (Gaussian). There are now over 250 published distributions, the majority of which are offspring of a much smaller number of parent distributions. The software industry has responded to this complexity by developing products that embed the complex theory and so remove any need for the user ...