Preface

There are those that have a very cynical view of statistics. One only has to search the Internet to find quotations such as those from the author Mark Twain:

There are three kinds of lies: lies, damned lies, and statistics.
Facts are stubborn, but statistics are more pliable.

From the American humourist Evan Esar:

Statistics is the science of producing unreliable facts from reliable figures.

From the UK's shortest-serving prime minister George Canning:

I can prove anything by statistics except the truth.

And my personal favourite, attributed to many - all quoting different percentages!

76.3% of statistics are made up.

However, in the hands of a skilled process control engineer, statistics are an invaluable tool. Despite advanced control technology being well established in the process industry, the majority of site managers still do not fully appreciate its potential to improve process profitability. An important part of the engineer's job is to present strong evidence that such improvements are achievable or have been achieved. Perhaps one of the most insightful quotations is that from the physicist Ernest Rutherford.

If your experiment needs statistics, you ought to have done a better experiment.

Paraphrasing for the process control engineer:

If you need statistics to demonstrate that you have improved control
of the process, you ought to have installed a better control scheme.

Statistics is certainly not an exact science. Like all the mathematical techniques that are applied to process control, or indeed to any branch of engineering, they need to be used alongside good engineering judgement. The process control engineer has a responsibility to ensure that statistical methods are properly applied. Misapplied they can make a sceptical manager even more sceptical about the economic value of improved control. Properly used they can turn a sceptic into a champion. The engineer needs to be well versed in their application. This book should help ensure so.

After writing the first edition of Process Control: A Practical Approach, it soon became apparent that not enough attention was given to the subject. Statistics are applied extensively at every stage of a process control project from estimation of potential benefits, throughout control design and finally to performance monitoring. In the second edition this was partially addressed by the inclusion of an additional chapter. However, in writing this, it quickly became apparent that the subject is huge. In much the same way that the quantity of published process control theory far outstrips more practical texts, the same applies to the subject of statistics - but to a much greater extent. For example, the publisher of this book currently offers over 2,000 titles on the subject but fewer than a dozen covering process control. Like process control theory, most published statistical theory has little application to the process industry, but within it are hidden a few very valuable techniques.

Of course, there are already many statistical methods routinely applied by control engineers - often as part of a software product. While many use these methods quite properly, there are numerous examples where the resulting conclusion later proves to be incorrect. This typically arises because the engineer is not fully aware of the underlying (incorrect) assumptions behind the method. There are also too many occasions where the methods are grossly misapplied or where licence fees are unnecessarily incurred for software that could easily be replicated by the control engineer using a spreadsheet package.

This book therefore has two objectives. The first is to ensure that the control engineer properly understands the techniques with which he or she might already be familiar. With the rapidly widening range of statistical software products (and the enthusiastic marketing of their developers), the risk of misapplication is growing proportionately. The user will reach the wrong conclusion about, for example, the economic value of a proposed control improvement or whether it is performing well after commissioning. The second objective is to extract, from the vast array of less well-known statistical techniques, those that a control engineer should find of practical value. They offer the opportunity to greatly improve the benefits captured by improved control.

A key intent in writing this book was to avoid unnecessarily taking the reader into theoretical detail. However the reader is encouraged to brave the mathematics involved. A deeper understanding of the available techniques should at least be of interest and potentially of great value in better understanding services and products that might be offered to the control engineer. While perhaps daunting to start with, the reader will get the full value from the book by reading it from cover to cover. A first glance at some of the mathematics might appear complex. There are symbols with which the reader may not be familiar. The reader should not be discouraged. The mathematics involved should be within the capabilities of a high school student. Chapters 4 to 6 take the reader through a step-by-step approach introducing each term and explaining its use in context that should be familiar to even the least experienced engineer. Chapter 11 specifically introduces the commonly used mathematical functions and their symbology. Once the reader's initial apprehension is overcome, all are shown to be quite simple. And, in any case, almost all exist as functions in the commonly used spreadsheet software products.

It is the nature of almost any engineering subject that the real gems of useful information get buried among the background detail. Listed here are the main items worthy of special attention by the engineer because of the impact they can have on the effectiveness of control design and performance.

• Control engineers use the terms 'accuracy' and 'precision' synonymously when describing the confidence they might have in a process measurement or inferential property. As explained in Chapter 4, not understanding the difference between these terms is probably the most common cause of poorly performing quality control schemes.
• The histogram is commonly used to help visualise the variation of a process measurement. For this, both the width of the bins and the starting point for the first bin must be chosen. Although there are techniques (described in this book) that help with the initial selection, they provide only a guide. Some adjustment by trial and error is required to ensure the resulting chart shows what is required. Kernel density estimation, described in Chapter 6, is a simple-to-apply, little-known technique that removes the need for this selection. Further it generates a continuous curve rather than the discontinuous staircase shape of a histogram. This helps greatly in determining whether the data fit a particular continuous distribution.
• Control engineers typically use a few month's historical data for statistical analysis. While adequate for some applications, the size of the sample can be far too small for others. For example, control schemes are often assessed by comparing the average operation post-commissioning to that before. Small errors in each of the averages will cause much larger errors in the assessed improvement. Chapter 7 provides a methodology for assessing the accuracy of any conclusion arrived at with the chosen sample size.
• While many engineers understand the principles of significance testing, it is commonly misapplied. Chapter 8 takes the reader through the subject from first principles, describing the problems in identifying outliers and properly explaining the impact of repeatability and reproducibility of measurements.
• In assessing process behaviour it is quite common for the engineer to simply calculate, using standard formulae, the mean and standard deviation of process data. Even if the data are normally distributed, plotting the distribution of the actual data against that assumed will often reveal a poor fit. A single data point, well away from the mean, will cause the standard deviation to be substantially overestimated. Excluding such points as outliers is very subjective and risks the wrong conclusion being drawn from the analysis. Curve fitting, using all the data, produces a much more reliable estimate of mean and standard deviation. There are a range of methods of doing this, described in Chapter 9.
• Engineers tend to judge whether a distribution fits the data well by superimposing the continuous distribution on the discontinuous histogram. Such comparison can be very unreliable. Chapter 6 describes the use of quantile-quantile plots, as a much more effective alternative that is simple to apply.
• The assumption that process data follows the normal (Gaussian) distribution has become the de facto standard used in the estimation of the benefits of improved control. While valid for many datasets, there are many examples where there is a much better choice of distribution. Choosing the wrong distribution can result in the benefit estimate being easily half or double the true value. This can lead to poor decisions about the scope of an improved control project or indeed about whether it should be progressed or not. Chapter 10...