Statistical Process Control

Nearly all of the books about Statistical Process Control are quite awful. They contain errors, poor examples, and promote bad practices. Except for a few that may still exist, there is only one book one can recommend for sure: it’s “Statistical Method from the Viewpoint of Quality Control” by Walter A. Shewhart, the original founder of Industrial Quality Management.

For superficial readers and students in statistics, this book could be easily misunderstood as an other book on Probability Calculations whereas it does fundamentally deal with the Epistemology of Probability and Mathematics in the Real World of Manufacturing and Science.

The current publisher’s description on Amazon doesn’t say much. It’s better to read the original publisher’s description of the book in the 1920s: The application of statistical methods in mass production makes possible the most efficient use of raw materials and manufacturing processes, economical production, and the highest standards of quality for manufactured goods. In this classic volume, based on a series of ground-breaking lectures given to the Graduate School of the Department of Agriculture in 1938, Dr Shewhart illuminates the fundamental principles and techniques basic to the efficient use of statistical method in attaining statistical control, establishing tolerance limits, presenting data, and specifying accuracy and precision.

In the first chapter, devoted to statistical control, the author broadly defines the three steps in quality control: specification, production and inspection; he then outlines the historical background of quality control. This is followed by a rigorous discussion of the physical and mathematical states of statistical control, statistical control as an operation, the significance of statistical control and the future of statistics in mass production.

Chapter II offers a thought-provoking treatment of the problem of establishing limits of variability, including the meaning of tolerance limits, establishing tolerance limits in the simplest cases and in practical cases, and standard methods of measuring. Chapter III explores the presentation of measurements of physical properties and constants. Among the topics considered are measurements presented as original data, characteristics of original data, summarizing original data (both by symmetric functions and by Chebyshev’s theorem), measurement presented as meaningful predictions, and measurement presented as knowledge.

Finally, Dr Shewhart deals with the problem of specifying accuracy and precision - the meaning of accuracy and precision, operational meaning, verifiable procedures, minimum quantity of evidence needed for forming a judgment and more.

In this book Shewhart asks:-

What can statistical practice, and science in general, learn from the experience of industrial quality control?

He wrote in this book:-

The definition of random in terms of a physical operation is notoriously without effect on the mathematical operations of statistical theory because so far as these mathematical operations are concerned random is purely and simply an undefined term. The formal and abstract mathematical theory has an independent and sometimes lonely existence of its own. But when an undefined mathematical term such as random is given a definite operational meaning in physical terms, it takes on empirical and practical significance. Every mathematical theorem involving this mathematically undefined concept can then be given the following predictive form: If you do so and so, then such and such will happen.

From 1703 until his death in 1705, Jacob Bernoulli exchanged a number of letters with Gottfried Leibniz. Leibniz wrote to him:

“La nature a sans doute ses habitudes, provenant du retour des causes, mais ce n’est que la plupart du temps. C’est pourquoi, ne peut-on pas objecter qu’une nouvelle expérience puisse s’écarter un tant soit peu de la loi de toutes les précédentes, du fait de la variabilité même des choses ? De nouvelles maladies se répandent souvent sur le genre humain et par conséquent quelque soit le nombre de morts dont vous avez fait l’expérience ce n’est pas pour autant que vous avez établi les limites des choses de la nature au point qu’elle ne puisse en varier dans le futur.”

“Nature has established patterns originating in the return of events but only for the most part. Therefore, can’t we argue that a new experience could deviate from the law of all the previous ones, even a little bit, because of the very essence of variability of things ? New illnesses often flood the human race, so that no matter how many experiments you have done, you have not thereby established a limit on the nature of events so that in the future they could not vary.”

Later, John Maynard Keynes directly refers to Leibniz in his essay on “Probability in relation to the theory of knowledge“. According to a Cambridge Journal’s article, “Keynes’s Treatise on Probability contains some quite unusual concepts, such as non-numerical probabilities and the ‘weights of the arguments’ that support probability judgements. Their controversial interpretation gave rise to a huge literature about ‘what Keynes really did mean’, also because Keynes’s later views in macroeconomics ultimately rest on his ideas on uncertainty and expectations formation”. But what Keynes really means was just what he once told clearly:

“By uncertain knowledge … I do not mean merely to distinguish what is known for certain from what is only probable. The game of roulette is not subject, in this sense, to uncertainty …

The sense in which I am using the term is that in which the prospect of a European war is uncertain, or the price of copper and the rate of interest twenty years hence, or the obsolescence of a new invention … About these matters there is no scientific basis on which to form any calculable probability whatever. We simply do not know!”

At the same time, during the 1920s, Walter A. Shewhart, statistician and engineer, was commissioned to improve the quality of telephones manufactured by Bell Laboratories.

Shewhart framed the problem in terms of Common and Special-Causes of variation. Though Shewhart may not have been the first to reveal this concept, he is the first who has established an operational mean to distinguish between the two: on May 16, 1924, he wrote an internal memo introducing Statistical Process Control with a Control Chart as a tool for Continuous Process Improvment.