Thursday, November 1, 2007

Shewhart's PDSA Cycle

[to be continued ...]

W. A Shewart vs the frequentist theory of probability

There is a thesis that "Keynes wrote A Treatise on Probability in opposition to the frequentist theory of probability" in an Oxford Journals article.

Prediction and pragmatism in Shewhart’s theory of statistical control

Author(s): Mark Wilcox
Journal: Management Decision
ISSN: 0025-1747
Year: 2004 Volume: 42 Issue: 1 Page: 152 - 165
DOI: 10.1108/00251740310495090
Publisher: Emerald Group Publishing Limited
Abstract: Dr W.A. Shewhart, “founder” of the modern quality movement and inventor of the control chart, was greatly influenced by the pragmatist philosopher, C.I. Lewis. However, Lewis's influence is less clear. Shewhart did not refer to Lewis in his 1931 book and it was not until the 1939 publication of his lectures that we find references to Lewis. While Shewhart's work has been read and understood by statisticians, this paper argues that to fully understand his work, one needs a background in philosophy of science. To make the point, this paper uncovers similarities between Lewis's pragmatism and Shewhart's invention of the control chart. Not least is a theory of prediction. The paper concludes that Shewhart had formed the core of his theory before reading Lewis, and that Mind and the World Order (Lewis, C.I., Mind and the World Order: Outline of a Theory of Knowledge, Dover Publications, New York, NY, 1929) provided a convenient post hoc rationalisation. The basis for a theory of management by prediction is a significant outcome of this paper.

Sunday, October 28, 2007

Walter A. Shewhart

Walter A. Shewhart was founding editor of the Wiley Series in Mathematical Statistics, a role that he maintained for twenty years.

Originally an Engineer and Statistician, Walter A. Shewhart is above all known as the true "Father of Modern Quality" whereas W. Edwards Deming was his student and spiritual son. Shewhart introduced the concept of Statistical Process Control (SPC) in Manufacturing.

As influential as SPC is, this is not the essential contribution made by Shewhart. His essential idea he planted in the head of Deming was the concept of Profound Knowledge and PDCA (Plan-Do-Check-Action) or PDSA (Plan-Do-Study-Act) spiral: Plan what you want to do, do it, study the results, make corrections, and start the cycle again (so the spiral not a circle only).

From the late 1930s onwards, Shewhart's interests expanded out from industrial quality to wider concerns in science and statistical inference. The title of his second book Statistical Method from the Viewpoint of Quality Control (1939) asks the audacious question: What can statistical practice, and science in general, learn from the experience of industrial quality control?

Shewhart's approach to statistics was radically different from that of many of his contemporaries. He possessed a strong operationalist outlook, largely absorbed from the writings of pragmatist philosopher C. I. Lewis, and this influenced his statistical practice. In particular, he had read Lewis's Mind and the World Order many times.

His more conventional work led him to formulate the statistical idea of tolerance intervals and to propose his data presentation rules, which are listed below:

1. Data has no meaning apart from its context.

2. Data contains both signal and noise. To be able to extract information, one must separate the signal from the noise within the data.

Walter Shewhart died at Troy Hills, New Jersey in 1967.In his obituary for the American Statistical Association, Deming wrote of Shewhart:

As a man, he was gentle, genteel, never ruffled, never off his dignity. He knew disappointment and frustration, through failure of many writers in mathematical statistics to understand his point of view.

More on Walter Shewhart

by J J O'Connor and E F Robertson

It was the Inspection Engineering Department of the Western Electric Company at Hawthorne that Shewhart joined in 1918. He worked there on statistical tools to examine when a corrective action must be applied to a process. His writings were on statistical control of industrial processes and applications to measurement processes in science. The control chart techniques which he developed have been widely adopted. His contributions are explained in more detail in [8]:-

By the turn of the century, Western Electric had trained individuals as inspectors to assure specification and quality standards, in order to avoid sending bad products to the customer. In the 1920's, Western Electric's Dr Walter Shewhart took manufacturing quality to the next level - employing statistical techniques to control processes to minimize defective output. When Dr Shewhart joined the Inspection Engineering Department at Hawthorne in 1918, industrial quality was limited to inspecting finished products and removing defective items. That all changed in May 1924. Dr Shewhart's boss, George Edwards, recalled:

"Dr Shewhart prepared a little memorandum only about a page in length. About a third of that page was given over to a simple diagram which we would all recognize today as a schematic control chart. That diagram, and the short text which preceded and followed it, set forth all of the essential principles and considerations which are involved in what we know today as process quality control."

Mr Edwards had observed the birth of the modem scientific study of process control. That same year, Dr Shewhart created the first statistical control charts of manufacturing processes, which involved statistical sampling procedures. Shewhart published his findings in a 1931 book, Economic Control of Quality of Manufactured Product.

The Bell Telephone Laboratories were founded in 1925 and Shewhart moved to them when the Laboratories opened and worked there until his retirement in 1956. He expanded his interests to a broader use of statistics over this period. During this period he published many articles papers in the Bell System Technical Journal. In addition, he published Random sampling in the American Mathematical Monthly in 1931. In 1939 he published the important book Statistical Method from the Viewpoint of Quality Control. It is interesting to read the publisher's description of the book:-

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.