Process Behavior Charts and Chaos Theory

What do predictable processes have in common with chaos?

"Chaos Theory" Credit: Boon Chin Ng

Walter Shewhart made a distinction between common causes and assignable causes based on the effects they have upon the process outcomes. While Shewhart’s distinction predated the arrival of chaos theory by 40 years, chaos theory provides a way to understand what Shewhart was talking about.

Assignable causes

W. Edwards Deming described assignable causes as special causes. He then would say that the special causes are “not part of the system.” Thus, he considered a special cause as a temporary cause—fleeting and ephemeral. Shewhart saw things differently. He sometimes wrote of assignable causes as temporary, but at other times he had a different model in mind. For example, Shewhart defined “a state of statistical control” to exist when “the chance fluctuations in a phenomenon are produced by a constant system of a large number of chance causes in which no cause produces a predominating effect.” Here Shewhart clearly implies that when a chance cause begins to have a dominant effect it becomes an assignable cause.

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Process Behavior explained by Choas Theory

Beautiful, lucid explanation.

Thank you, Dr. Wheeler. As always, you do not disappoint.

Chaos

Thank you for another great article. I didn't know much about Chaos Theory.

I can connect the dots now to how Dr. Shewhart pointed to chaos when he said the "routine has broken down."

"Through the use of the scientific method, extended to take account of modern statistical concepts, it has been found possible to set up limits within which the results of routine efforts must lie if they are to be economical. Deviations in the results of a routine process outside such limits indicate that the routine has broken down and will no longer be economical until the cause of trouble is removed."

Source:

Shewhart, W. A. (1931). Economic control of quality of manufactured product. Van Nostrand.

No coincidence your most popular book below is all about managing chaos!

https://www.spcpress.com/book__data/toc_understanding_variation.pdf

Allen

Chaos and Order

Hi Dr. Wheeler

I never thought I'd see an article like this about Shewhart's work. I'm intrugued. I thought, perhaps, you are referring to Edward Lorenz's famour article "Deterministic Non-periodic Flow" when you mention the discovery of sensitive dependence on initial conditions, althugh his article was pblished a couple of years before 1965. I was introduced to his work through James Gleick's famout book, Chaos: Making a New Science. The thing that intrigued me most, coming out of Lorenz's work is that chaos arizes from order -- a deterministic process is the assignable cause of his famous weather-modelling attractor. And, it is quite predictable -- you can run the similation over and over and get the same result.

I came across your work through reading about Stacey Barr's PuMP Blueprint. A couple of us in our company took a PuMP workshop a couple of years ago. One of the XmR Charts used in the example case for the workshop was said to be "chaotic", which I questioned because all of the data points were within the limits and it looked like a stable process to me. I was not connecting the dots! You just did that for me with this article and provided delightful, additional education about Shewhart's work.

Always grateful for your insights!