The Right and Wrong Ways of Computing Limits

How does your software measure up?

Thu, 01/07/2010 - 05:00

Today virtually everyone uses software to create process behavior charts, yet the available software is notoriously unreliable in terms of the way the limits are computed. This column will explain and illustrate the difference between the correct and some of the incorrect ways of computing three-sigma limits for average charts. It will also provide a simple data set that can be used to evaluate the various options in your software so that, hopefully, you can select an option that uses one of the correct computations.

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The purpose of analysis

The fundamental purpose of any statistical analysis is to separate the potential signals from the probable noise. Once we have said this, the immediate problem becomes how to use our data, which may contain signals, to compute a measure of dispersion that can be used to filter out the noise. When the signals are mixed up with the noise, the signals are likely to contaminate our filter and undermine our analysis.

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Comments

Not just software: there must be an engineering text somewhere that tells students to use the n-standard-deviation approach. Home-grown control charts often look like your second-to-last example. Thanks for giving me a published illustration to debunk some of my customers' unhelpful notions. -- Ken

Submitted by rderoeck on Thu, 01/07/2010 - 11:32

SPC is often treated as a after-thought in most Statistics textbooks (usually last chapter). It doesn't get the respect and importance it deserves for some reason. I have no clue why. If it did, subjects such as local vs. global dispersion and rational subgrouping would be better understood .

Rich DeRoeck

Glad to hear you speak out on this, especially on the use of pooled standard deviation (currently the default in Minitab; easily reset, but it is the default, both for XbarR and XbarS charts).

Submitted by Tom Pyzdek on Wed, 12/05/2018 - 09:39

This will help me respond to my students who ask why the results their software gives are different than the results shown in my lessons. Now, rather than a long explanation, I'll send them a link to this article! Of course, they'll still need to review the lesson to see why they missed this point in the first place. Maybe I need to emphasize that this is *really* important.

Thomas Pyzdek

www.pyzdekinstitute.com

As always, Dr. Wheeler, you have taken the complex and made it practical! Thank-you for this insightful treatment of the right and wrong approaches to computing control limits. I often have to remind people of some of the very errors you point out in this article. I always recommend that people confirm that their software is using the proper techniques by giving them a data set from one of your articles or books and having them compare the computed results.

We can argue and bicker over the fine points of statistical analysis; however, as Walter Shewhart determined 80+ years ago, it is what works in the "real world" that is important. Origins in highbrow statistics do not determine the usefulness of any method.

Best regards,
Steven J. Moore
Director Quality Improvement Systems
Wausau Paper Corp.

I am confident that Tom Pyzdek got the scaling factors right, and I suspect that AIAG did also. However, since there are at least 17 different sets of formulas (all of which are right) for computing limits on process behavior charts, it is important to be very careful here.

Donald J. Wheeler, Ph.D.
Fellow American Statistical Association
Fellow American Society for Quality

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