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The Right and Wrong Ways of Computing Limits

How does your software measure up?

Donald J. Wheeler
Thu, 01/07/2010 - 05:00
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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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Comments

Submitted by American Carpenter on Thu, 01/07/2010 - 10:40

Thanks, Don.

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

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

Right Way of Calculating Control Limits

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

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Submitted by Rip Stauffer on Thu, 01/07/2010 - 11:41

Another Great Article!

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).

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

This should help instructors

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

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Submitted by Steve Moore on Fri, 01/08/2010 - 09:27

Practicality

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.

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Submitted by knowwareman on Fri, 01/08/2010 - 12:47

Median Chart Formulas

Median chart formulas used in this article (from your Guide to Data Analysis) differ significantly from Pyzdek's article: http://www.qualitydigest.com/dec98/html/spctool.html
and AIAG SPC 2nd Edition.
How does the user community decide which set of formulas and constants to use?

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Submitted by Donald J. Wheeler on Mon, 01/11/2010 - 08:21

In reply to Median Chart Formulas by knowwareman

Median Chart Formulas

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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