Myths About Process Behavior Charts

How to avoid some common obstacles to good practice

Wed, 09/07/2011 - 10:56

The simplicity of the process behavior chart can be deceptive. This is because the simplicity of the charts is based on a completely different concept of data analysis than that which is used for the analysis of experimental data. When someone does not understand the conceptual basis for process behavior charts, they are likely to view the simplicity of the charts as something that needs to be fixed. Out of these urges to fix the charts all kinds of myths have sprung up, resulting in various levels of complexity and obstacles to the use of one of the most powerful analysis techniques ever invented. The purpose of this article is to help you avoid this complexity.

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Comments

Submitted by shrikale on Thu, 09/08/2011 - 11:33

Dear Dr. Wheeler,

 

Thank you for your column explaining the myths away. I was just discussing how important it was to understand an idea's historical context to appreciate its intent. It was a pleasant coincidence to see you do that in your explanation. With distance in time, it is easy to lose the operational definition of an idea and inadvertently corrupt it to fit a particular perspective.

 

I will share your post with others to reconnect them with Dr. Shewhart's intent.

 

Regards,
Shrikant Kalegaonkar

twitter: shrikale

We've been taught in school and have been reinforced and practiced in work that to use process behavior charts, the data needs to be normal and that there should be no outliers.

 

Now I know that:

 

  1. We do not need to check for normality or transform the data to make them “more normal.” 
  2. We do not have to use subgrouped data in order to receive the blessing of the central limit theorem before the chart will work. 
  3. We do not need to examine our data for autocorrelation. 
  4. And we do not need to wait until our process is “well-behaved” before computing limits.

Hoping that your article will help our organization see the correct way of using process behavior charts.

 

Presenting this article will be a challenge, but worth the effort.

 

-Red Anderson

Red,

I have ALWAYS included tests for distributional fit (histogram and chi square test, and quantile-quantile plot) in any process capability study (including control chart preparation) I have ever done, and I recall counseling suppliers whose reports it was my job to review to do the same. First, if it isn't normal, the process capability estimate can be off by orders of magnitude (as measured by nonconforming fraction) especially if you have a gamma distribution with a long upper tail--the end at which the specification limit usually lies. A "Six Sigma" process can in such a case give you 10 or more DPMO and that is without the 1.5 sigma process shift assumed by Motorola.

Second, the false alarm risk can be enormous, and I am again talking about at least an order of magnitude in extreme cases. The practical implication is that production workers will waste time and eventually lose confidence in SPC. The apparent Weibull distribution in Figure 1, by the way, looks sufficiently bell-shaped that the false alarm risk will not be extreme and the traditional Shewhart chart might be adequate for it. There are in fact practical situations in which, even if the critical to quality characteristic is known to be non-normal, it will behave sufficiently normal so as to pass goodness of fit tests for normality.

From what I have seen of sample ranges, the distribution of R becomes more bell shaped with increasing sample size. The same for the s chart noting that the chi square distribution (for s squared) becomes more bell shaped with increasing degrees of freedom.

It is to be noted that Shewhart developed his methods in the 1920s and 1930s, during which it would have been computationally prohibitive to set exact control limits for non-normal distributions. It is now almost routine to do so with StatGraphics, Minitab, or even spreadsheet functions. Therefore, it seems reasonable to do it that way; fit the actual distribution, set control limits for the desired false alarm risks, and calculate the process performance index that corresponds to the nonconforming fraction (an approach now approved by AIAG's SPC manual).

Donald,

AIAG's Statistical Process Control manual (2nd ed, p. 113) agrees with you that Shewhart did not develop his charts under the assumption of normality, and that the charts can be used for all processes as you say. It also agrees with me that "However, as the process distribution deviates from normality, the sensitivity to change decreases, and the risk associated with the Type I error increases."

The manual also says you can use standard Shewhart control charts (as you recommend) with appropriate sample sizes, OR adjust the limits to reflect the non-normal form, OR use a transformation, OR use control limits based on the native non-normal form (which is what I recommend). "Appropriate sample sizes" seems to suggest reliance on the Central Limit Theorem, which certainly mitigates the effects of non-normality.

Even if the traditional Shewhart chart is adequate for control purposes in the shop (as seems likely for Figure 1), though, one must still deal with the process capability estimate. According to pages 140-143 of the AIAG reference, you can compute the nonconforming fraction and the corresponding normal-equivalent performance index (e.g. 1 ppb above the upper specification limit => PPU = 2.0). Another is to compute Pp = (USL-LSL)/(Q(0.99865)-Q(0.00135)) where Q refers to the quantile of the distribution. The latter, also known as the ISO method, is attractive because it converts directly to Pp = (USL-LSL)/(6 standard deviations) if the distribution is normal.

Use of either of these, however, requires us to fit the non-normal distribution to the process data. Since we HAVE to do this to provide a meaningful performance index (I say "performance" rather than "capability" because the maximum likelihood estimation methods rely on the body of the data instead of subgroups), we may as well then use the fitted distribution to set control limits with known false alarm risks and average run lengths.

Submitted by Dr Burns on Thu, 09/08/2011 - 17:07

Another excellent article.  However you can be sure that the masses will not let the truth get in the way of popular opinion.  The myths of Six Sigma rule !  There is a strong parallel with the man caused global warming scam.  There is not a shred of evidence to support AGW but the masses still follow blindly.

Dr Wheeler,

If we do not have to use subgrouped data, why is subgrouping used and explained in your books?

Jose,

We subgroup for many reasons, but some will insist that we have to subgroup the data to invoke the blessing of the central limit theorem.  Thus my comment was saying that subgrouping is not mandatory, not that it was not useful in many cases.  When producing widgets, where we can choose both the subgroup size and the subgroup frequency, subgrouping is recommended.  When working with data that come one number at a time, we usually will want to use subgroups of size one, and here subgrouping can get in the way.

 

Submitted by rderoeck on Mon, 09/12/2011 - 09:08

Don't put too much faith in the AIAG manuals. Both the MSA and FMEA books publisheed by AIAG have serious flaws (as Dr. Wheeler has pointed out).

Learn SPC from a master.

Rich DeRoeck

Dr. Wheeler,

The last two paragraphs under Myth 1 were very enlightening for me.  Thanks for explaining something that I have wondered about for a long time.  These two paragraphs were an "A-Ha! moment" for me.

Steve Moore

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