Control Charts – Why 3-Sigma Limits?

First of all, I am not a statistician, but have learned from what I consider to be the best people in the statistical realm.  Dr. Don Wheeler, Dr. “Frony” Ward and a gentleman named Tim Baer.  These folks understand in statistical terms how control charts work and also understand the message of W. Edwards Deming and Walter Shewhart.  If you want to understand Dr. Deming’s System of Profound Knowledge. you have to understand variation.  David S. Chambers and Dr. Wheeler’s book Understanding Statistical Process Control is a must read.

The question came to me recently about why three standard deviations (3-sigma) and not two to discern data.  I reacted rather badly as it had been awhile since 3-sigma limits had been challenged.

Wheeler and Chambers (in the fore-mentioned book) point out that 3-sigma limits are “not solely based upon probability theory.  Further . . . “this point has been repeatedly misunderstood by those who would use  probability theory to “adjust” control chart  limits.

Shewhart identified his reasoning in the Economic Control of Quality of Manufactured Product:

” . . . we must use limits such that through their use we will not waste too much time looking unnecessarily for trouble.”

“The method of attack is to establish limits of variability . . . such that, when an observation is found outside these limits, looking for an assignable (special) cause is worthwhile.”

” . . . we usually choose a symmetrical range characterized by limits

Ø ± t σӨ

Experience indicates t=3 seems to be an acceptable economic value”

“Three-sigma limits are not probability limits.  The strongest justification of three-sigma limits is the empirical evidence that three-sigma limits work well in practice – that they provide effective action limits when applied to real world data.  Thus, the  . . . arguments cannot further justify the use of three-sigma limits, but they can reveal one of the reasons why they work so well.” –  Wheeler and Chambers

So, there you have it.  Empirical evidence by their use is the reason that we have 3-sigma limits.  This fits with overwhelming evidence for when to look at special causes.  Occasionally, I find that I get a false signal in practice wither a special cause within the limits or a false signal outside the limits.  However, I have found that they serve me well in practice.

Further, I have found that in service that limits are much more robust in as systems display great variation.  Many times this has played itself out as I understand customer demand – meaning that homogeneity of the data is the issue, not the limits.

Tripp Babbitt is a speaker, blogger and consultant to service industry (private and public).  His organization helps executives find a better way to make the work work.  Read his articles at Quality Digest and his column for  Download free from “Understanding Your Organization as a System” and gain knowledge of systems thinking or contact us about our intervention services at [email protected].  Reach him on Twitter at LinkedIn at

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