Question: Why is there a scaling factor for the Upper and Lower Natural Process Limits?

A reader question:

“Mark, Thanks to your help, and some push from an IHI conference there is some pull in our organization for Process Behavior Charts.  As we are putting together a template and training, we are looking for the stats behind the 2.66 and 3.268 scale factors used in calculating limits.  I bought your book but it doesn’t go into detail.  Do you have a link you can share where I can find a basic explanation to share with MDs who are curious?”

My response:

Great question. The Natural Process Limits on the X-Chart are essentially plus or minus 3-sigma around the center line (average). There is a scaling factor that makes the formula:

Natural Process Limits = Average +/- 3 * MR-bar /1.128

The 1.128 is a statistical scaling factor.

Or you can express the formula as:

Natural Process Limits = Average +/- 2.66 * MR-bar

That does not mean that the X-Chart has “plus and minus 2.66 sigma” limits. The scaling factor is used to create an estimate of the 3-sigma limits.

For the MR-Chart, the Upper Range Limit is:

Upper Range Limit = 3.268 * MR-bar

You can read Don Wheeler’s article: “Scaling Factors for Process Behavior Charts” for an in-depth discussion. You can also read more in his book Understanding Statistical Process Control.

I’ve read those and I’ve taken Wheeler’s four-day seminar where he goes into great depth and detail about these topics. For most practitioners of this method, I wouldn’t recommend worrying too much about these details. I’ll defer to Dr. Wheeler and his Ph.D. in statistics.

You can also read his articles:



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