Question: Why Are There Different Ways of Expressing the Formulas for the Limits?

Here’s a good question from a reader:

In your KaiNexus webinar on PBCs you use:

LCL = Mean – 3*(MR bar)/1.128

and

UCL = Mean + 3*(MR bar)/1.128

When 3.0/1.128~=2.66

I use: Ave(x) +/- (2.66 × Ave(mR))

Those are just different ways of expressing the same formula.

“Mean” and “Ave(x)” are two different notations for the average of the metric over the baseline period.

“MR bar” and “Ave(mR)” are two different notations for the average of the moving range values.

The formula with 2.66 is a bit simpler, mathematically.

But, using the 3 (divided by the statistical constant of 1.128) means that the 3 is used to represent the estimate of “3 sigma” limits.

3/1.128 = 2.66 like you said…. which simplifies the formula slightly but sometimes confuses people into thinking its “2.66 Sigma” limits. But, again, 3/1.128 helps give us the proper estimate of 3 sigma limits… it’s not 2.66 sigma.

I hope that clarifies things…

Read more about that “scaling factor” or statistical constant.

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