Calculating Within Sigma for Capability

[#1]

Hello:

I trying to understand the details in how JMP's process capability platform reports "within sigma" metrics. I found there are several options for this in the JMP documentation but there is still ambiguity about how it calculates the within sigma value (which then determines CpK). For example, the first option to calculate the "within sigma" value if a subgroup is specified (what I am trying to find) is this formula,

rxrodriguez_0-1634128481165.png

I don't understand what d2(ni) is exactly. The description is a bit vague. Does anyone know or know where more detail is?

[#2]

The d2 constant is a bias correction factor. The within group ranges are pooled by averaging. So this average represents the typical short-term variation. But it is not sigma. It is proportional to it, but it is biases. So d2 corrects this bias. Dividing by d2 removes the bias.

The same idea is used in most of the other control charts.

Any textbook about SQC / SPC that covers control charts will explain it.