The definition of capability is:

Cp = (USL-LSL) / 6 sigma

We don't know this parameter but need to estimate it with Cp*.

How to do?
Somewhere I have read that We simply have to put S (taken fron the sample) in place of sigma.
Elsewhere that we should multiply S for 1/c4 because S is a biased estimator of sigma.
In other words, the distribution S^2 (proportional to chi^2), has a shape that is different from the one of S.

What I would like to know is: following the definition of Cp, sigma is on the denominator and not on the numerator.
Shouldn't we find a coefficient for calculating the mean of the distribution 1/sigma (a different coefficient from 1/c4), isn't it?

The definition of capability is:

Cp = (USL-LSL) / 6 sigma

We don't know this parameter but need to estimate it with Cp*.
... we should multiply S for 1/c4 because S is a biased estimator of sigma.


I don't know why '*' stand for, but I have seen then mostly used for biased / unbiased estimates.

For 'R' as dispersion statistic the biased estimator for SD(x) = R/d2*

But as Donald Wheeler said in his book "Advanced Topics in Statistical Process Control", "In any given instance, using and unbiased estimator will not guarantee that the error of estimation will be any less than it would be with a biased estimator". ;)

For Cp* I mean "estimate of actual Cp".
maybe it is usually said as "Cp hat", I hadn't the way to draw it.