A brief tutorial on the estimation of the process standard deviation

We consider the common sequential quality control problem of estimating a process standard deviation based on several sample ranges or sample standard deviations. Simple, well-known facts that are used to produce ‘control chart constants’ can also provide guidance in the combining of such ranges or standard deviations for normal processes. Root mean squared errors for both unbiased linear estimators common in the literature and some (biased) optimal estimators are shown to be simple functions of these constants.