On sigma estimators for the case of M>1 subgroups and quality control S charts of varying sample sizes

摘要

This article discusses the (precision and accuracy) relative efficiencies of all estimators of a normal population standard deviation sigma = sigma(X) for M 1 subgroups of different sample sizes. We have examined the statistical properties of seven estimators of sigma(X) which are (1) the pooled estimator S-p, (2) the pooled unbiased estimator sigma^pub, (3) the maximum likelihood estimator sigma^mle, (4) Irving W. Burr's weighted ranges, (5 and 6) the last two Burr estimators, and the author's optimal estimator sigma^XO. Unlike the case of M = 1 subgroup, our introduction section shows that the sigma^mle for M 1 subgroups is the least accurate of sigma estimators and should be avoided in all applications only when M 1. As a consequence of our findings, modifications of at least two choices to control limits of S chart are provided. Part 1 of this article (Sections 1-6) compares estimators assuming a process is under statistical control, and Part 2 (Sections 7-10) discusses all statistical aspects of the S chart of varying sample sizes.