An Optimal Property of S2 Charts

摘要

Let tau sub 1 be the class of all procedures for monitoring the variance of a process at level alpha using control charts based on statistics (T (Y1), T(Y2),...) from independent random samples. Suppose the control variance squared sigma sub zero is known. Under Gaussian assumptions the squared S chart using the sample variance is shown to be optimal in the class tau sub 1 in that its run length is stochastically smallest under both stationary and drifting processes not in control. Weaker properties are given in terms of stochastic bounds when squared sigma sub zero is not known and instead is estimated in a base period using the sample variance. (Author)