A Cusum for a Scale Parameter

Abstract

Standard cusum procedures are available for controlling the mean of a process. However, in many industrial applications it is important to control the process variability as well. This article presents a technique for employing the same cusum procedure used for the mean for controlling the variance. The technique is based on cusumming |Xi/σ|1/2, which is very nearly normally distributed if X is N(O, σ2). If the process has a nonzero unknown mean, then the same technique may be applied with Xi replaced by the difference between successive observations.