A Change-Point Model for a Shift in Variance

Abstract

A control chart for detecting shifts in the variance of a process is developed for the case where the nominal value of the variance is unknown. As our approach does not require that the in-control variance be known a priori, it avoids the need for a lengthy Phase I data-gathering step before charting can begin. The method is a variance-change-point model, based on the likelihood ratio test for a change in variance with the conventional Bartlett correction, adapted for repeated sequential use. The chart may be used alone in settings where one wishes to monitor one-degree-of-freedom chi-squared variates for departure from control; or it may be used together with a parallel change-point methodology for the mean to monitor process data for shifts in mean and/or variance. In both the solo use and as the scale portion of a combined scheme for monitoring changes in mean and/or variance, the approach has good performance across the range of possible shifts.