Enhancements for the $S^2$ Control Chart

Abstract

The S2 control chart is often used in the monitoring of shifts in the process variance. The $S^2$ chart is quick in detecting big shifts but is less sensitive to small shifts. This paper aims at increasing the sensitivity of the $S^2$ chart in the detection of small shifts while maintaining its sensitivity towards big shifts. Numerous runs rules schemes will be considered and incorporated into the conventional $S^2$ chart. The suggested approach involves a simple transformation of the $S^2$ statistic which does not complicate the application of the chart by industrial practitioners and engineers. Keywords: $S^2$ chart; runs rules; process variance; Markov chain; Type-I error; average run length; out-of-control; in-control.