Combined mean and variance control charts

Abstract

Many types of control charts are available. These control charts include the Shewhart control chart, cumulative sum (CUSUM) control chart and exponentially weighted moving average (EWM) control chart. A precise comparison of the average run length (ARL) of these control charts is performed using ARL computed from theoretical results. The control chart parameters of the CUSUM and EWM control charts are selected such that they have the same in control and a particular out of control ARL. The performance of these control charts are investigated under shifts of the process mean and inflations of the process variance. The ARL of the CUSUM and EWM control charts with nonzero starting values are compared with their respective control charts with zero starting values. The control charts designed for monitoring the process mean have no provision for monitoring the process variance. The ARL of combined schemes like combined Shewhart mean and Shewhart variance control charts, combined CUSUM mean and Shewhart variance control charts and, combined EWM mean and Shewhart variance control charts are compared. Recommendations on the choice of combined schemes for joint monitoring of the process mean and process variance are proposed.