Design of the Side Sensitive Group Runs Chart with Estimated Parameters Based on Expected Average Run Length

The assumption when constructing a control chart is that the process parameters, i.e. mean and standard deviation, are known. Nevertheless, this assumption is not realistic in practical situations. In most of the application of a control chart, the mean and standard deviation are unknown and are estimated from an in-control Phase-I samples. When the process parameters are estimated, the control chart performs differently compared with the corresponding chart with known process parameters because of the variability of estimators. The usual practice to evaluate the performance of a control chart is to use the average run length (ARL). The ARL is the average number of samples plotted on a control chart before an out-of-control signal is detected. In addition, the expected ARL (EARL) is used as a performance measure for the random process mean shift. In this article, the performance of the side sensitive group runs (SSGR) chart with known and estimated process parameters are studied and examined in terms of ARL and EARL.