A comparison between the standard deviation of the run length SDRL) performance of optimal EWMA and optimal cusum charts

Abstract

The Exponentially Weighted Moving Average (EWMA) and Cumulative Sum (CUSUM) control charts are very effective in detecting small shifts in the process mean or variance. The average run length (ARL) has always been used as a sole measure of the performances of control charts. Generally, the performances of the EWMA and CUSUM charts are comparable and most comparative studies are based on the ARL. Therefore, this study is aimed at comparing the performances of the optimal EWMA and optimal CUSUM charts, based on their standard deviation of the run lengths (SDRLs). The Statistical Analysis System (SAS) software version 9.1.3 is used to conduct the simulation studies, for the optimal EWMA and optimal CUSUM charts. The SDRL results show that the optimal EWMA chart is slightly superior to the optimal CUSUM chart, when the process is out-of-control. However, when the process is in-control, the converse is true.