Study of the median run length (MRL) performance of the EWMA t chart for the mean

Abstract

The exponentially weighted moving average (EWMA) X chart is effective in detecting small shifts. However, the EWMA X chart is not robust enough to prevent errors in estimating the process standard deviation or a changing standard deviation. To overcome this problem, Zhang et al. suggested the EWMA t chart in 2009. The existing optimal design of the EWMA t chart is based on the average run length (ARL) criterion. This paper proposes that the optimal design of the EWMA t chart be based on the median run length (MRL). The MRL performances of the optimal EWMA X and optimal EWMA t charts are compared.