Comparing the median run length (MRL) performances of the Max-EWMA and Max-DEWMA control charts for skewed distributions

The maximum double exponentially weighted moving average (Max-DEWMA) chart and the maximum exponentially weighted moving average (Max-EWMA) chart are applied to simultaneously monitor small and moderate shifts in the process mean and/or variability. The Max-DEWMA chart has lower Type I error rates compared to the Max-EWMA chart for all levels of skewnesses. Noting that the performances of both charts in the existing literature are based on average run length (ARL) measure. In this paper, the primary objective is to compare the performances of the two charts based on the median run length (MRL) measure. A Monte Carlo simulation was conducted using the Statistical Analysis Software (SAS) to study and compare the MRL performances for various magnitudes of process mean and/or variability shifts. The skewed distributions considered are the Weibull and gamma distributions. Overall, the results show that the Max-DEWMA chart has in-control MRLs which are closer to the specified value compared to that of the Max-EWMA chart, for all levels of skewnesses considered. Quality practitioners are recommended to apply the Max-DEWMA chart when the underlying distribution is skewed.