A Study on the Effects of Non-Normality on the Performances of Max-DEWMA Versus SS-DEWMA Charts

Abstract

Problem statement: The called the Sum of Squares Double Exponentially Weighted Moving Average (SS-DEWMA) chart which is effective in detecting shifts in the mean and/or variance is compared with the Max-DEWMA (called the maximum double exponentially weighted moving average) chart. The comparison is based on the assumption that the distribution of the quality characteristic of the process is normal or approximately normally distributed. In many real world situations, this assumption may be violated. This study compares the effects of various forms of non-normality on the Max-DEWMA and SS-DEWMA control charts. Approach: A Monte Carlo simulation using the Statistical Analysis Software (SAS) is conducted to compare the performances of the two charts for the case of skewed distributions, such as the Weibull, lognormal and gamma distributions. Results: The overall results show that the Max-DEWMA chart has in-control Average Run Lengths (ARLs) closer to the specified value, as compared to that of the SS-DEWMA chart, for all levels of skewnesses considered. Conclusion/Recommendation: Practitioners are advised to use the Max-DEWMA chart for a joint monitoring of the process mean and/or variance, when the underlying distribution is non-normal.