Comparing the effects of skewed distributions on the S-chart and S² -EWMA chart based on the median run length criterion

The S²-EWMA (called the S square exponentially weighted moving average) control chart is effective in detecting small and moderate process variance shifts. Previously, the chart was designed based on the assumption that the distribution of the quality characteristic is normally distributed. This study designs the S²-EWMA control chart for skewed distributions. The skewed distributions considered in this paper are the lognormal and gamma distributions. The performance of the S²-EWMA control chart is compared with that of the traditional Shewhart S-chart, in terms of median run length (MRL), based on simulation using the Statistical Analysis System (SAS). The results show that regardless of the type of skewed distributions, sample size and skewness level, γ, in most of the cases, the S²-EWMA chart outperforms the S-chart. Moreover, the findings reveal that the MRL performances of the S-chart and S²-EWMA chart are significantly influenced by skewed distributions.