A study on the effects of skewed distributions on the performances of Max-EWMA and Max-GWMA charts

Abstract

The Max-GWMA (called the Maximum Generally Weighted Moving Average) chart is comparable to the Max-EWMA (called the Maximum Exponentially Weighted Moving Average) chart for simultaneously monitoring the process mean and/or variability. These charts require fulfilling the usual assumption in Statistical Process Control (SPC), i.e., the distribution of the process is normal or approximately normal. The main objective of this study is to conduct a comparative study of the perfor- mances of the single Max-GWMA and Max-EWMA charts, for skewed populations. A Monte Carlo simulation is conducted using the Statistical Analysis Software (SAS) to study and compare the Average Run Length (ARL) performances for various magnitudes of mean and/or variance shifts for different levels of skewnesses. The skewed distributions considered are the log- normal and gamma distributions. Overall, the results show that the Max-GWMA chart has lower false alarm rates (or similarly, higher in-control ARLs) for more levels of skewnesses, compared to the Max-EWMA chart.