A Comparison on the MRL Performances of Optimal MEWMA and Optimal MCUSUM Control Charts

Abstract

The MEWMA (called the multivariate exponentially weighted moving average) chart and the MCUSUM (called the multivariate cumulative sum) chart are used in process monitoring when a quick detection of small or moderate shifts in the mean vector is desired. The primary objective of this study is to compare the performances of the optimal MEWMA and optimal MCUSUM charts based on their median run length (MRL) profiles. The number of quality characteristics considered is p = 2. Two cases are studied, i.e., Case 1 (a shift in only one variable) and Case 2 (a shift in two variables). A Monte Carlo simulation is conducted using Statistical Analysis Software (SAS) to study and compare the MRL performances for various magnitudes of mean shifts when the process is normally distributed. Overall, the results show that the MRL performances of the MEWMA and MCUSUM charts are comparable.