A Study on the Performances of Multivariate Exponentially Weighted Moving Average (MEWMA) and Multivariate Synthetic Charts

A multivariate control chart is a common tool used for monitoring and controlling a process whose quality is determined by several related variables. The objective of this study is to compare the performances of the multivariate exponentially weighted moving average (MEWMA) and the multivariate synthetic T² control charts, for the case of a multivariate normally distributed process. A comparative study is made based on the average run length (ARL) performances of the control charts, using the simulation method, in order to identify the chart having the best performance in monitoring the process mean vector. The performances of the two charts, for different sample sizes and correlation coefficients, are presented in this paper. It was found that the MEWMA chart outperformed synthetic T² chart for small shifts but the latter prevailed for moderate shifts. Both charts performed equally well for larger shifts. In addition, the performances of both MEWMA and synthetic T² charts were found to be influenced by sample size and correlation coefficient. The two charts’ performances improved as the sample size and correlation coefficient increased for small and moderate shifts, but the charts’ performances did not depend on sample size and correlation coefficient when the shift was large.