Multivariate Monitoring Using an MEWMA Control Chart with Unequal Sample Sizes

When multivariate control charts are used to monitor a process, it is usually assumed that the same sample size is used for each variable. In this paper, we investigate the MEWMA control chart for monitoring the process mean vector when the sample sizes are unequal. Unequal sample sizes may arise because of sampling constraints or because the sample sizes of some variables are increased to provide more information about variables that are considered to be more important than other variables. Here we focus on the situation in which one variable is considered to be more important than the other variables, so that the sample size for this variable is increased and the sample sizes of the other variables are decreased. When the correlation between the variables is not high, increasing the sample size of the important variable improves the ability to detect shifts in this variable. However, the ability to detect shifts in the other variables is decreased. We compare the approach of using unequal sample sizes with the approach of using control charts that are designed to be sensitive to the specific shift direction of interest. We also investigate the use of unequal sample sizes along with control charts designed to be sensitive to the shift direction of interest.