Statistical Engineering Division
Seminar Series

Alexandra (Aleka) Kapatou
Department of Statistics
University of Michigan

A multivariate control chart can be used to simultaneously monitor the means of two or more correlated variables of a process. Most parametric control charts for process monitoring are based on the assumption that the data follow a multivariate normal distribution. If this assumption cannot be made, a multivariate control chart based on classical nonparametric statistics could be used. The control charts that we propose are based on the vector sign and vector signed-rank statistics. Past sample information for each variable is retained through an exponentially weighted moving average (EWMA) statistic in order to increase the sensitivity of the charts to detect small shifts from the target. It is assumed that the target values for the means and certain correlations (or proportions) for the variables can be estimated well at the beginning of the process. The properties of the proposed charts are evaluated using simulation. The proposed charts are compared with the multivariate EWMA (MEWMA) chart based on the sample means. We show that the charts based on the sign and signed-rank statistics are not only more robust but also more efficient for data that have heavy tail distributions.