In multivariate statistical process control it is generally assumed that the process variables follow a multivariate normal distribution with mean vector " and covariance matrix •, but this is rarely satisfied in practice. Some robust control charts have been developed to monitor the mean and variance of univariate processes, or the mean vector " of multivariate processes, but the development of robust multivariate charts for monitoring • has not been adequately addressed. The control charts that are most affected by departures from normality are actually the charts for • not the charts for ". In this article, the robust design of several MEWMA-type control charts for monitoring • is investigated. In particular, the robustness and efficiency of different MEWMA-type control charts are compared for the in-control and out-of-control cases over a variety of multivariate distributions. Additionally, the total extra quadratic loss is proposed to evaluate the overall performance of control charts for multivariate processes. / Ph. D.