Robustness to Non-Normality of the Multivariate EWMA Control Chart

We investigate the effects of non-normality on the statistical performance of the multivariate exponentially weighted moving average (MEWMA) control chart, and its special case, the Hotelling's chi-squared chart, when applied to individual observations to monitor the mean vector of a multivariate process variable. We show that the chi-squared chart is highly sensitive to non-normality. We argue that the performance is most sensitive to departures from multivariate normality with individual observations (subgroups of size one). We show that with individual observations, and therefore, by extension, with subgroups of any size, the MEWMA chart can be designed to be robust to non-normality and very effective at detecting process shifts of any size or direction, even for highly skewed and extremely heavy-tailed multivariate distributions.