A robust multivariate sign control chart for detecting shifts in covariance matrix under the elliptical directions distributions

Abstract

Most existing control charts monitoring the covariance matrix of multiple variables were restricted to multivariate normal distribution. When the process distribution is non-normal, the performance of these control charts could potentially be (highly) affected, especially for heavy-tail distributions. To construct a robust multivariate control chart for monitoring the covariance matrix, we applied spatial sign covariance matrix and maximum norm to the exponentially weighted moving average (EWMA) scheme and proposed a Phase II control chart. The novel chart is distribution-free under the family of elliptical directions distributions. Comparison studies demonstrate that the novel method is very powerful in detecting various shifts, especially for heavy-tailed distributions. The implementation of the proposed control chart is demonstrated by a white wine data.