A robust multivariate sign control chart for detecting shifts in covariance matrix under the elliptical directions distributions. Issue 1 (2nd January 2019) - Liang, Wenjuan; Xiang, Dongdong; Pu, Xiaolong; Li, Yan; Jin, Lingzhu
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.