Multivariate exponentially weighted moving sample covariance control chart for monitoring covariance matrix

In this paper, a control chart is proposed to detect changes in the covariance matrix of a multivariate normal process, when sample size is one. The proposed chart statistic is constructed based on the exponentially weighted form of sample covariance matrix given by individual observation over time. Distance between the values of variance and covariance components in this multivariate exponentially weighted moving sample covariance matrix and, the in-control corresponding elements of process variance-covariance matrix provides a basis for process variability monitoring. The statistical performance of the proposed method is evaluated through the use of a Monte Carlo simulation. The results show the superiority of the proposed control chart performance especially in the case of incremental changes in covariance matrix.