Directional monitoring and diagnosis for covariance matrices

Statistical surveillance for covariance matrices has attracted increasing attention recently. Many approaches have been developed for monitoring general shifts that are arbitrary deviations, as well as sparse shifts occurring in only a few elements. This paper considers directional shifts that occur in only one independent parameter, which is common if the process is relatively stable. A directional covariance matrix control chart is proposed, which fully exploits directional shift information and borrows the strong power of likelihood ratio test. Therefore, this chart provides a powerful tool for monitoring covariance matrices. In addition, the proposed chart does not require specifying the regularisation parameter, and it enjoys a concise quadratic form, thereby easy to implement. Furthermore, this chart naturally leads to a diagnostic prescription for identifying the shifting element in the covariance matrix. Simulation results have demonstrated the efficiency of the suggested control chart and its accompanying diagnostic scheme.