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.

协方差矩阵的统计监测最近引起了越来越多的关注。已经开发了许多方法来监测任意偏差的一般变化，以及仅发生在少数元素中的稀疏变化。本文考虑仅在一个独立参数中发生的方向变化，如果过程相对稳定，这种情况很常见。提出了一种方向协方差矩阵控制图，充分利用了方向平移信息，并借用了似然比检验的强大威力。因此，该图表提供了监控协方差矩阵的强大工具。此外，所提出的图不需要指定正则化参数，并且具有简洁的二次形式，因此易于实现。此外，该图表自然会得出用于识别协方差矩阵中的移位元素的诊断处方。仿真结果证明了所建议的控制图及其伴随的诊断方案的有效性。