An optimal control chart for finite matrix sequences at some unknown change point

We present a new measure for evaluating the performance of control charts to detect abrupt changes of finite matrix sequences. The objective is to minimize the probability that the control chart fails to raise the alarm at unknown change point time for a given in-control average run length. We construct and prove the optimal control chart with dynamic control limits in different pre- and post-change distributions. We validate the optimality of the proposed chart by conducting exhaustive experiments on both simulation study and real-world data.