An adaptive Shiryaev‐Roberts procedure for monitoring dispersion

In this paper, the Shiryaev‐Roberts (SR) procedure is examined and compared with the change point CUSUM (CPC) procedure for monitoring the dispersion of a normal process. It will be shown that the SR chart performs better than the CPC chart for the pre‐specified dispersion shift. In practice, when the magnitude of a future dispersion shift is unknown, it is always desired to design a control chart to perform reasonably well over a range of shifts rather than to optimize the performance at detecting a particular level of shifts. Compared with SR based on a pre‐specified dispersion shift, an adaptive SR (ASR) chart that continually adjusts its form to be efficient for signaling a smoothing exponentially weighted moving average (EWMA) statistic in deviation from its target value is proposed in this paper. It can be easily implemented and numerical results show that it balances protection against a broad range of shift sizes.