An Adaptive CUSUM Chart For Monitoring The Process Dispersion

The cumulative sum (CUSUM) chart for dispersion parameter in a normal process has an ARL performance that is superior to other procedures when the magnitude of shifts are correctly specified. In practical applications where the magnitudes of shifts are rarely known, 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 shift. Compared with the CUSUM chart based on a pre-specified dispersion shift, an adaptive CUSUM 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.