Abstract: This paper presents the asymptotic expressions of the average run length (ARL) for the cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) control charts in detecting an unknown mean shift in a stationary linear process. Based on the ARL expressions, we compare the detection performance of the two popular charts in monitoring the mean shifts in such autocorrelated processes. Both theoretical analysis and numerical simulation results show that auto-covariance can play an important role in the detection performance of the two charts.
Key words and phrases: Autocorrelated stationary processes, average run length, change point detection.