Performance comparison of some likelihood ratio-based statistical surveillance methods

Using Markov chain representations, we evaluate and compare the performance of cumulative sum (CUSUM) and Shiryayev–Roberts methods in terms of the zero- and steady-state average run length and worst-case signal resistance measures. We also calculate the signal resistance values from the worst- to the best-case scenarios for both the methods. Our results support the recommendation that Shewhart limits be used with CUSUM and Shiryayev–Roberts methods, especially for low values of the size of the shift in the process mean for which the methods are designed to detect optimally.