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.