Sequential common change detection, isolation, and estimation in multiple poisson processes

In this article, motivated by detecting the occurrence of an epidemic when the arrival rates of patients increase in a portion of M panels or detecting the deterioration of a system composed of M independent components that causes an increase in failure rates in a portion of components, we consider the detection of a common change when M independent Poisson processes are monitored simultaneously where only a portion of the processes have rate increases after the change time. M individual cumulative sum (CUSUM) processes and Shiryaev-Roberts (S-R) processes are calculated recursively in parallel at each pooled arrival time. A systematic procedure is proposed by using the sum of M S-R processes as the detection process for a common change. After the detection, the M individual CUSUM processes are used to isolate the changed panels with false discovery rate (FDR) control and then the medians of the change time estimates from each individual CUSUM process or S-R process based on the isolated panels are used to estimate the common change time. The model can be generalized to different prechange rates, jittered change time, and unknown postchange rates.