Sequential common rate decrease detection, isolation, and estimation in multiple Poisson processes

Abstract

ABSTRACT 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 decrease after the change time. In contrast to the detection of rate increase (Wu and Wu (2022)), the individual CUSUM and Shiryayev–Roberts (S–R) processes need to be calculated continuously in parallel. A combined CUSUM-SR procedure is proposed by using the sum of S–R processes as the detection process for a common change and after the detection, the M individual CUSUM processes are used to isolate the changed panels with FDR control. The medians of change time estimates from the individual CUSUM or S–R processes from the isolated changed panels are then used to estimate the common change time. Coal mining disaster data in USA are used for illustration.