Control Chart for Monitoring Processes With Recurrent Shifts

Control charts are widely used for sequential monitoring, but most existing methods are designed to detect only the first distributional shift because they were originally developed for manufacturing processes that are stopped after an out‐of‐control (OC) signal. In many real‐world applications, however, such as economic monitoring, environmental surveillance, and disease surveillance, the monitored process continues to operate and may repeatedly alternate between in‐control (IC) and OC states. This paper investigates online monitoring of such sequential processes with recurrent shifts (SPRS), where timely detection of both the onset and the termination of OC periods is essential for initiating and terminating interventions efficiently. We introduce new concepts and propose a general online monitoring framework for SPRS. For clarity, the methodology is presented for serially independent univariate normal observations, although the framework can be extended to more general settings. The proposed approach provides a foundation for sequential monitoring of processes exhibiting recurrent distributional shifts.