Real time control of partially observable deteriorating processes

We consider a deteriorating process under continuous time monitoring. The process starts in the in-control state and randomly shifts to the out-of-control state after an exponentially distributed time duration. The shift occurrence is not directly observable and can only be inferred from the monitoring signals, which are assumed to be generated by a Wiener process whose drift parameter shifts when the process goes out of control. Our objective is to develop the Bayesian control chart minimizing the long-run expected average cost of operating the process. We derive the integral equation from which the optimal control limit can be computed. The extension to a more complex system having multiple deteriorating processes is also examined. For such a system, we propose an effective approximation for the computation of near-optimal control limits. Numerical examples are provided to illustrate the methodology and to generate insights.