Optimal control-limit strategies for a partially observed replacement problem†

In this paper, we consider the problem of determining an optimal replacement strategy for a system subject to Markov deterioration, where replacement decisions can only be made on the basis of noise-corrupted observations of the system state. Three conditions are presented which guarantee that for the general case search for an optimal replacement strategy can be limited to control-limit strategies. Two of these conditions, both straightforward generalizations of assumptions due to Derman, are sufficient for the existence of control-limit strategies for the completely observed (Derman's result) and the completely unobserved (a new result) cases. The third condition is new and is concerned with the quality of data that the decision maker receives regarding the system state. Simplified assumptions which imply that this latter condition holds are also presented.