Optimal Sampling and Maintenance Policy for a Partially Observable System Subject to Random Failure

摘要

Stochastic control problems that arise in reliability and maintenance typically assume that information used for decision making is obtained according to a pre-determined sampling schedule. In many real applications however, observable data can only be obtained at a high sampling cost, so a decision maker must dynamically determine when information should be collected as well as when full preventive maintenance should be carried out. This type of joint optimization is a well known problem in maintenance optimization and operations research. Although many researchers have proposed a variety of heuristic policies, little progress has been made to characterize the form of the optimal sampling and maintenance policy. In this paper, we formulate and analyze the joint optimization problem in the partially observable Markov decision process (POMDP) framework. Using recent advancements in the area of POMDPs, we establish the optimality of a policy that is characterized by three critical thresholds, which have practical and intuitive interpretation. A numerical example is developed, which illustrates the benefits of the joint optimization of sampling and maintenance.