| This research focuses on making maintenance and replacement decisions for deteriorating systems using probabilistic monitoring. The goal is to characterize the structure of optimal policies to assist the decision maker in selecting maintenance and replacement actions over a finite or infinite horizon. For the finite horizon, the optimal policy minimizes the total expected cost. For the infinite horizon, the optimal policy minimizes the expected cost per unit time. To obtain these policies, we model this process as a partially observed Markov decision process. We solve the problem of detecting change in the context of machine monitoring when: (1) the process can operate in either good, worn or failed states and (2) observations are related probabilistically to the state of the process. When imperfect information is available about the state of the process, a probability threshold rule, similar to one found to be optimal for a two-state (good or failed) model, may not be optimal.; We prove that the optimal policy has a certain property called a monotonic structure. This allows us to represent the optimal policy by a collection of threshold-like decision rules. Some of these structural results are extended to an N-state process. |
