Optimum Maintenance with Incomplete Information

The maintenance of a system characterized by a discrete-parameter, non-stationary, finite-state Markov process is considered. Prior to each transition the decision maker selects one of a finite number of available actions (replacements, repairs, inspections, etc.) on the basis of a time sequence of noisy state measurements. The action selected and the system's age determine the subsequent one-step transition probabilities and the conditional (on the system states) distributions of the next measurement. Costs dependent on the action selected, the system's state, and age are assigned to each possible transition. It is shown that the action that minimizes the discounted value of expected immediate and future costs (assuming optimum future actions) is determined by the system's age and the posterior distribution over the states. With this result a dynamic-programming method is presented for the calculation of optimum maintenance policies.