Maintenance policies in markovian deterioration models of parallel unit systems

Markovian deterioration models of parallel unit systems are dealt with. Units of a system are supposed to be of different types, and a state of the system is represented by a vector whose component corresponds to the state of each unit. Therefore all the states of the system are only partially ordered, while they are totally ordered in ordinary markovian deterioration models. It is proved under some conditions that the optimal maintenance policy is a partial control limit policy, which is a generalization of the well-known control limit policy in the ordinary case. An algorithm improving the successive approximation method is proposed for obtaining the optimal policy. A typical case of the model is also discussed.