Optimal Maintenance Problems for Markovian Deteriorating Systems

This chapter deals with optimal maintenance problems for Markovian deteriorating systems. The function of the system deteriorates with time, and the grade of deterioration is classified as one of s+2 discrete states, 0, 1,..., s,s+1, in the order of increasing deterioration. State 0 is a good state, i.e., the system is like new, the states 1,..., s are deterioration states and the state s+ 1 is a failure state. In a normal operation, these states are assumed to constitute a discrete or continuous time Markovian process with an absorbing state s+ 1. In Section 8.1, we first introduce a basic replacement problem for a discrete time Markovian deteriorating system. In Section 8.2, we discuss an optimal inspection and replacement problem for the system in Section 8.1. In Section 8.3, we consider an optimal inspection and replacement problem under incomplete system observation. In Section 8.4, we treat a continuous time Markovian deteriorating system and discuss an optimal inspection and replacement problem. In Section 8.5, we deal with a maintenance problem in queueing system and discuss an optimal maintenance policy based on both the queue length and the server state.