Optimal maintenance policies for deteriorating systems.

Abstract

In this thesis, continuous time multi-state Markovian and Semi-Markovian maintenance models are developed for systems which are continuously deteriorating and subject to random shocks. The cost and time parameters of these models are the operating cost, inspection cost, replacement cost, downtime cost, inspection time, replacement time, and the sojourn time in each state. The objective is to obtain optimal maintenance policies such that the expected long run cost rate is minimized. Two classes of maintenance strategies--replacement strategies and inspection and replacement strategies are investigated, depending upon the type of monitoring device available. With continuous monitoring, the current state of a system is always known and the maintenance problem is simply to determine a replacement policy. Four replacement strategies are considered--failure, age-dependent, state-dependent, and state-age-dependent replacement strategies. Without continuous monitoring, it is assumed that the current state of a system is known only through inspection and the maintenance problem becomes to determine both inspection and replacement policies simultaneously. Three inspection and replacement strategies are considered--age, periodic, and sequential inspection and replacement strategies. Under various maintenance strategies, efficient algorithms are developed to derive optimal maintenance policies for both Markovian and Semi-Markovian deteriorating systems. In particular, the phase-type approximation to a general sojourn time distribution is introduced to analyze Semi-Markovian deteriorating systems. Under this approximation, a Semi-Markovian deteriorating system is modeled by a multi-phase Markovian model and the optimal inspection and replacement policies can be easily obtained by iterative algorithms. The structures of both optimal replacement and optimal inspection and replacement policies are investigated in detail. Under some sufficient conditions, it is shown that these optimal policies have monotonic properties. The control-limit-type rule holds for replacement and the time period between successive inspections decreases as a system deteriorates. Furthermore, numerical examples and simulation results are given to demonstrate the structures and to compare the performances of these optimal policies.