A generalized maintenance model for stochastically deteriorating equipment

the objective of this paper is to develop a generalized maintenance model in a stochastic environment. The basic model of our study focuses on a production system which deteriorates stochastically over time, leading to a lower productivity and smaller income rates. At any time, a repair action can be carried out in order to restore the system to an improved state. The cost associated with a repair action depends on the state of the system on one hand and the degree of repair on the other hand. In contrast to the classical models in the literature, we consider maintenance strategies in which the degree of repair is a decision variable determined endogeneously. Our objective in this paper is to characterize the structure of optimal repair policies under the discounted net return optimality criterion over an infinite planning horizon. The results for the discounted case are carried over to the long-run average case. Throughout the analysis various assumptions regarding the repair cost function are considered. In the final part of the paper we develop an algorithmic procedure for the optimal policy in the undiscounted case under a special cost function.