Optimal corrective maintenance policy for a multi-unit production system considering demand satisfaction

In this paper, we propose a maintenance policy for a multi-unit production system considering external demand satisfaction with given probability. We consider a system composed of N identical units, where each unit deteriorates independently. The deterioration process of units can be monitored through system inspection. Deterioration process of each unit is modeled as a three-state continuous time homogeneous Markov chain with two working states and a failure state. The production rate of each unit decreases as the unit deteriorates. At each inspection time, a decision is made to perform corrective system maintenance or to continue operation. The objective is to determine the optimal maintenance policy minimizing the long run expected average cost per unit time subject to a demand satisfaction constraint. The problem is formulated and solved in the semi-Markov decision process (SMDP) framework. An effective algorithm is developed to obtain the optimal policy considering demand satisfaction with a given probability. A numerical example is presented to demonstrate the proposed policy. The optimal policy shows monotonicity property for the decision making