Optimal maintenance policy for a three-unit system considering production and demand rates

Effective preventive maintenance (PM) planning of systems should depend on the production and demand requirements. However, PM actions are usually performed independently, not taking into account these requirements. In this paper, we develop a new maintenance model for a three-unit system considering production and demand rates. The system consists of three identical, independent units. Deterioration process of each unit is described by a three-state continuous time Markov chain with two working states and a failure state, that are observable by inspection. Demand rate is constant and average production rate is the same for both working states. Economic dependency exists among the systems' units because of the high cost of sending maintenance crew to the field, therefore group maintenance of several units can be cost effective. If the production rate of the system at an inspection time is below a critical level, maintenance crew is sent to do maintenance on failed units. Our objective is to find the maintenance policy minimizing the long run expected average cost per unit time. The problem is formulated and solved in the semi-Markov decision process (SMDP) framework. Numerical example is developed to demonstrate the proposed model.