Optimal preventive maintenance for a two dimensional lease contract

In this paper, we study a two dimensional lease equipment contract with involving imperfect preventive maintenance. The two dimensional lease contract is characterized by two parameters - age and usage limits. The lessor performs both preventive and corrective maintenance and a penalty cost incurred to the lessor when the time required to perform a corrective maintenance exceeds a pre-specified target. Failures are influenced by the age and usage of the equipment and modelled by using a one dimensional approach. We consider that an imperfect preventive maintenance (PM) policy reduces the equipment failure rate and hence it will decrease the penalty cost and maintenance cost during the lease contract. We find the optimal PM interval, number of PM, PM degree (reduction in failure rate) minimizing the expected total cost.