Optimal imperfect maintenance strategy for leased equipment

This paper presents a preventive maintenance (PM) policy for leased equipment over a finite lease period L. Maintenance is entrusted to the lessor. The purpose is to determine the PM period T minimizing the expected total cost over the lease period in a context where repairs and PM actions are imperfect and have non-negligible durations. The leased equipment is periodically subjected to imperfect PM restoring it to the state 'as good as new' with probability p and keeping it at state 'as bad as old' with probability q. In case of failures between successive PM actions, imperfect repairs are performed with a given efficiency following a decreasing quasi-renewal process. Besides the maintenance costs, the lessor may incur a penalty cost if the total expected equipment downtime due to repair and PM during the lease period exceeds a pre-specified threshold. A mathematical model and a numerical algorithm are developed to find the optimal maintenance strategy T* over the lease period for any given set of input parameters (equipment reliability, the lease period length, the repair and PM efficiency levels, and the maintenance and penalty costs). A numerical example is presented and the obtained results are discussed.