Optimal hybrid imperfect preventive maintenance policy for leased equipment

Abstract

This paper presents a mathematical model for a sequential hybrid imperfect preventive maintenance (PM) policy for leased equipment over a finite lease period in a context where PM actions are imperfect and minimal repairs are performed following failures. Maintenance is entrusted to the lessor. The latter incurs a penalty if the number of failures exceeds a specified threshold over the lease period. Imperfect PM is executed whenever the equipment reliability reaches a certain threshold. It simultaneously reduces the effective age and increases the failure rate of the equipment. The proposed model allows finding the number n of PM actions to be performed on the equipment together with the reliability threshold Rth minimizing the expected total cost over the lease period. And therefore obtain the optimal PM intervals durations Tj*(j* = 1, 2, …, n) corresponding to the optimal reliability threshold. The model considers the expected costs of PM, repairs and penalty during the lease period. A numerical example is presented to illustrate the use of the proposed model. The optimal PM strategy is computed for a leased equipment whose time to failure follows a Weibull distribution. We investigate numerically the effect of the variation of the PM action cost and the age reduction factor on the optimal policy.