The optimal preventive-maintenance policy for a NHPBP repairable system under free-repair warranty

Abstract This investigation focuses on deriving an optimal preventive maintenance (PM) scheme for a system under the free-repair warranty (FRW). We utilize a Non-Homogeneous Pure Birth Process (NHPBP) to model the process of more general failures and repairs during the coverage period of FRW, propose a type of PM model for such a NHPBP repairable system, and develop the expected cost function. Under the special case of failure intensity, we first prove that there exists a unique optimal PM schedule for FRW with a finite number of PMs and then compute the optimal number of PMs and their implementation times for a given FRW coverage period. Numerical computation and sensitivity analysis are conducted to gain more insights about the NHPBP repairable system under FRW with and without PMs. Our results offer an important analytical tool for marketing managers to design more competitive and cost minimal warranty policies for durable and complex systems with a more general failure process and ‘worse-than-minimal repair’.