Periodical preventive maintenance contract for leased equipment with random failure penalties

•The periodical preventive maintenance strategies under uncertain business environment is investigated.•Introduce the concept of real option theory to construct preventive maintenance strategies.•The penalty function in expected total cost model is evaluated using Black-Scholes equation.•An algorithm for finding the optimal periodical preventive maintenance strategies is obtained.

Production decisions for leased equipment often depend on many market factors. In this study, we take the penalty of changing market environment into account for the expected total cost model of preventive maintenance (PM) to obtain an optimization PM strategy. The lessor in the proposed model will incur a penalty for overdue minimal repair time. The penalty is considered as a function of expected revenue during the period of minimal repair, and the Black-Scholes equation is used to model the penalty function for establishing the expected total cost model. An optimal PM strategy is obtained to minimize the expected total cost for lessor through an analytical optimal procedure. Numerical examples for Weibull lifetime equipment are used to illustrate the applications of the proposed method under different scenarios.