Optimal threshold value of failure-rate for leased products with preventive maintenance actions

This paper investigates the optimal threshold value of failure rates for leased products with a Weibull lifetime distribution. Within a lease period, any product failure is rectified by minimal repairs and the lessor may incur a penalty when the time required to perform a minimal repair exceeds a reasonable time limit. To reduce product failures, additional preventive maintenance actions are carried out when the failure rate reaches a threshold value. Under this maintenance scheme, a mathematical model of the expected total cost is established. Based on the model, the optimal threshold value and the corresponding maintenance degrees are derived such that the expected total cost is minimized. The structural properties of the optimal policy are investigated and an efficient algorithm is provided to search for the optimal policy. Finally, numerical examples are given to illustrate the features of the optimal policy.