Optimal periodic preventive maintenance policies for systems subject to shocks

•A maintenance model based on the shot-noise process is studied.•The failure rate increments caused by shocks needn’t be identically distributed.•Periodical PM policy is adopted for the system subject to shocks.•Expression of the long-run average cost rate is derived explicitly.•Existence and uniqueness of the optimal PM policy are proved theoretically. External shock process, known as the shot-noise process, will lead to the failure rate increasing of systems operating under random environment. In this paper, assuming that each shock may cause a random increment of the system failure rate, the optimal periodic preventive maintenance (PM) policy for the system is investigated. The system is preventively maintained at periodic time points nT,n=1,2,…,N−1, and is preventively replaced at time point NT. The PM is not perfect, however, it can remove the accumulated failure rate increments caused by external shocks occurred during the last PM interval. When the system fails during the PM intervals, a minimal repair is performed to restore the function of the system. The expression of the average cost rate of the system is derived explicitly. The existence and uniqueness of the optimal bivariate PM policy (N,T) that minimizes the average cost rate are proved theoretically. Numerical examples are presented to illustrate the maintenance model and show the effectiveness of the proposed method.