Extended periodic imperfect preventive maintenance model of a system subjected to shocks

This article deals with a periodic imperfect preventive maintenance (PM) model of a system subjected to random shocks. A system is subject to shocks that arrive according to a non-homogeneous Poisson process. As shocks occur, the system experiences one of the two types of failures: type-I failure (minor) and type-II failure (catastrophic). Type-I failures are rectified by minimal repair. The system is maintained following the occurrence of a type-II failure or at age T, whichever takes place first. At the N-th PM, the system is replaced. An approach that generalises the existing works on the periodic imperfect PM policy is proposed. The imperfect PM model adopted is hybrid in the sense that it not only reduces the effective age of the system but also alters the system hazard rate. Taking random minimal repair costs into consideration, the objective consists of finding the optimal PM and replacement schedules that minimise the expected cost per unit time over an infinite time-horizon.