Optimal Age Policy for a Used System with Imperfect Preventive Maintenance and Cumulative Damage Model

In this article, the concept of imperfect preventive maintenance is discussed and an age maintenance policy is developed based on the cumulative damage model for a used system with initial variable damage. The deterioration of the system is assumed to suffer the non-homogeneous Poisson shocks which can be divided into two types with stochastic probability: Type-I shock (minor) yields a random amount of additive damage of the system, or Type-II shock (catastrophic) causes the system to fail. An age preventive maintenance policy T is presented in which the system undergoes preventive maintenance at a scheduled lifetime T, or corrective maintenance at first Type-II shock and the total damage exceeds a threshold level, whichever occurs first. The objective is to determine the optimal preventive maintenance schedule such that the expected cost rate is minimized. The optimal solution is derived analytically and discussed numerically.