ABSTRACT
This chapter introduces a non-homogeneous continuous time Markov chain to describe the system evolution when external shocks arrive in a non-homogeneous Poisson process. It investigates the reliability of multi-state systems subject to non-homogeneous Poisson shock, design an age replacement first maintenance mechanism after reliability evaluation and compare which is better and more economic concerning replacing the component at a planned time T (policy T), or at the Nth working cycles (policy N), or at failure, whichever comes first. As a preventive replacement maintenance policy, policy T or policy N decreases the long-run maintenance cost rate than replacement at failure because the replacement cost at failure is rather higher. Maintenance policies are arranged to improve the reliability and to reduce the catastrophic fault. In general, maintenance is categorized into three types: preventive maintenance, corrective maintenance, and condition-based maintenance.
