State-dependent age replacement policy for a system subject to cascading failures

A cascading failure is a failure in a system of interconnected parts in which the failure of a part triggers the failure of successive parts. Although some initial and empirical studies for probabilistic modeling and analysis of the cascading failures have been performed in the literature, general modeling frameworks and relevant maintenance policies have been barely reported yet. However, in this article, based on a general framework for modeling cascading failures, we study the optimal preventive maintenance problem for the system. A new state-dependent age replacement policy is developed. The comparison with the ordinary age replacement policy is also discussed.