Optimal replacement of systems subject to shocks and random threshold failure

The purpose of this paper is to generalize Yeh and Zhang's 2004 random threshold failure model for deteriorating systems.

An N‐policy was adopted by which the system was replaced after the Nth failure.

The model was found to have practical applications in warranty cost analysis.

By identifying the instance of a shock as the failure of the system and the threshold times as the warranty period offered and changing the definition of lethal shock (system failure in this case) as the occurrence of a shock within a threshold period in our generalized model, one can study the renewing warranty cost analysis.