Condition-based maintenance for a degradation-shock dependence system under warranty

In this paper, we derive a condition-based maintenance strategy for a degradation-shock dependence system subject to two causes of failure, degradation and random shocks. We develop a reliability model for a system under warranty for failure in which we consider the dependence between the degradation process and random shocks and do a warranty cost analysis based on the suggested model. We consider a degradation-shock dependence system that is under warranty with three separate services: repair, replacement, and preventive maintenance. These are triggered when a product degradation crosses one of three predetermined degradation thresholds. We also investigate the dependence between random shocks and degradation modelled by a time-scaled covariate factor. We study the random shock considering fatal shocks that require replacement and nonfatal shocks that require only repair and the degradation caused by nonfatal shocks. The condition-based maintenance strategy for a degradation-shock dependence system is a novel approach to analysing system degradation, with a goal of optimising warranty costs; we also minimise the expected total system cost to find an optimal warranty length. We present several numeric examples and real-world applications to illustrate our proposed approach.