Modeling the dependent competing risks with degradation processes and random shock under warranty

In this paper we consider a condition-based maintenance strategy for systems subject to two dependent causes of a failure, degradation and random shocks and develop a degradation threshold shock model considering repair service, replacement service and a preventive maintenance action under warranty. When the degradiation level exceeds pre-determined values, it indicates that a degradation failure occurs and repair, replacement or/and preventive maintenance actions are provided for failed products. We investigate the relationships between random shock and degradation modeled by a time-scaled covariate factor as well as the relationships between degradation processes, considering fatal shocks that require immediate replacement service and nonfatal shocks that just need repair for failed parts. For the degradation threshold shock model, we consider degradation to the threshold for repair and also to the threshold for replacement, but we also consider not only degradation but also random shocks as decision variables. We minimize the expected cost of total system to determine an optimal warranty length for the warranty cost analysis.