Reliability analysis of periodically inspected systems with competing risks under Markovian environments

Abstract

We develop a reliability and maintenance model for a periodically inspected system with competing risks subject to a randomly evolving operating environment, which is modeled as a continuous-time homogeneous absorbing Markov process. The natural wear rate and shock arrival rate are both modulated by Markovian environments. Specifically, three competing failure processes are considered. System failures may occur when an extremely harsh environment arrives, when the magnitude of a shock load exceeds a fixed value, or when the overall cumulative degradation caused jointly by the natural wear and abrupt additions due to shocks hits a preset threshold. Explicit formulas for reliability functions and first failure time moments of systems are derived. A Monte-Carlo simulation algorithm to obtain the first failure time of the system when shock arrivals are governed by non-homogenous Poisson processes is proposed. An optimal maintenance policy using periodic inspection is developed by minimizing the average long-run cost rate where the decision variable is the inspection interval. A case study of micro-engine systems is given to illustrate the developed reliability and maintenance model, which exhibits that an increased failure threshold value improves the system reliability and reduces the minimum average long-run cost rate.