Reliability and maintenance analysis of a degradation-threshold-shock model for a system in a dynamic environment

In this paper, a degradation-threshold-shock model for a system in a dynamic environment is studied. Unlike most existing works assuming the independence between different failure mechanisms, this study considers a two-fold stochastic dependence between the degradation process and the shock arrival process. First, the evolutions of the two processes depend on the changing environment; secondly, shocks may trigger the system failure or increase the degradation level alternatively. The degradation is generally described by a monotone Stochastic process. Upon periodical inspection, the system is preventively replaced whenever its degradation level exceeds a pre-determined threshold or failure occurs. Under this policy, the reliability measures, the maintenance costs in the short-run and long-run, and the optimization of the maintenance cost with respect to the decision parameters: the preventive maintenance threshold and the inspection period are investigated. Theoretical results are presented and numerical examples are given to illustrate the applicability of the proposed model.