Designing optimal proactive replacement strategies for degraded systems subject to two types of external shocks

This paper mainly investigates a proactive replacement policy for a stochastically deteriorating system concurrently subject to two types of shocks. Firstly, the closed form representation of system reliability function suffering from both a degradation process and environmental shocks is derived based on the degradation-threshold failure (DTS) modelling framework. An age- and state-dependent competing risks model with mutual dependence between the two failure processes is embedded into system reliability modelling, where two types of shocks are taken into consideration upon arrival of an external shock including a minor one and a major one. Based on which, a bivariate maintenance policy is put forward for the deteriorating system, where the system is proactively replaced before failure at a planned time, or at an appropriate number of minimal repairs, whichever takes place first. The expected long-run cost rate (ELRCR) is formulated, and optimal solutions are evaluated analytically for two special cases. Finally, an illustrative example is redesigned to validate the theoretical results, exploring the significance of two types of shocks and mutual dependence in system reliability modelling, and illustrating the potential applications in maintenance decisions in various manufacturing systems.