Scheduling optimal replacement policies for a stochastically deteriorating system subject to two types of shocks

This paper is aimed at scheduling optimal preventive replacement policies for a single unit system which is subject to stochastic deterioration and concurrently suffers from external shocks. Different from existing literature, two types of shocks are taken into account according to the effectiveness upon arrival of a random shock, in which Type Ⅰ shock is a non-fatal one increasing the damage magnitude on current degradation amount and Type Ⅱ shock is a fatal one resulting in system catastrophic failure immediately. System survival function is investigated numerically based on the degradation-threshold-shock (DTS) modelling framework, and subsequently, two categories of bivariate maintenance policies are scheduled from different perspectives. The optimal solutions for both policies are derived analytically, and the relative gain on the optimal average maintenance cost rate is incorporated to determine which policy is more profitable. An illustrative example is provided to validate the theoretical results.