Optimization of replacement policy for a one-component system subject to Poisson shocks

In reliability engineering, system failures may occur due to intrinsic or extrinsic factors. For example, drinking water systems may fail due to ageing and deterioration (i.e., intrinsic factors) or flooding (i.e., extrinsic factors). An interesting question is: for such systems, how should preventive maintenance be scheduled? This paper investigates this question. The paper develops a maintenance policy for repairable systems subject to extrinsic shocks. It assumes that a system may fail due to either intrinsic factors or extrinsic factors. Reliability indexes and the expected long run cost rate are then derived. A numerical example is given to illustrate the theoretical results