Optimal Replacement Policy Based on Cumulative Damage for a Two-Unit System

This article studies a two-unit system with failure interactions. The system is subject to two types of shocks (I and II). A type I shock, removed by a minimal repair, causes a minor failure of unit A and type II shock causes a complete system failure that calls for a corrective replacement. Each unit A minor failure also results in a random amount of damage to unit B and such a damage to unit B can be accumulated to trigger a preventive replacement or a corrective replacement action. Besides, unit B with cumulative damage of level z may become minor failed with probability π(Z) at each unit A minor failure and fixed by a minimal repair. This paper proposes a more general replacement policy which prescribes that a system is preventively replaced at the Nth type I shock, or the time which the total damage to unit B exceeds a pre-specified level Z (but less than the failure level K where K>Z) or is replaced correctively either at the first type II shock or when the total damage to unit B exceeds a failure level K, whichever occurs first.