Scheduling of imperfect inspections for reliability critical systems with shock-driven defects and delayed failures

The paper considers systems that perform missions in a random environment modeled by the Poisson process of shocks. Shocks may inflict defects that result in a failure after a random delay. The generalized extreme shock model is employed for stochastic description of systems resistance to shocks. If a defect is detected, a mission is aborted and a rescue operation is activated to prevent a failure. Imperfect inspections are performed during a mission to detect the defects. A system survives if the rescue operation is completed before a failure occurs. A probabilistic model is developed for deriving two system's performance metrics: the mission success probability (MSP) and the failure avoidance probability (FAP). It is shown that there exists a tradeoff between these metrics. An inspection schedule optimization problem is formulated and solved to maximize the MSP while providing the desired level of the FAP.