Optimal mission duration for systems subject to shocks and internal failures

At many instances, it is more cost-effective to terminate operation of a system than to wait for its failure or completion of a mission. Usually, completion of a mission (contract) results in an additional reward, whereas premature termination results in a penalty. However, the system failure during the mission can incur considerable expenses. As the failure probability increases with the mission time, this can make the mission completion too risky and not beneficial. This article analyzes the optimal mission duration for non-repairable systems subject to shocks and internal failures. Under certain assumptions, an optimal time of mission termination is obtained. It is shown that, if for some reason, the termination is not technically possible at this optimal time, the mission should be terminated within a specific time interval and, if this is not possible, it should not be terminated beyond this interval. Illustrative examples are presented.