Optimal loading of system with random repair time

This paper considers single-component repairable systems supporting different levels of workloads and subject to random repair times. The mission is successful if the system can perform a specified amount of work within the maximum allowed mission time. The system can work with different load levels, each corresponding to different productivity, time-to-failure distribution, and per time unit operation cost. A numerical algorithm is first suggested to evaluate mission success probability and conditional expected cost of a successful mission for the considered repairable system. The load optimization problem is then formulated and solved for finding the system load level that minimizes the expected mission cost subject to providing a desired level of the mission success probability. Examples with discrete and continuous load variation are provided to illustrate the proposed methodology. Effects of repair efficiency, repair time distribution, and maximum allowed time on the mission reliability and cost are also investigated through the examples.