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. total amount of work in the mission maximal possible number of repairs during the mission maximum allowed mission time mission success probability conditional expected cost of successful mission conditional expected mission time given that the mission succeeds after j repairs event when the jth failure happens at time Tj and the system spends time Xj in operation mode before the failure joint distribution function of random values Tj and Xj probability that jth failure happens in time interval v and the system spent in operation mode w intervals before the failure random repair time for system minimal and maximal possible realizations of D productivity of system working with load level L pdf of time-to-failure distribution of system working with load level L cdf of time-to-failure distribution of system working with load level L pdf of repair time cdf of repair time number of discrete intervals considered in the numerical algorithm duration of a discrete time interval: Δ = τ/m number of time intervals needed to complete the mission if no failures occur floor operation that returns the maximal integer not exceeding x event when the mission is completed after j repairs Pr(Yj ) scale, shape parameters of Weibull time-to-failure distribution for load level L per time unit repair cost per time unit operation cost under load level L repair efficiency coefficient 
Optimal loading of system with random repair time