Stochastic programming for selective maintenance optimization with uncertainty in the next mission conditions

This paper studies selective maintenance for multi-component systems that undergo consecutive missions with scheduled breaks after each mission. To increase the likelihood of mission success, maintenance activities are performed on system components during the breaks. This study considers uncertainties in mission time and operating conditions. A two-stage stochastic programming approach is applied to model the uncertainties in the operating conditions of the next mission. Uncertainties in the operating conditions of the next mission affect the likelihood of successfully completing the mission, which may require reducing the mission time in worst-case scenarios. In the proposed two-stage model, the first stage involves making decisions on the maintenance actions required on selected components during the break. In the second stage, decisions are made regarding the completion or termination of the mission, and a penalty is assigned based on the probability of system failure during the next mission. The Sample Average Approximation algorithm, Wait-and-See, and Expected Value approaches are employed to demonstrate the efficiency of the optimal solution obtained from stochastic programming and to conduct large-scale analyses of the problem under various scenarios. Moreover, the effectiveness of the proposed model underscores the importance of incorporating uncertainty into the model.