A two-stage stochastic programming model for selective maintenance optimization

The problem of selective maintenance exists in many multicomponent systems carrying out an alternating sequence of missions, with scheduled breaks where only a limited number of components can be maintained due to time limit. In this paper, a stochastic programming approach is proposed for determining an optimum maintenance plan to minimize maintenance costs and expected failure costs, while maximizing the probability of successful accomplishment of the next mission under uncertainties in future operating conditions. Traditionally, future operating conditions that affect failure time distribution when calculating reliability in selective maintenance models were assumed as deterministic. In this study, future operating conditions are assumed to be uncertain. The system is subject to several uncertain condition scenarios of exposure, conditional, usage, stress, etc. Each scenario is modeled with its associated occurrence probability. The presented model is a two-stage stochastic mixed-integer nonlinear programming model with fixed recourse, where the first stage is associated with maintenance decisions made before uncertainties are revealed, and the second stage is modeled as a recourse function which is related to the occurrence probability of system failure. A numerical example of a series-parallel system is used to demonstrate the effectiveness of the suggested model.