Selective maintenance optimization for systems operating missions and scheduled breaks with stochastic durations

This paper deals with selective maintenance of a multi-component system, performing several missions seceded by scheduled breaks. To improve the probability of successfully completing its next mission, the system's components are maintained during these breaks. A list of possible maintenance actions on each component of the system, ranging from minimal repair to overhaul through intermediate imperfect maintenance actions, is available. Durations of the missions as well as those of the breaks are assumed stochastic variables with known distributions. The resulting selective maintenance optimization problem is thus modeled as a mixed-integer non-linear stochastic program. Its objective is to determine a cost-optimal subset of maintenance actions to be performed on the system's components, during the limited stochastic duration of the break, to meet a predetermined minimum system's reliability to operate the next mission. The fundamental constructs and the relevant parameters of this decision-making problem are developed and discussed. An illustrative example is provided to demonstrate the added value of solving this selective maintenance problem as a stochastic optimization program.