This article proposes a novel condition-based selective maintenance model for a multi-component system running multiple missions interspersed with scheduled intermission breaks. Each component in the system degrades according to a time-dependent stochastic process and fails whenever its degradation level reaches a prespecified threshold. Failures of system components are revealed only through periodic inspections performed during a mission. The decision to repair components found in a failed state is made at the beginning of the following break. However, a penalty cost proportional to the expected component downtime is incurred. To improve the probability of the system successfully completing its next mission, maintenance activities are carried out on its components during the breaks. Each component can be imperfectly maintained or replaced. The level at which maintenance is performed determines the improvement degree in the component health. Cost and time structures are developed to take into account the trade-offs between the cost of an imperfect maintenance action and its resulting health improvement. Given the limited duration of the break and the required reliability target for the next mission, the condition-based selective maintenance problem aims at finding an optimal subset of maintenance actions to be performed on the selected components to minimize the total expected cost which is the sum of the total expected maintenance, inspection and penalty costs. All parameters and components of this nonlinear selective maintenance optimization problem are developed and thoroughly discussed. Numerical experiments are provided to illustrate the modelling steps and show the validity of the proposed approach.
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