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[en] This paper addresses the selective maintenance optimization problem in a multi-component system, carrying out several missions with scheduled inter-mission breaks. To improve the probability of the system successfully completing the next mission, maintenance is performed on the system's components during the break. Each component is assigned a list of eligible maintenance actions ranging from minimal repair, through intermediate imperfect maintenance actions, to replacement. The quality of a maintenance action is assumed to be stochastic, reflecting the degree of expertise of the repairman and the tools used to perform the maintenance action. This quality is thus treated as a random variable with an identified probability distribution. The selective maintenance problem aims thus at finding a cost-optimal subset of maintenance actions, to be performed on the system during the limited duration of the break, which guarantees that the pre-set minimum probability of successfully completing the next mission is attained. The fundamental constructs and the relevant parameters of this nonlinear and stochastic optimization problem are developed and thoroughly discussed. It is then put into practice for a series–parallel system and the added value of solving it as a stochastic problem is demonstrated on some test cases. - Highlights: • A stochastic selective maintenance optimization problem is modeled and investigated. • Each component of the system may be maintained at different maintenance levels. • Variability of maintenance actions' effects are accounted for in the optimization process. • The selective maintenance problem is solved as a nonlinear stochastic optimization program. • Cost-effective maintenance solutions and accurate system's reliability are obtained.