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            <funder>This work is partially supported by the China Scholarship Council, China and the Initiative d’Excellence d’Aix-Marseille Université, France .</funder>
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              <p>&lt;div&gt;&lt;p&gt;This paper proposes a maintenance model for a Proton-Exchanged Membrane Fuel Cells system. Two types of failures are considered: non repairable internal failures and possibly repairable external failures. The maintenance involves replacing one or more cells. Therefore the maintenance can be perfect or imperfect. Moreover after each repair, the maintenance operator improves and the down time due to maintenance is reduced. A semi-Markov process is proposed to model the system's lifetime. In this framework, the reliability measures and the remaining useful lifetime are derived. The long run average maintenance cost is studied. A sensitivity analysis of model parameters and maintenance unit costs is performed and a maintenance optimization strategy is proposed.&lt;/p&gt;&lt;/div&gt;</p>
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