Optimizing upgrade and imperfect preventive maintenance in failure-prone second-hand systems

•A maintenance optimization problem is investigated for failure-prone second-hand systems.•The system is subjected to upgrade and imperfect maintenance actions.•A maintenance optimization problem is developed and fully discussed.•Conditions to ensure the optimal solution are provided for general cost-structures of acquisition and upgrade costs.•Cost-effective solutions and system's reliability assessment are demonstrated. Upgrade operations are improvement actions that can be carried out on recovered end-of-life systems to rejuvenate them and make them fit for subsequent lifecycles. These operations are costly but improve the reliability of these second-hand systems and consequently can reduce their maintenance costs. In this paper, a mathematical model for the joint determination of the optimal acquisition age, upgrade level, and imperfect preventive maintenance strategy is developed for a second-hand system. The system is acquired and upgraded, if necessary, before being put into operation and preventively maintained each time its reliability reaches a minimum required reliability threshold. Preventive maintenance actions are imperfect and modeled using the hybrid hazard rate approach. Optimality conditions are derived and discussed for general cost structures of the acquisition and upgrade actions. A test case is provided to illustrate the validity of the proposed approach. Numerical experiments and sensitivity analysis are also conducted to investigate the interactions between the upgrade level decisions, the optimal maintenance policy decisions and the total costs incurred during the lifetimes of these refreshed second- hand systems.