Optimal preventive maintenance policy of the balanced system under the semi-Markov model

Reliability problems of new systems such as balanced systems have received more attention in recent years due to the rapid development of technology. However, the research on maintenance optimization for balanced systems is still underexplored, and the existing policies for orthodox systems cannot solve the maintenance problem of balanced systems. Thus, an optimal preventive maintenance optimization model is formulated under the semi-Markov model for a balanced system with n identical units, where each unit is subject to degradation failure and sojourn times in different function zones follow Erlang distribution with different parameters, respectively. Different from orthodox systems, the failure criterion of the balanced system is given according to the system balance degree. Namely, when any two symmetric components do not perform the same function, the system is out of balance. To avoid system unbalance, a preventive maintenance action is performed once the state difference on any two symmetric units exceeds the maintenance threshold. Finally, some numerical examples are used to demonstrate the priority of the proposed preventive maintenance policy, and the obtained results provide a good insight for repairmen to maintain components on the balanced system.