A multi-state k-out-of-n:F balanced system with a rebalancing mechanism

Balanced systems have extensive applications in engineering fields such as new energy storage and aeronautics. The reliability analysis of such systems has been reported in literature. However, most existing studies focus on the binary-state situation, and research on multi-state cases and the relevant rebalancing mechanism is still limited. To fill this gap, a multi-state k-out-of-n:F balanced system with a rebalancing mechanism is studied in this paper. Both components and the system have multiple states, and all the components are required to be working in similar states to ensure that the system operates in a balanced condition. It means that the difference between the maximum and minimum component states should not exceed a threshold. Otherwise, the system is out of balance and should be rebalanced by identifying the components whose states are too high and adjusting them into lower states. A continuous-time Markov process is used to describe the component operation process and relevant reliability indices are derived accordingly. An age maintenance strategy is also proposed and an optimization model is constructed to obtain the optimal results. Finally, numerical examples based on a product line balancing problem are presented to demonstrate the application of the proposed model.