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.

中文翻译：

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具有再平衡机制的多状态 k-out-of-n:F 平衡系统

平衡系统在新能源存储、航空等工程领域有着广泛的应用。此类系统的可靠性分析已在文献中报道。然而，现有的研究大多集中在二元状态的情况下，对多状态情况和相关再平衡机制的研究仍然有限。为了填补这一空白，一个多态k -out-of- n本文研究了具有再平衡机制的:F平衡系统。组件和系统都有多种状态，所有组件都需要工作在相似的状态，以确保系统运行在平衡状态。这意味着最大和最小组件状态之间的差异不应超过阈值。否则，系统将失去平衡，应通过识别状态过高的组件并将其调整为较低状态来重新平衡。采用连续时间马尔科夫过程描述组件运行过程，并据此推导出相关的可靠性指标。还提出了年龄维护策略，并构建了优化模型以获得最佳结果。最后，