Reliability evaluation for a multi-state balanced system with a performance sharing mechanism in a multi-source shock environment

The operating environment of balanced systems with performance sharing is complex in practice, and the balanced concept of these systems has diverse implications according to the engineering applications. Nevertheless, existing studies only consider the impact of shocks from a single source and the limited balanced criterion of the performance-balanced systems. Additionally, prior research has considered a constant transmission loss rate, which is inconsistent with the reality of increased losses during performance transmission caused by the degradation of a common bus. To address the above research gaps, this paper constructs a new multi-state balanced system with the performance sharing mechanism, which operates in a multi-source shock environment. The performance levels of the components and the common bus deteriorate owing to internal degradation and the impact of multi-source shocks. The proposed system keeps balanced when the maximum performance difference among all units in the system is not greater than a certain threshold. The transmission loss rate of the common bus is determined by its state. An insufficient total performance of all components or a system imbalance after the proposed performance sharing mechanism via the common bus leads to the system failure. The Markov process imbedding approach is utilized to describe the state transitions of the components and common bus, and the universal generating function technique is employed to analyze the probabilistic indicators of the entire system. Finally, the applicability and effectiveness of the proposed model are validated through examples of a lithium battery pack system and sensitivity analyses of relevant model parameters.