Reliability analyses of k-out-of-n: F capability-balanced systems in a multi-source shock environment

Research on balanced systems has sparked intense attentions due to their widespread engineering applications. Previous studies all considered that balanced systems operate in a single-source shock environment and the existing concepts of system balance are limited. Nevertheless, some balanced systems operate in more complex shock environment with multiple sources and new system balance requirements can be explored based on real engineering cases. To make up research gaps, this paper proposes a k-out-of-n: F capability-balanced system working in a multi-source shock environment, where the shock impacts from various sources can differ significantly. The components have multiple states owing to shocks and an operating capability is taken for each component state. The concept of system capability balance is defined based on the largest capability difference between components and a random probability of system to keep capability-balanced within a certain range is considered. System failure can be caused by dissatisfying the capability-balanced conditions and reaching the critical number of failed components. A two-stage finite Markov chain imbedding approach and _PH distribution are combined to evaluate the probabilistic quantities of the system. Finally, illustrative examples are provided to validate the proposed model and future studies are discussed.