不确定多状态权重k/n系统可靠性分析  

Reliability Analysis of Uncertain Multi-State Weighted k-out-of-n Systems

作　　者：高荣 杨硕然 GAO Rong;YANG Shuoran(School of Economics and Management,Hebei University of Technology,Tianjin 300401)

机构地区：[1]河北工业大学经济管理学院,天津300401

出　　处：《系统科学与数学》2025年第1期197-210,共14页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(72101080);河北省自然科学基金(F2020202056);河北省教育厅科学研究项目(ZD2020125)资助课题。

摘　　要：多状态权重k/n系统含有n个元件,每个元件有多种可能的状态,不同状态下有不同的权重,当工作元件的权重和不低于预设值k时,系统工作.针对实际系统中大量数据缺失或数据失效等情形,将不确定理论引入多状态权重k/n系统的可靠性分析中.假设系统中各元件状态及其权重是不确定变量并且相互独立,建立了系统可靠性的数学模型,并通过严格数学推导将其转换为逆分布等价模型.同时设计了二元搜索算法推导出该系统的可靠性测度,丰富了不确定系统可靠性的现有理论.另外,还对系统中元件的重要性测度进行分析,并给出相应算法.结果表明,所建模型和提出的算法能够通过元件的离散不确定状态变量和连续不确定权重变量来获得系统可靠性测度和元件重要性测度并有针对性的对整个系统的性能进行改善.The multi-state weighted k-out-of-n system contains n components where each component has a variety of possible states and each state has its corresponding weight.The system works if and only if the total weight of working components is at least k,a pre-specified value.For situations where a large amount of data is missing or invalid in actual systems,uncertainty theory is introduced into the reliability analysis of multi-state weighted k-out-of-n system.Assuming that the states and weights of all components are independent uncertain variables,a mathematical model of system reliability is established,red and convert it into an inverse distribution equivalent model through strict mathematical derivation.A binary search algorithm is designed to derive the reliability indicators of the system,enriching the existing theory of uncertain system reliability.In addition,the importance measure of components in the system is evaluated,and corresponding algorithm is provided.The results show that the established model and algorithm can obtain reliability index of system and importance measure of components through discrete uncertain variables of state and continuous uncertain variables of weight of the components,and improve the performance of the entire system in a targeted manner.

关 键 词：不确定变量 多状态权重k/n系统 可靠性分析 重要性测度 

分 类 号：O213.2[理学—概率论与数理统计]