基于重试机制与转换失效的k/(M+N):G系统可靠性建模与优化  

Reliability modeling and optimization of k/(M+N):G system based on retrial mechanism and switching failure

作　　者：李晶 胡林敏[1] 李明佳 LI Jing;HU Linmin;LI Mingjia(School of Science,Yanshan University,Qinhuangdao 066004,Hebei,China;School of Economics and Management,Yanshan University,Qinhuangdao 066004,Hebei,China)

机构地区：[1]燕山大学理学院,河北秦皇岛066004 [2]燕山大学经济与管理学院,河北秦皇岛066004

出　　处：《运筹学学报(中英文)》2024年第4期44-56,共13页Operations Research Transactions

基　　金：国家自然科学基金(No.72071175);中央引导地方科技发展资金项目(No.246Z0305G);石家庄市驻冀高校基础研究项目(No.241790737A)。

摘　　要：本文建立了具有贮备转换失效、Bernoulli休假和工作故障的k/(M+N):G可修重试系统可靠性和优化模型。假设当工作部件发生失效时,由尚未失效的温贮备部件去替换,替换操作会以一定概率导致温贮备部件发生失效。在重试空间中,失效部件遵循随机重试原则。利用Runge-Kutta方法和Carmer法则分别求解了系统的瞬态和稳态状态概率,得到了系统的瞬态和稳态可靠性指标以及一些其他稳态性能指标。基于所定义的成本元素和系统的稳态性能指标,构建了单位时间总成本函数最小化模型,采用遗传-粒子群(GA_PSO)混合算法对该优化设计模型进行了求解。通过数值实验评估了不同系统参数对单位时间总成本函数和稳态性能指标的影响。实验结果验证了所建模型的可靠性。In this paper,the reliability and optimization model of repairable k/(M+N):G retrial system with standby switching failure,Bernoulli vacation and working breakdown is established.It is assumed that when the working component fails,it is replaced by a warm standby component that has not yet failed.The replacement operation will lead to the failure of the warm standby component with a certain probability.In retrial space,the failed components follow the principle of random retrial.By using Runge-Kutta method and Cramer's rule,the transient and steady-state probabilities of the system are solved respectively,and the transient and steady-state reliability indexes and some other steady-state performance indexes of the system are obtained.Based on the defined cost elements and the steady-state performance indexes of the system,a minimization model of the total cost function per unit time is constructed,and the genetic particle swarm optimization(GA_PSO)hybrid algorithm is used to solve the optimization design model.The effects of different system parameters on the total cost function per unit time and steady-state performance index are evaluated by numerical experiments.The experimental results verify the reliability of the established model.

关 键 词：重试 BERNOULLI休假 工作故障 转换失效 可靠性 优化 

分 类 号：O213.2[理学—概率论与数理统计] O224[理学—数学]