离散时间冷贮备可修重试系统可靠性建模  

Reliability modeling of discrete-time cold standby repairable retrial systems

作　　者：马梦饶 胡林敏[1] 于晓芸 MA Mengrao;HU Linmin;YU Xiaoyun(School of Science,Yanshan University,Qinhuangdao,Hebei 066004,China)

机构地区：[1]燕山大学理学院,河北秦皇岛066004

出　　处：《燕山大学学报》2025年第2期177-188,共12页Journal of Yanshan University

基　　金：国家自然科学基金资助项目(72071175);中央引导地方科技发展资金项目(246Z0305G);河北省软件工程重点实验室项目(22567637H);石家庄市驻冀高校基础研究项目(241790737A)。

摘　　要：研究了离散时间冷贮备可修重试系统,该系统考虑了失效部件的两阶段维修行为和Bernoulli休假机制。系统中所有失效部件都进行第一阶段基本维修,经过基本维修之后的部件会以一定概率进行第二阶段可选维修。修理工每完成一个阶段的维修均会以一定的概率进行休假或继续留在系统中。针对离散时间多个事件可能会同时发生的情形,定义了多个事件同时发生的先后次序。基于两类优先级规则,提出了两种不同的模型。利用差分方程迭代解法和母函数法等推导出了系统可用度、可靠度和首次失效前平均时间等关键可靠性指标。通过数值算例,演示了各个参数的变化对系统性能指标的影响,得到了成本效益比最小值所对应的两类维修率的最优值,比较了两种模型瞬态可靠性指标的数值结果。A discrete-time cold standby repairable retrial system is studied,which takes into account the two-phase maintenance behavior of failed components and Bernoulli vacation mechanism.All the failed components in the system are carried out the first phase of basic maintenance,and the components after basic maintenance will be carried out the second phase of optional maintenance with a certain probability.Upon completion of a phase of maintenance,the repairman will take a vacation or stay in the system with a certain probability.For the situation where multiple events may occur simultaneously in the discrete time,the priority order of multiple events occurring simultaneously is defined.Two different models are proposed based on two types of priority rules.The key reliability indexes such as system availability,reliability and mean time to first failure are derived by means of iterative algorithm of difference equation and generative function method.A numerical example is given to demonstrate the influence of each parameter on the system performance indexes,and the optimal values of two repair rates corresponding to the minimum value of the cost-benefit ratio are obtained,and the numerical results of transient reliability indexes of the two models are compared.

关 键 词：重试 冷贮备 两阶段维修 BERNOULLI休假 可靠度 可用度 

分 类 号：O213.2[理学—概率论与数理统计]