具有两类部件的三状态可修系统的动态分析  

Dynamic analysis of three-state repairable system consisting of two types of components

作　　者：阿布都瓦力·阿布都克热木 艾合买提·卡斯木[1] Abuduwali ABUDUKEREMU;Ehmet KASIM(College of Mathematics and Systems Science,Xinjiang University,Urumqi 830046,China)

机构地区：[1]新疆大学数学与系统科学学院,新疆乌鲁木齐830046

出　　处：《高校应用数学学报（A辑）》2023年第2期166-180,共15页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：新疆维吾尔自治区自然科学基金(2022D01C46);国家自然科学基金(11801485)。

摘　　要：研究了由S_(1)和S_(2)两类部件构成的三状态可修系统,其中S_(1)中只有一个部件S_(2)中有n个不同型部件.如果S_(2)中的部件故障系统会完全故障,S_(1)中的部件故障,不会导致系统完全故障,而降低系统的工作效率.首先利用线性算子的强连续半群理论证明了该系统具有唯一的非负时间依赖解.然后运用相应算子的谱性质,证明该时间依赖解指数收敛于它的稳态解.最后讨论系统的瞬时可靠性指标的渐近行为,并用数值例子分析各参数对系统瞬时可靠性指标的影响.该文的研究结果将有助于使系统在使用过程中更加可靠,安全和经济有效.This paper considers a three state repairable system with two classes of components,S_(1)and S_(2),where S_(1)contains only one component and S_(2)has n different components.In this system,a failure in S_(1)only contributes to reduction in normal effciency whereas a failure in S_(2)brings about the complete breakdown of the system.Firstly,it is proved that the system has a unique non-negative time-dependent solutions,by using the C_(0)-semigroup theory.Then using the spectral properties of the corresponding operator,it is proved that the time-dependent solution exponentially converges to its steady-state solution.Finally,the asymptotic behavior of the instantaneous reliability indices of the system is discussed,and the effect of each parameter on the system's instantaneous reliability of indices is analyzed with numerical examples.The results of this project can be useful to make the robot-safety system more reliable,safe and cost-effcient.

关 键 词：三状态可修复系统 C_(0)-半群 适定性 渐近行为 可靠性指标 

分 类 号：O231.2[理学—运筹学与控制论]