随机和非随机部件组成的串并联系统寿命比较  

Comparisons of series and parallel systems with random and non-random dependent components

作　　者：李松臣[1] 李育鹏[1] 陈迎运 魏正红[1] 

机构地区：[1]深圳大学数学与计算科学学院,深圳518060

出　　处：《深圳大学学报（理工版）》2014年第3期312-316,共5页Journal of Shenzhen University(Science and Engineering)

基　　金：国家自然科学基金资助项目(71101095)~~

摘　　要：针对随机数N个部件和非随机数n个部件组成的串并联系统,引入可交换Copula函数度量串并联系统中各部件寿命的相依性,研究串并联系统寿命的随机比较问题.利用离散函数的凸性及詹森不等式的概率论形式,证明当随机数N的期望满足条件E(N)≤n时,随机N部件组成串联系统的寿命以一般随机序优于非随机n部件组成串联系统的寿命;而当E(N)≤n时,非随机n部件组成并联系统的寿命以一般随机序优于随机N部件组成并联系统的寿命.Stochastic comparisons of series and parallel systems composed of random N and non-random n components were studied by implementing an exchangeable copula function.This copula function measures the dependence among the lifetime of each component in the series and parallel systems.By the use of the convexity of discrete functions and the Jensen inequality,when the random variable N satisfies E（N） ≤ n,we show that the lifetime of a series system composed of random N components is better than that of the system composed of non-random n components under the usual stochastic order;meanwhile,the lifetime of a parallel system composed of non-random n components is better than that of the system composed of random N components under the usual stochastic order.

关 键 词：应用统计数学 可靠性理论 次序统计量 可交换Copula函数 串并联 一般随机序 詹森不等式 离散凸性 

分 类 号：O211.9[理学—概率论与数理统计]