部件Gumbel-Barnett Copula相依竞争失效的k/n系统可靠性分析  

Reliability of k/n System with Competing Failures Component Connected by Gumbel-Barnett Copula

作　　者：时炎杰 彭秀云[1] 刘文博 SHI Yanjie;PENG Xiuyun;LIU Wenbo(College of Science,Inner Mongolia University of Technology,Hohhot,010051,China)

机构地区：[1]内蒙古工业大学理学院,呼和浩特010051

出　　处：《应用概率统计》2023年第3期317-332,共16页Chinese Journal of Applied Probability and Statistics

基　　金：国家自然科学基金项目(批准号:11861049、81860605);内蒙古自然科学基金项目(批准号:2021LHMS01001);内蒙古自治区生命数据统计分析理论与神经网络建模重点实验室资助.

摘　　要：考虑具有两个相互关联的竞争失效机理导致部件失效的k/n系统可靠性问题,关联性由Gumbel-Barnett (GB) Copula连接,边缘分布为尺度和形状参数不同的Weibull分布.研究了GB Copula对部件和k/n系统失效率和可靠度的影响.证明了当边缘分布形状参数相等时,在不同取值下,部件对应单调递增、单调递减和浴盆状失效率.模拟发现k/n (n> 1)系统可靠度并不一致优于简单系统(即k/n=1/1).基于逐步Ⅱ型截尾样本,讨论了k/n系统参数和可靠度的Bayes估计,并进行了Monte Carlo试验与分析.最后,提供了一个实例演示本文构建的模型和提出的方法.The reliability of k=n system with two interrelated competitive failure mechanisms leading to component failure is considered.The competitive correlation is connected by Gumbel-Barnett(GB)Copula with Weibull marginal distributions that have different scale parameters and shape parameters.The effects of GB Copula on the failure rate and reliability of components and k/n system are studied when the shape parameters are equal.We proved that the components have increasing,decreasing and bathtub failure rate in terms of the same shape parameter but different values.The reliability of the k/n(n>1)system is not consistently superior to that of the simple system(i.e.,k/n=1=1).Based on progressively Type-II censored samples,the Bayes estimation of the parameters and reliability of the k/n system are discussed,and Monte Carlo experiments are carried out to illustrate proposed methods.Finally,a real-life data is provided to demonstrate the model and method proposed in this paper.

关 键 词：k/n系统 Gumbel-Barnett Copula函数 WEIBULL分布 逐步Ⅱ型截尾 

分 类 号：O213.2[理学—概率论与数理统计]