Reliability of a Multicomponent Stress-strength Model Based on a Bivariate Kumaraswamy Distribution with Censored Data  

作　　者：Cong-hua CHENG 

机构地区：[1]School of Mathematics and Statistics,Zhaoqing University,Zhaoqing 526061,China

出　　处：《Acta Mathematicae Applicatae Sinica》2024年第2期478-507,共30页应用数学学报（英文版）

基　　金：supported by the Natural Science Foundation of Guangdong(No.2024A1515010983);the project of Guangdong Province General Colleges and Universities with Special Characteristics and Innovations(No.2022KTSCX150);Zhaoqing Science and Technology Innovation Guidance Project(No.2023040317006);Zhaoqing Institute of Education Development Project(No.ZQJYY2023021);Zhaoqing College Quality Project and Teaching Reform Project(No.zlgc202112).

摘　　要：In this paper,we consider a system which has k statistically independent and identically distributed strength components and each component is constructed by a pair of statistically dependent elements with doubly type-II censored scheme.These elements(X1,Y1),(X2,Y2),…,(Xk,Yk)follow a bivariate Kumaraswamy distribution and each element is exposed to a common random stress T which follows a Kumaraswamy distribution.The system is regarded as operating only if at least s out of k(1≤s≤k)strength variables exceed the random stress.The multicomponent reliability of the system is given by Rs,k=P(at least s of the(Z1,…,Zk)exceed T)where Zi=min(Xi,Yi),i=1,…,k.The Bayes estimates of Rs,k have been developed by using the Markov Chain Monte Carlo methods due to the lack of explicit forms.The uniformly minimum variance unbiased and exact Bayes estimates of Rs,k are obtained analytically when the common second shape parameter is known.The asymptotic confidence interval and the highest probability density credible interval are constructed for Rs,k.The reliability estimators are compared by using the estimated risks through Monte Carlo simulations.

关 键 词：stress-strength model bivariate Kumaraswamy distribution multicomponent reliability doubly Type-II censored scheme interval estimation 

分 类 号：O213.2[理学—概率论与数理统计]