刘斌,霍美玲,许靖,崔学英,谢秀峰

• 1:太原科技大学应用科学学院

摘要(Abstract)：

应力-强度系统是一种普遍的系统结构，估计系统平均剩余强度时通常假设部件间相互独立。然而，基于部件独立假设会造成平均剩余强度估计的不准确。利用copula理论建立部件强度间的相依关系，得到了系统平均剩余强度的表达式。采用非参数贝叶斯方法估计了系统的平均剩余强度，对串联系统和并联系统数据进行蒙特卡罗模拟，验证了方法的有效性。结果表明，在部件强度相依的情况下，基于独立假定的串联系统平均剩余强度被低估，并联系统的平均剩余强度则被高估。因此，系统部件间的相依影响不能忽略。

关键词(KeyWords)： 应力-强度模型;非参数贝叶斯估计;平均剩余强度,相依部件强度

Abstract:

Keywords:

基金项目(Foundation): 国家自然科学基金(11701406,11901134,12061091,11972019);; 山西省基础研究计划(202103021224274,201901 D111261);; 山西省社会经济统计科研课题(KY[2021]145)

作者(Author): 刘斌,霍美玲,许靖,崔学英,谢秀峰

参考文献(References)：

• [1] BIRNBAUM Z W.On a use of the Mann-Whitney statistic[J].Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability,1956,1954-1955(1):13-17.
• [2] AKGüL F G.Reliability estimation in multicomponent stress-strength model for Topo-Leone distribution[J].Journal of Statistical Computation and Simulation,2019,89(5):1-16.
• [3] 耿延鹏.基广义指数分布的应力强度模型可靠度的估计[D].杭州：浙江工商大学，2017.
• [4] 戴林送，王枞.基于广义逆威布尔分布的应力强度模型可靠度估计[J].统计与决策，2020,36(9):25-29.
• [5] AKGüL F G.Classical and Bayesian estimation of multicomponent stress-strength reliability for exponentiated Pareto distribution[J].Soft Computing,2021,25(5):1-13.
• [6] CHEN J,CHENG C.Reliability of stress-strength model for exponentiated Pareto distributions[J].Journal of Statistical Computation and Simulation,2017,87:791-805.
• [7] GüRLER S,BAIRAMOV I.The mean remaining strength of systems in a stress-strength model[J].Hacettepe Journal of Mathematics and Statistics,2013,42(2):181-187.
• [8] BAIRAMOV I,GURLER S,UCER B.On the mean remaining strength of the k-out-of-n:F system with exchangeable components[J].Communications in Statistics Simulation and Computation,2015,44(1):1-13.
• [9] SKLAR M.Fonctions de répartition àn dimensions et leurs marges[J].Publications de l’Institut Statistique de l’Université de Paris,1959,8:229-231.
• [10] CHERUBINI U,LUCIANO E,Vecchiato W.Copula methods in finance[M].New York,Wiley,2004.
• [11] WEI Y H,ZHANG S Y.Copula theory and its applications in financial analysis[M].Beijing,Tsinghua University Press,2008.
• [12] 巨红岩，李俊林，董安强.基于copula函数的沪市资金流强弱指数相关性研究[J].太原科技大学学报，2017,37(1):71-78.
• [13] BAI X,SHI Y,LIU Y,et al.Reliability estimation of multicomponent stress-strength model based on copula function under progressively hybrid censoring[J].Journal of Applied Mathematics and Computing,2018,344:100-114.
• [14] BAI X,LI X,BALAKRISHNAN N.Statistical inference for dependent stress-strength reliability of multi-state system using generalized survival signature[J].Journal of Applied Mathematics and Computing,2021,390:113316.
• [15] SINHA D,POLPO A,PEREIRA C.Nonparametric Bayesian estimation of reliabilities in a class of coherent systems[J].IEEE Transactions on Reliability,2013,62(2):455-465.
• [16] LIU B,SHI Y.Nonparametric Bayesian reliability analysis of masked data with dependent competing risks[J].Reliability Engineering & System Safety,2021,210:107502.
• [17] JOE H.Asymptotic efficiency of the two-stage estimation method for copula-based models[J].Journal of Multivariate Analysis,2005,94(2):401-419.
• [18] GENEST C,GHOUDI K,RIVEST L P.A semiparametric estimation procedure of dependence parameters in multivariate families of distributions[J].Biometrika,1995,82(3):543-552.
• [19] ZHANG X,SHANG J.Statistical inference of accelerated life testing with dependent competing failures based on copula theory[J].IEEE Transactions on Reliability,2014,63(3):764-780.
• [20] KOJADINOVIC I,YAN J.Comparison of three semiparametric methods for estimating dependence parameters in copula models[J].Insurance:Mathematics and Economics,2010,47(1):52-63.
• [21] FERGUSON T S.A Bayesian analysis of some nonparametric problems[J].Annals of Statistics,1973,1(2):209-230.
• [22] CHEN M H,SHAO Q M.Monte Carlo estimation of Bayesian credible and HPD intervals[J].Journal of Computational and Graphical Statistics,1999,8(1):69-92.