基于多元copula函数的串联系统应力-强度模型可靠度的非参数估计 Nonparametric Estimation for the Reliability of a Series System Stress-Strength Model Based on Multiple Copula Function

Keywords: 应力-强度模型,连接函数,Kaplan-Meier估计量,右删失

Full-Text   Cite this paper   Add to My Lib

Abstract:

针对多部件的串联系统应力-强度模型可靠度的估计问题,利用多元Farlie-Gumbel-Morgenstern copula(FGM)函数或多元Clayton copula函数来度量变量之间的相关性,给出了在变量非删失或右删失情形下模型可靠度的非参数估计,并证明了估计量的渐近性质.数值模拟的结果表明该方法在有限样本下表现良好

References

[1]	ABID S H,HASSAN H A.The Marshall-Olkin extended uniform stress-strength model[J].American Journal of Mathematics and Statistics,2015,5(1):1-10.DOI:10.5923/j.ajms.20150501.01.
[2]	GHITANY M E,AL-MUTAIRI D K,ABOUKHAMSEEN S M.Estimation of the reliability of a stressstrength system from power Lindley distributions[J].Communications in Statistics—Simulation and Computation,2015,44(1):118-136.DOI:10.1080/03610918.2013.767910.
[3]	SHARMA V K,SINGH S K,SINGH U,et al.The inverse Lindley distribution:A stress-strength reliability model with application to head and neck cancer data[J].Journal of Industrial and Production Engineering,2015,32(3):162-173.DOI:10.1080/21681015.2015.1025901.
[4]	BAKLIZI A.Interval estimation of the stress-strength reliability in the two-parameter exponential distribution based on records[J].Journal of Statistical Computation and Simulation,2014,84(12):2671-2679.DOI:10.1080/00949655.2013.816307.
[5]	SHORACK G,WELLNER J.Empirical Processes with Applications to Statistics[M].New York:Wiley,1986.
[6]	LIN D Y,WEI L J,YANG I,et al.Semiparametric regression for the mean and rate functions of recurrent events[J].Journal of the Royal Statistical Society:Series B,2000,62(4):711-730.DOI:10.1111/1467-9868.00259.
[7]	RICE J A.Mathematical Statistics and Data Analysis[M].3rd ed.Massachusetts:Duxbury Resource Center,2006.
[8]	HANAGAL D D.Estimation of system reliability in multicomponent series stress-strength model[J].Journal of Indian Statistics Association,2003,41(1):1-7.
[9]	NELSEN R B.An Introduction to Copulas[M].2nd ed.New York:Springer-Verlag,2006.
[10]	CHANDRA S,OWEN D B.On estimating the reliability of a component subject to several different stresses(strengths)[J].Naval Research Logistics Quarterly,1975,22(1):31-39.DOI:10.1002/nav.3800220104.
[11]	叶慈南.强度为MOBVE分布时并联结构系统可靠度的估计[J].高等应用数学学报,2000,14(4):484-490.DOI:10.13299/j.cnki.amjcu.000941.YE C N.Structural system with strength having MOBVE distribution[J].Applied Mathematics A Journal of Chinese Universities,2000,14(4):484-490.DOI:10.13299/j.cnki.amjcu.000941(Ch).
[12]	HANAGAL D D.Estimation of system reliability from stress-strength relationship[J].Communications in Statistics—Theory and Methods,1996,25(8):1783-1797.DOI:10.1080/1532415X.1996.11877454.
[13]	HANAGAL D D.A multivariate pareto distribution[J].Communications in Statistics—Theory and Methods,1996,25(8):1471-1488.DOI:10.1080/03610929608831779.
[14]	DOMMA F,GIORDANO S.A copula-based approach to account for dependence in stress-strength models[J].Statistical Paper,2013,54(3):807-826.DOI:10.1007/s00362-012-0463-0.
[15]	QI H,QI F,YU J C.Nonparametric inference for the stress-strength model under right censoring[J].Wuhan University Journal of Natural Sciences,2015,20(3):202-206.DOI:10.1007/s11859-015-1082-0.
[16]	LO S H,SINGH K.The product-limit estimator and the bootstrap:Some asymptotic representations[J].Probability Theory and Related Fields,1986,71(3):455-465.DOI:10.1007/BF01000216.
[17]	BRESLOW N,CROWLEY J.A large sample study of the life table and product limit estimates under random censorship[J].The Annals of Statistics,1974,2:437-453.DOI:10.1214/aos/1176342705.
[18]	OEHLERT G W.A note on the Delta method[J].The American Statistician,1992,46(1):27-29.DOI:10.1080/00031305.1992.10475842.
[19]	BIRNBAUM Z W.On a use of Mann-Whitney statistics[C]//Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability.Berkeley:University of California Press,1956:13-17.
[20]	KOTZ S,LUMELSKII Y,PENSKY M.The StressStrength Model and Its Generalizations:Theory and Applications[M].Singapore:World Scientific Publishing,2003.
[21]	王炳兴.指数分布场合系统应力强度模型可靠度的统计推断[J].高校应用数学学报,2012,27(3):265-273.DOI:10.13299/j.cnki.amjcu.001713.WANG B X.Statistical inference for reliability of system stress-strength model under exponential distribution[J].Applied Mathematics A Journal of Chinese Universities,2012,27(3):265-273.DOI:10.13299/j.cnki.amjcu.001713(Ch).
[22]	ERYILMAZ S,TTNCG Y.Stress strength reliability in the presence of fuzziness[J].Journal of Computational and Applied Mathematics,2015,282:262-267.DOI:10.1016/j.cam.2014.12.047.

Full-Text