Reliability Research of Dependent Failure Systems Using Copula

References

• Fleming , K. N. , Mosleh , N. and Deremer , R. K. 1986 . A systematic procedure for incorporation of common cause events into risk and reliability models . Nuclear Engineering and Design , 93 : 245 – 273 .
   Web of Science ®Google Scholar
• Gera , A. E. 2000 . A consecutive k-out-of-n:G system with dependent elements-a matrix formulation and 了solution . Reliability Engineering and System Safety , 68 : 61 – 67 .
   Web of Science ®Google Scholar
• Ge , Guangping and Wang , Linshu . 1990 . Exact reliability formula for consecutive-k-out-of-n: F systems with homogeneous Markov dependence . IEEE Trans. Reliability , 39 ( 5 ) : 600 – 602 .
   Web of Science ®Google Scholar
• Jia , Xujie and Cui , Lirong . 2010 . A study on the reliability of consecutive k-out-of-n: G systems based on Copula . Communications in Statistics - Theory and Methods , 39 ( 13 ) : 2455 – 2472 .
   Web of Science ®Google Scholar
• Jia , Xujie and Cui , Lirong . 2012 . Reliability research of k-out-of-n: G supply chain system based on Copula . Communications in Statistics - Theory and Methods , 41 ( 21 ) : 4023 – 4033 .
   Web of Science ®Google Scholar
• Kotz , S. , Lai , C. D. and Xie , M. 2003 . On the effect of redundancy for systems with dependent components . IIE Trans , 35 : 1103 – 1110 .
   Web of Science ®Google Scholar
• Navarro , J. and Balakrishan , N. 2010 . Study of some measures of dependence between order statistics and systems [J] . Journal of Multivariate Analysis , 101 : 52 – 67 .
   Web of Science ®Google Scholar
• Navarro , J. , Ruiz , J. M. and Sandoval , C. J. 2005 . A note on comparisons among coherent systems with dependent components using signatures . Statist Probab Lett , 72 : 179 – 185 .
   Web of Science ®Google Scholar
• Nelsen , R. 1999 . An Introduction to Copulas , New York : Springer-Verlag .
   Google Scholar
• Noh , Y. , Choi , K. K. and Liu , D. 2009 . Reliability-based design optimization of problems with correlated input variables using a Gaussian Copula [J] . Structural and Multidisciplinary Optimization , 38 ( 1 ) : 1 – 16 .
   Web of Science ®Google Scholar
• Papastavridis , S. and Lambiris , M. 1987 . Reliability of a consecutive-k-out-of-n:F system for Markov-dependent components . IEEE Trans. Reliability , R-36 : 78 – 79 .
   Web of Science ®Google Scholar
• Page , L. B. and Perry , J. E. 1989 . A model for system reliability with common cause failures . IEEE Trans. Reliability , 38 ( 4 ) : 406 – 410 .
   Web of Science ®Google Scholar
• Ranm , M. and Singh , S. B. 2008 . Availability and cost analysis of a parallel redundant complex system with two types of failure under preemptive-resume repair discipline using Gumbel-hougaard family Copula in repair [J] . International Journal of Reliability, Quality and Safety Engineering , 5 ( 4 ) : 341 – 365 .
   Google Scholar
• Sklar , A. 1959 . Functions de repartition à n dimensions et luers marges . Publications de l’Institut de Statistique de l’Universitè de Paris , 8 : 229 – 231 .
   Google Scholar
• Vaurio , J. K. 1998 . An implicit method for incorporating common-cause failures in system analysis . IEEE Trans. Reliability , 47 ( 2 ) : 173 – 180 .
   Web of Science ®Google Scholar
• Vaurio , J. K. 2005 . Uncertainties and quantification of common cause failure rates and probabilities for system analyses . Reliability Engineering and System Safety , 90 ( 2–3 ) : 186 – 195 .
   Web of Science ®Google Scholar
• Xiao , G. , Li , Z. and Li , T. 2007 . Dependability estimation for non-Markov consecutive k-outof-n:F repairable systems by fast simulation . Reliability Engineering and System Safety , 92 ( 3 ) : 293 – 299 .
   Web of Science ®Google Scholar
• Xie , L. , Zhou , J. and Wang , X. 2005 . Data mapping and the prediction of common cause failure probability . IEEE Trans. Reliability , 54 ( 2 ) : 291 – 296 .
   Web of Science ®Google Scholar
• Yun , W. Y. , Kim , G. R. and Yamamoto , H. 2007 . Economic design of a circular consecutive k-out-of-n:F system with k−1 step Markov dependence . Reliability Engineering and System Safety , 92 : 464 – 478 .
   Web of Science ®Google Scholar