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Vine copula constructions of higher-dimensional dependent reliability systems

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  • Xujie Jia
  • Jingyuan Shen
  • Liying Wang
  • Zhongping Li

Abstract

Copulas have proved to be very successful tools for the flexible modeling of dependence. Bivariate copulas have been deeply researched in recent years, while building higher-dimensional copulas is still recognized to be a difficult task. In this paper, we study the higher-dimensional dependent reliability systems using a type of decomposition called “vine,” by which a multivariate distribution can be decomposed into a cascade of bivariate copulas. Some equations of system reliability for parallel, series, and k-out-of-n systems are obtained and then decomposed based on C-vine and D-vine copulas. Finally, a shutdown system is considered to illustrate the results obtained in the paper.

Suggested Citation

  • Xujie Jia & Jingyuan Shen & Liying Wang & Zhongping Li, 2017. "Vine copula constructions of higher-dimensional dependent reliability systems," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(18), pages 9126-9136, September.
    • Handle: RePEc:taf:lstaxx:v:46:y:2017:i:18:p:9126-9136
    DOI: 10.1080/03610926.2016.1205620
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