Vine copula constructions of higher-dimensional dependent reliability systems

Xujie Jia, Jingyuan Shen, Liying Wang and Zhongping Li

Communications in Statistics - Theory and Methods, 2017, vol. 46, issue 18, 9126-9136

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.

Date: 2017
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DOI: 10.1080/03610926.2016.1205620

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