A practical non-parametric copula algorithm for system reliability with correlations

Fan Wang, Heng Li

Research output: Journal article publicationJournal articleAcademic researchpeer-review

7 Citations (Scopus)


System reliability analysis involving correlated random variables is challenging because the failure probability cannot be uniquely determined under the given probability information. This paper proposes a system reliability evaluation method based on non-parametric copulas. The approximated joint probability distribution satisfying the constraints specified by correlations has the maximal relative entropy with respect to the joint probability distribution of independent random variables. Thus the reliability evaluation is unbiased from the perspective of information theory. The estimation of the non-parametric copula parameters from Pearson linear correlation, Spearman rank correlation, and Kendall rank correlation are provided, respectively. The approximated maximum entropy distribution is then integrated with the first and second order system reliability method. Four examples are adopted to illustrate the accuracy and efficiency of the proposed method. It is found that traditional system reliability method encodes excessive dependence information for correlated random variables and the estimated failure probability can be significantly biased.

Original languageEnglish
Pages (from-to)641-657
Number of pages17
JournalApplied Mathematical Modelling
Publication statusPublished - Oct 2019


  • Kendall rank correlation
  • Minimum information copula
  • Pearson linear correlation
  • Spearman rank correlation
  • System reliability

ASJC Scopus subject areas

  • Modelling and Simulation
  • Applied Mathematics


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