Impact of copulas for modeling bivariate distributions on system reliability

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Structural reliability analysis using a copula-function-based evidence theory model (2014, methodology): “[48] analyzed the influences of different bivariate copula functions to reliability analysis results, and subsequently used the copula functions to conduct system reliability analysis [49].”
Copula-based approaches for evaluating slope reliability under incomplete probability information (2015, background): “The copula theory provides a general and flexible way for modeling nonlinear dependence among multivariate data in isolation from their marginal probability distributions [11,33,34,14,39].”
Response surface methods for slope reliability analysis: Review and comparison (2016, methodology): “If spatial variability of soil properties is not considered, NMC random variable samples X are obtained using the Nataf transformation (e.g., Lebrun and Dutfoy, 2009; Li et al., 2011; Tang et al., 2013).”
Characterization of uncertainty in probabilistic model using bootstrap method and its application to reliability of piles (2015, background): “, [10,11]) has been received increasing attention in geotechnical engineering for constructing the joint CDF or PDF of multivariate data, particularly bivariate data [12–19].”