In this study, we investigate whether copula modeling contributes to the improvement of reliability evaluation in a cascading failure-occurrence environment. In particular, as a basic problem, we focus on a 2-unit parallel system whose units may fail dependently each other. As a result, the reliability assessment of the system by using the maximal copula provides more accurate evaluation than the traditional Weibull analysis, if the degree of dependency between two units are high. We show this result by using several simulation studies.

An n-variate Farlie-Gumbel-Morgenstern (FGM) copula consists of 2n - n - 1 parameters that express multivariate dependence among random variables. Motivated by the dependence structure of the n-variate FGM copula, we derive the exact range of the n-variate FGM copula's parameter. The exact range of the parameter is given by a closed-form expression under the condition that all parameters take the same value. Moreover, under the same condition, we reveal that the n-variate FGM copula becomes the independence copula for n → ∞. This result contributes to the dependence modeling such as reliability analysis considering dependent failure occurrence.

This paper deals with the minimum and maximum value distributions based on the n-variate FGM copula with one dependence parameter. The ranges of dependence parameters are theoretically determined so that the probability density function always takes a non-negative value. However, the closed-form conditions of the ranges for the dependence parameters have not been known in the literature. In this paper, we newly provide the necessary conditions of the ranges of the dependence parameters for the minimum and maximum value distributions which are derived from FGM copula, and show the asymptotic properties of the ranges.