MODELING BIVARIATE DISTRIBUTION USING COPULAS AND ITS APPLICATION TO COMPONENT RELIABILITY ANALYSIS

The method for constructing the joint probability distribution of correlated variables based on incomplete probability information and its effect on component reliability has not been studied systematically. This paper aims to propose a method for modeling bivariate distribution using copulas and investigate the effect of a copula choice on component reliability. First, the method for constructing the joint probability distribution of correlated variables using copulas is briefly introduced. Thereafter, the formulae for the component probability of failure using direct integration are derived. Finally, an example of reliability analysis with linear performance functions is presented to demonstrate the effect of a copula choice on component reliability. The results indicate that component reliability cannot be determined uniquely with given marginal distributions and covariance. Copula choice has a significant effect on the component reliability. The probabilities of failure produced by different copulas differ considerably. Such a difference increases with the increase of reliability indexes or the decrease of failure probability. Tail dependence can result in a significant impact on the probability of failure. When tail dependence associated with a specified copula exists in a failure domain, the resulting probability of failure will become larger. The reliability index defined by the mean and standard deviation of a performance function cannot capture the difference among various copulas, while the probability of failure based on the actual distribution of a performance function can effectively accounts for the difference underlying various copulas.