PARALLEL STRUCTURAL SYSTEM RELIABILITY ANALYSIS FROM THE COPULA VIEWPOINT

Structural system reliability can not be determined uniquely based on incomplete probability information of correlated variables. This paper aims to investigate the effect of copula choice on system reliability when probability information is incomplete. First, the method for constructing the joint probability distribution of correlated variables using copulas is introduced. Thereafter, a parallel system reliability model is formulated and the formulae for calculating the system probability of failure are derived. Finally, several typical copulas are selected to model the dependence structure between correlated variables. A parallel system with two components is presented to demonstrate the effect of copula choice on system reliability. The results indicate that the copula choice has a significant effect on the system reliability. The system probabilities of failure produced by different copulas can differ considerably, and the level of difference increases with decreasing component probability of failure. Tail dependence has a significant impact on the system probability of failure. When tail dependence associated with a specified copula falls in a failure domain, the resulting system probability of failure will rise. The system probability of failure increases with increasing dependence between variables for positively correlated component performance functions, while it decreases with increasing correlation between variables for negatively correlated component performance functions. In addition, the system probabilities of failure associated with different copulas will be restricted within the upper bound and lower bound underlying the parallel system probability of failure for any given component probability of failure and correlation coefficient between variables.