Abstract: Two bivariate construction methods are investigated, namely, the approximation method P using the Pearson correlation coefficient and the approximate method S using the Spearman correlation coefficient. The formulae for component probability of failure based on a direct integration are derived. The results indicate that the only difference in the joint PDFs between the approximate method P and the approximate method S is the Pearson correlation coefficient between two correlated standard normal variables. The errors in probabilities of failure for the two approximate methods highly depend on the level of probability of failure, the form of a performance function, and the degree of correlation. Such errors increase significantly with decreasing probabilities of failure. Significant errors in component probabilities of failure from the two approximate methods will be obtained only when the failure domain is able to capture the significant difference in the joint PDF surfaces and the component probability of failure is lower than 10^-3.