"BIVARIATE DISTRIBUTION CONSTRUCTION METHOD AND ITS APPLICATION TO STRUCTURAL PARALLEL SYSTEM RELIABILITY ANALYSIS "

This paper aims to study the errors of the method P and method S. Firstly, method P and method S as well as the exact method are presented. Thereafter, the formulae for system probability of failure based on direct integration are derived. Finally, an illustrative example is investigated to demonstrate the errors associated with the two methods. The results indicate that the errors in system probabilities of failure for the two methods highly depend on the level of system probability of failure, the performance function underlying the system and the degree of correlation. Such errors increase greatly with the decreasing of system probabilities of failure. When the target system probability of failure is above 1.0×10?3, the errors in the system probabilities of failure obtained from the two methods are significant, implying that the two approximate methods should be used carefully. The errors in system probability of failure for negative correlated performance functions are significantly higher than those for positive correlated performance functions. The maximum error in the system probability of failure may not be associated with a large correlation. It can happen at an intermediate correlation.