Augmenting approximate solutions for consistent reliability analysis

Approximate solutions provide a great source of insight for understanding system behavior. Due to their approximate nature, however, their use in reliability analysis does not lead to ‘consistent’ reliability estimates, in the sense that the resulting estimates do not converge to the reliability based on the original target response as the computational effort spent in the reliability procedure increases. This paper intends to develop a method that incorporates the information from approximate solutions to yield efficient and consistent reliability estimates. The governing formula is developed using the Theorem of Total Probability to relate information provided by approximate solutions to the target reliability. The method is applied to studying first passage reliability of structures subjected to stochastic loadings.