An algorithm for finding a sequence of design points in reliability analysis

In the analysis of structural reliability, often a sequence of design points associated with a set of thresholds are sought in order to determine the tail distribution of a response quantity. In this paper, after a brief review of methods for determining the design point, an inverse reliability method named the λ-method is introduced for efficiently determining the sequence of design points. The λ-method uses Broyden's "good" method to solve a set of nonlinear simultaneous equations to find the design points for the values of an implicitly defined threshold that is associated with parameter λ. In a special parameter setting, the λ parameter equals the reliability index, thus allowing convenient implementation of the method. Three numerical examples illustrate the accuracy and efficiency of the proposed method.