Estimating the Interval of Failure Probability Fluctuation Under Uncertain Input Variable Distributions

Structural reliability analysis often faces the problem that the input variable distributions are uncertain and thus the interval for reliability measures must be determined. A Monte Carlo simulation consists in estimating the failure probability for several sets of random realizations of the distributions, thus implying a huge computational labor, much higher than in conventional Monte Carlo. In this paper a method for drastically simplifying this task is proposed. The method exploits the ordering statistics representation property of the reliability plot, which is shown to approximately obey an orthogonal hyperbolic pattern. Accordingly a two-level FORM approach is used to derive the polar vectors for building two plots, one for the input variable space and another for the uncertain distribution parameter space. It is demonstrated that the extrema of the failure probability are contained amongst the samples located in extreme sectors of the parameter plot as pointed out by the hyperbolae.