SORM applied to hierarchical parallel system

The old hierarchical stochastic load combination model of Ferry Borges and Castanheta and the corresponding problem of determining the distribution of the extreme random load effect is the inspiration to this paper. The evaluation of the distribution function of the extreme value by use of a particular first order reliability method (FORM) was first described in a celebrated paper by Rackwitz and Fiessler more than a quarter of a century ago. The method has become known as the Rackwitz-Fiessler algorithm. The original RF-algorithm as applied to a hierarchical random variable model is recapitulated so that a simple but quite effective accuracy improving calculation can be explained. A limit state curvature correction factor on the probability approximation is obtained from the final stop results of the RF-algorithm. This correction factor is based on Breitung’s asymptotic formula for second order reliability evaluation (asymptotic SORM). Example calculations with comparisons with simulated results show a surprisingly good accuracy improvement also in cases where the FORM results are grossly in error.