### Abstract

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.

Original language | English |
---|---|

Title of host publication | Advances in Reliability and Optimization of Structural Systems |

Place of Publication | London/Leiden/New York/Philadelphia/Singapore |

Publisher | Taylor & Francis/Balkema |

Publication date | 2006 |

Pages | 101-106 |

ISBN (Print) | 04-15-39901-7 |

Publication status | Published - 2006 |

Event | 12th IFIP WG 7.5 Working Conference on Reliability and Optimization of Structural Systems - Aalborg, Denmark Duration: 22 May 2005 → 25 May 2005 |

### Conference

Conference | 12th IFIP WG 7.5 Working Conference on Reliability and Optimization of Structural Systems |
---|---|

Country | Denmark |

City | Aalborg |

Period | 22/05/2005 → 25/05/2005 |

## Cite this

Ditlevsen, O. D. (2006). SORM applied to hierarchical parallel system. In

*Advances in Reliability and Optimization of Structural Systems*(pp. 101-106). Taylor & Francis/Balkema.