## Abstract

The present paper presents a new scheme for probability integral solution for system reliability analysis, which takes basis in the approaches by Naess et al. (2009) and Bucher (2009). The idea is to evaluate the probability integral by extrapolation, based on a sequence of MC approximations of integrals with scaled domains. The performance of this class of approximation depends on the approach

applied for the scaling and the functional form utilized for the extrapolation. A scheme for this task is derived here taking basis in the theory of asymptotic solutions to multinormal probability integrals. The scheme is extended so that it can be applied to cases where the asymptotic property may not be valid and/or the random variables are not normally distributed. The performance of the scheme is investigated by four principal series and parallel systems and some practical examples. The results indicate that the proposed scheme is efficient and adds to generality for this class of approximations for

probability integrals.

applied for the scaling and the functional form utilized for the extrapolation. A scheme for this task is derived here taking basis in the theory of asymptotic solutions to multinormal probability integrals. The scheme is extended so that it can be applied to cases where the asymptotic property may not be valid and/or the random variables are not normally distributed. The performance of the scheme is investigated by four principal series and parallel systems and some practical examples. The results indicate that the proposed scheme is efficient and adds to generality for this class of approximations for

probability integrals.

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

Journal | Advances in Structural Engineering |

Volume | 15 |

Issue number | 11 |

Number of pages | 19 |

ISSN | 1369-4332 |

Publication status | Published - 2012 |

## Keywords

- System reliability
- Scaled probability integrals
- Asymptotic Laplace integral solutions
- Monte Carlo simulations
- Meta-level representation
- Extrapolation scheme