### Abstract

Computation of sensitivities of the 'system' failure probability with respect to various parameters is essential in reliability based design optimization (RBDO) and uncertainty/risk management of a complex engineering system. The system failure event is defined as a logical function of multiple component events representing failure modes, locations or time points. Recently, the sequential compounding method (SCM) was developed for efficient calculations of the probabilities of large-size, general system events for a wide range of correlation properties. To facilitate the use of SCM in RBDO and uncertainty/risk management under a constraint on the system failure probability, a method, termed as Chun-Song-Paulino (CSP) method, is developed in this paper to compute parameter sensitivities of system failure probability using SCM. For a parallel or series system, the derivative of the system failure probability with respect to the reliability index is analytically derived at the last step of the sequential compounding. For a general system, the sensitivity of the probability of the set involving the component of interest and the sensitivity of the system failure probability with respect to the super-component representing the set are computed respectively using the CSP method and combined by the chain-rule. The CSP method is illustrated by numerical examples, and successfully tested by examples covering a wide range of system event types, reliability indices, number of components, and correlation properties. The method is also applied to compute the sensitivity of the first-passage probability of a building structure under stochastic excitations, modeled by use of finite elements.

Original language | English (US) |
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Pages (from-to) | 26-36 |

Number of pages | 11 |

Journal | Structural Safety |

Volume | 55 |

DOIs | |

State | Published - Jul 1 2015 |

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### Keywords

- First-passage probability
- Parameter sensitivity
- Reliability based design optimization
- Sequential compounding method
- System reliability

### ASJC Scopus subject areas

- Civil and Structural Engineering
- Building and Construction
- Safety, Risk, Reliability and Quality

### Cite this

*Structural Safety*,

*55*, 26-36. https://doi.org/10.1016/j.strusafe.2015.02.001