### Abstract

This paper presents a methodology to calculate probabilities of failure using Probabilistic Support Vector Machines (PSVMs). Support Vector Machines (SVMs) have recently gained attention for reliability assessment because of several inherent advantages. Specifically, SVMs allow one to construct explicitly the boundary of a failure domain. In addition, they provide a technical solution for problems with discontinuities, binary responses, and multiple failure modes. However, the basic SVM boundary might be inaccurate; therefore leading to erroneous probability of failure estimates. This paper proposes to account for the inaccuracies of the SVM boundary in the calculation of the Monte Carlo-based probability of failure. This is achieved using a PSVM which provides the probability of misclassification of Monte Carlo samples. The probability of failure estimate is based on a new sigmoidbased PSVM model along with the identification of a region where the probability of misclassification is large. The PSVM-based probabilities of failure are, by construction, always more conservative than the deterministic SVM-based probability estimates.

Original language | English (US) |
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Pages (from-to) | 156-173 |

Number of pages | 18 |

Journal | International Journal of Reliability and Safety |

Volume | 7 |

Issue number | 2 |

DOIs | |

State | Published - Sep 26 2013 |

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### Keywords

- Discontinuous and binary behaviour
- Multiple failure modes
- Probabilistic support vector machines
- Probability of failure
- Probability of misclassification

### ASJC Scopus subject areas

- Safety, Risk, Reliability and Quality