Local Sensitivity of Failure Probability through Polynomial Regression and Importance Sampling

Marie Chiron, Jérôme Morio () and Sylvain Dubreuil
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Marie Chiron: ONERA/DTIS, Université de Toulouse, F-31055 Toulouse, France
Jérôme Morio: ONERA/DTIS, Université de Toulouse, F-31055 Toulouse, France
Sylvain Dubreuil: ONERA/DTIS, Université de Toulouse, F-31055 Toulouse, France

Mathematics, 2023, vol. 11, issue 20, 1-19

Abstract: Evaluating the failure probability of a system is essential in order to assess its reliability. This probability may significantly depend on deterministic parameters such as distribution parameters or design parameters. The sensitivity of the failure probability with regard to these parameters is then critical for the reliability analysis of the system or in reliability-based design optimization. Here, we introduce a new approach to estimate the failure probability derivatives with respect to deterministic inputs, where the bias can be controlled and the simulation budget is kept low. The sensitivity estimate is obtained as a byproduct of a heteroscedastic polynomial regression with a database built with simulation methods. The polynomial comes from a Taylor series expansion of the approximated sensitivity domain integral obtained with the Weak approach. This new methodology is applied to two engineering use cases with the importance sampling strategy.

Keywords: failure probability; reliability-based sensitivity analysis; local sensitivity; heteroscedastic polynomial regression (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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