Global failure probability function estimation based on an adaptive strategy and combination algorithm

Xiukai Yuan, Yugeng Qian, Jingqiang Chen, Matthias G.R. Faes, Marcos A. Valdebenito, Michael Beer

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


The failure probability function (FPF) expresses the probability of failure as a function of the distribution parameters associated with the random variables of a reliability problem. Knowledge on this FPF is of much relevance for reliability sensitivity analysis and reliability-based design optimisation. However, its calculation is usually a challenging task. Therefore, this paper presents an efficient approach for estimating the FPF based on an adaptive strategy and a combination algorithm. The proposed approach involves three basic elements: (1) a Weighted Importance Sampling approach, which allows determining local FPF estimates; (2) an adaptive strategy for determining at which realisations of the distribution parameters it is necessary to perform local FPF estimation; and (3) an optimal combination algorithm, which allows to aggregate local FPF estimations together to form a global estimate of the FPF. Test and practical examples are presented to demonstrate the efficiency and feasibility of the proposed approach.

Original languageEnglish
Article number108937
JournalReliability Engineering and System Safety
StatePublished - Mar 2023
Externally publishedYes


  • Adaptive strategy
  • Combination algorithm
  • Failure probability function
  • Importance sampling


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