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An efficient method for solving system failure probability functions based on subset simulation and probability reanalysis techniques

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  • Wang, Hao
  • Li, Luyi
  • Liu, Junchao
  • Yuan, Xiukai

Abstract

Estimating the system failure probability function (FPF) is critical in reliability-based system design and optimization. However, multiple failure modes in a system challenge the estimation process. The probability reanalysis (PRA) method can estimate failure probabilities under various distribution parameters using only a single set of input-output samples. However, combining it with efficient numerical simulation methods can improve its computational efficiency. This paper combines the importance sampling subset simulation (SS-IS) method with the PRA method to propose the SS-IS-PRA method for estimating the system FPF. The proposed method transforms the system FPF into a product of a series of conditional FPFs. Then, a single set of input-output samples is used to solve conditional FPFs layer by layer based on the PRA approach. Furthermore, this paper introduces an IS center selection strategy based on mixed sampling and K-means clustering to enhance the applicability of the SS-IS-PRA method in multi-failure mode problems without additional computational cost. Finally, an adaptive Kriging surrogate model is embedded within the SS-IS-PRA method to enhance the computational efficiency of SS-IS-PRA and better suit real engineering structure analysis. Hence, the SS-IS-PRA-AK method is obtained. The effectiveness and efficiency of the proposed method are validated through four examples.

Suggested Citation

  • Wang, Hao & Li, Luyi & Liu, Junchao & Yuan, Xiukai, 2025. "An efficient method for solving system failure probability functions based on subset simulation and probability reanalysis techniques," Reliability Engineering and System Safety, Elsevier, vol. 262(C).
    • Handle: RePEc:eee:reensy:v:262:y:2025:i:c:s0951832025004491
    DOI: 10.1016/j.ress.2025.111248
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    References listed on IDEAS

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    1. Li, Zhen & Lu, Zhenzhou, 2026. "Estimating predictive failure probability and its update under newly available observations by a layered cluster importance sampling algorithm," Reliability Engineering and System Safety, Elsevier, vol. 267(PA).

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