The analysis of small failure probability in the overall longitudinal strength of a ship's hull structure is a complex, high-dimensional and time-consuming task which is challenging to calculate accurately using traditional reliability analysis methods. To address the precise calculation of small failure probabilities in the reliability analysis of complex structures, this paper establishes a computational process for assessing structural small failure probabilities.

The subset simulation method is used to reduce the overall sample demand. Samples within each subset are generated through Markov Chain Monte Carlo (MCMC) sampling to cover all scenarios within the sample space, and precise computations are performed on these samples using the stochastic finite element method (SFEM), resulting in accurate sample response values which enhance the accuracy of the failure probability calculations. Furthermore, the introduction of the dynamic Kriging surrogate model significantly reduces the number of FEM computations within each subset.

The process is applied to a case study on the reliability analysis of an icebreaker's hull structure, and the analyzed lifecycle structural failure probability is 9.58 × 10^-6.

The accuracy and efficiency of the proposed method are validated through comparisons with the computational results under various parameter settings.