AK-MCS-C2 : Active Kriging Monte Carlo Simulation method with conformal certification for failure probability estimation

We introduce a novel active-learning framework for failure probability estimation in structural reliability analysis that integrates Active Kriging Monte Carlo simulation with conformal prediction. The proposed approach employs an adaptive cross-conformal strategy specifically designed for small-sample settings and kriging surrogate models using the J+GP conformal estimator. Unlike standard AK-MCS methods, the proposed framework provides distribution-free guarantees on prediction errors, leading to more reliable classification of samples near the limit-state surface. This improved uncertainty quantification enhances both the accuracy and robustness of failure probability estimates, especially for rare-event regimes where such efficiency is crucial. Reproducible numerical results illustrate the effectiveness of the method and also compare it to classical approaches on well-established benchmarks.