In aerospace certification and other safety-critical domains, conservative quantile estimation such as A- and B-basis values is essential to guarantee reliability. While these metrics are traditionally derived from experimental campaigns, this work focuses on their estimation using a validated deterministic numerical model. The problem is formulated under mixed aleatory-epistemic uncertainty, accounting for limited material data, finite sampling effects, and surrogate modeling errors. We propose a methodology for estimating conservative design quantiles with statistical guarantees under mixed uncertainties. The proposed method leverages importance sampling and control variates to achieve accurate and efficient estimates within a fixed computational budget. One key point is the surrogate model's role solely as a variance reduction device, which guarantees unbiased and consistent quantile estimation. By explicitly integrating all sources of uncertainty, the proposed framework provides a numerical alternative to estimate A-basis and B-Basis. Furthermore, Sobol-based sensitivity indices are obtained at no additional cost, offering insight into the dominant epistemic sources. Numerical experiments on structural models demonstrate the method's reliability and computational efficiency. In particular, the application to large-scale industrial simulations confirms its suitability for aerospace certification workflows and highlights its relevance for real world engineering environments.

翻译：在航空航天认证及其他安全关键领域，保守分位数估计（如A基准和B基准值）对保障可靠性至关重要。传统上这些指标通过实验获取，但本研究聚焦于利用经过验证的确定性数值模型进行估计。在混合偶然-认知不确定性框架下，我们综合考虑了材料数据有限性、有限采样效应及替代模型误差等因素。本文提出了一种在混合不确定性条件下具有统计保证的保守设计分位数估计方法。该方法通过重要性采样和控制变量技术，在固定计算预算内实现精确高效估计。关键创新在于将替代模型仅作为方差缩减工具，从而保证分位数估计的无偏性与一致性。通过显式整合所有不确定性来源，该框架为A基准和B基准估计提供了数值替代方案。此外，基于Sobol的灵敏度指标可在不增加额外计算成本的情况下获取，有助于识别主导认知不确定性源。在结构模型上的数值实验验证了方法的可靠性与计算效率，尤其在大规模工业仿真中的应用证实了其适用于航空航天认证流程，凸显了其在真实工程环境中的实用价值。