针对非参数化概率盒的可靠性分析问题，提出了一种基于贝叶斯主动学习的自适应离散累积分布函数的可靠性分析方法，用于高效求解失效概率边界。首先，采用贝叶斯主动学习框架训练高斯过程代理模型，替代概率积分过程中的功能函数调用；其次，推导该积分关于离散网格间距的误差显式表达式，建立数值积分误差上界的定量估计；再次，提出基于综合误差估计器的自适应离散准则，将新增节点配置于对失效概率边界精度影响最大的子区间，实现离散化计算资源的局部最优分配；最后，在积分误差上界控制的收敛准则下，求解失效概率的收敛上下界。数值算例验证了所提方法的有效性与高效性。

Focusing on reliability analysis of nonparametric probability boxes, an adaptive discrete cumulative distribution function method based on Bayesian active learning is proposed to efficiently estimate failure probability bounds. First, a Bayesian active learning framework is employed to train a Gaussian Process (GP) surrogate model, replacing direct functional evaluations in the probability integration process. Second, an explicit expression for the error induced by discretization grid spacing is derived, establishing a quantitative estimation of the numerical integration error bound. Third, an adaptive discretization criterion based on a comprehensive error estimator is developed; this criterion allocates new nodes to subintervals that most significantly impact the accuracy of failure probability bounds, achieving a locally optimal allocation of computational resources. Finally, under a convergence criterion controlled by the upper bound of integration error, convergent upper and lower bounds of the failure probability are obtained. Numerical examples demonstrate the effectiveness and efficiency of the proposed method.