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For the reliability analysis of complex engineering structures, the estimation of the bounds of failure probability with interval distribution parameters is an important task when the perfect information of random variables is unavailable and the corresponding probability distributions are imprecise. The present work proposes an active learning Kriging‐based method combining with adaptive radial based importance sampling to compute the bounds of failure probability. For computing the bounds, the classical double‐loop optimization model is always investigated in the standard normal space. To decouple the computation, the inner‐loop optimization is addressed with the monotonicity of the commonly used probability distributions. When suffering the high dimensional problem, the dimension reduction method is introduced in monotonic analysis. While for the outer‐loop optimization, the normal space is decomposed with spheres, then the proposed method with an adaptive updated procedure is given. With this method, the bounds of failure probability can be estimated efficiently, especial for the rare event. Numerical examples are investigated to validate the rationality and superiority of the proposed method. Finally, the proposed method is applied to the reliability analysis of turbine blade and aeronautical hydraulic pipeline system with interval distribution parameters.

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