Structural reliability analysis, when accounting for non-parameterized probability box (P-box) uncertainty, typically entails multiple calls to performance functions and poses significant computational hurdles, largely attributable to its inherently nested double-loop structure. Therefore, this paper proposes a new reliability analysis method tailored for structures with uncertain parameters represented using non-parameterized P-boxes. This method leverages double-loop deep learning models to efficiently calculate both the upper and lower bounds of the failure probability. In the development p...