In order to quantify the capacity of stay cables to resist construction errors during installation and hence improve the constructability of cable-stayed bridges in industrialized construction processes, an interval inversion framework for mining the performance of assembly tolerance was proposed. The lower bound of interval reliability index was used to describe the extreme interference of multi-source uncertainty, and the inversion process was solved as a multi-objective optimization problem with reliability constraints. A decoupling prediction algorithm based on machine learning was developed, with the direct mapping of the worst-case reliability index realized by integrating finite element calculation, reliability boundary prediction, and surrogate models. The fault-tolerant planning for the cable stretching process of a real-scale cable-stayed bridge was carried out. Results show that when uncertainties were reasonably quantified, the maximum allowable tension errors of target cables ranged from 217.4 to 317.3 kN, with an anti-error rate of 7.29% to 12.98%. The interval inversion method proposed in this paper avoids the huge computational effort required by multi-loop nested optimization. On the premise of ensuring structural reliability and design optimality, the compatibility and controllability of the on-site tensioning process can be effectively improved.