Beam quality in accelerator transport lines can be significantly degraded by component imperfections such as alignment errors, magnetic field deviations, and rf phase fluctuations. In complex accelerator systems, accurately quantifying the influence of these errors and their interactions is essential for performance optimization. In this study, a variance-based global sensitivity analysis using the Sobol method is applied to the medium energy beam transport section of the CAFe facility to systematically evaluate the impact of multiple error sources on key beam quality metrics, including centroid position, envelope, Twiss parameters, and emittance. Two complementary strategies are employed: a component-level analysis that considers all error types of each element collectively, and an individual-error analysis that examines each source separately. The results show that centroid, envelope, and Twiss parameters are primarily influenced by independent error contributions, dominated by quadrupole translational and magnetic field strength errors, whereas emittance change arises from strong coupling among multiple sources. The model-independent nature of the Sobol method enables comprehensive exploration of parameter interactions, allowing clear identification of the most influential errors and providing guidance for tolerance definition, targeted correction, and system optimization. This work highlights the potential of global sensitivity analysis as a powerful framework for performance evaluation in accelerator design, commissioning, and operation.