Among the various types of faults in battery systems, connection faults are among the most common and serious. Accurate diagnosis of connection faults is crucial for improving the safety and performance of battery systems, as undetected connection faults can lead to inefficiencies, potential failures, and safety hazards. This study proposes a novel quantitative diagnosis method for detecting connection faults using incremental capacity (IC) curves and correlation analysis. Firstly, the morphological changes in the IC curves caused by connection faults at various charging rates are analyzed. Next, correlation analysis between the IC curves of adjacent cycles is performed to quantify the translation degree caused by connection faults. This allows for the estimation of fault resistance. Finally, experiments are conducted to verify the proposed diagnostic methods, demonstrating high precision in connection fault detection. The proposed method enables rapid diagnosis of battery connection faults across various charging rates, showing excellent potential for real applications in battery management systems.