Ensuring the quality of printed circuit boards (PCBs) in gas meters is essential to the reliable operation and safety of these devices. Traditional methods for detecting welding defects on PCBs, such as machine vision and deep learning, present significant limitations. Machine vision-based approaches lack the precision required in complex environments, while deep learning methods demand large, labeled datasets that are costly and impractical in industrial contexts. This paper introduces a novel melding defect detection method based on discrete optimal transport (DOT) theory, focused on identifying discrepancies in welding areas between sample and reference images. By limiting analysis to the welding regions, the proposed approach reduces computational costs associated with high-resolution image processing while maintaining detection precision and independence from large datasets. The DOT model calculates the optimal mass flow between images, pinpointing specific defects and providing actionable insights for defect tracing and repair, thereby overcoming the limitations of existing methods. Experimental results demonstrate that this approach is both effective and efficient, offering a robust solution for quality assurance in PCB manufacturing for gas meters.