Despite the broad adoption of robotic welding, automated quality assessment of the resulting welds is still in its infancy and therefore quality checks are commonly performed by human experts. In this study, we conduct quality testing simultaneously with the welding process (online). For this purpose, a camera positioned behind the welding head provides images of the weld pool and parts of the solidified bead, which is tracked in successive frames. We suggest a weld bead segmentation algorithm, which links the outcome of several local hough transforms with two spline functions in each frame. The actual quality assessment is based on shape features, which can easily be extracted from the segmented weld bead. We propose several distance measures (e.g., dynamic time warping) enabling a comparison between the currently observed weld bead and a reference. Additionally, we suggest variance-based ad hoc quality measures, making reference information expendable. A novel database featuring a large variety of welding tasks, materials and sources of error forms the basis of our experiments. An evaluation of the proposed online quality assessment framework yielding an equal error rate of less than 3 %, based on more than 250 single welds, corroborates the robustness of the approach.