Automated inspection plays a critical role in many industrial processes, including modern assembly lines. In these processes, components are inspected to ensure adherence to design specifications. Components that are determined to be out-of-specifications are rejected. The benefits of inspection are two-fold. First, defects can be removed early in the process, preventing higher costs incurred in detecting them downstream. Second, the inspection results provide information for manual troubleshooting of root-causes, potentially leading to an improvement in overall quality. However, this form of inspection may also incurs costs if there are false alarms associated with the automated inspection method. Analysis of false alarm costs are rarely addressed in the data mining literature. In this paper, we develop a simple framework to estimate the value of an inspection process, and demonstrate how predictive modeling can be used to increase this value under the right circumstances. In the second part of the paper, we report results from a case-study at a Bosch manufacturing plant, involving tens of thousands of parts and hundreds of quality attributes. A key challenge in this study was the extremely low rate of defects resulting from the operation of a highly-optimized manufacturing process. We show that for such modern assembly lines, machine learning techniques that are robust to class imbalance are particularly well suited. The solution from the case-study yields a positive ROI for the manufacturing plant.