We analyze the assembly process of electronic devices, in particular the initial deposition of Solder Paste Deposits (SPD) over Printed Circuits Boards (PCB), that will later on provide the necessary fixation for all the electronic components as well as functionalize their operation. In this stage, thousands of SPD's, differing in shape and volume, are quickly and accurately placed in different positions of the PCB's. Monitoring the status of this operation raises very important problems, particularly during the initial production runs, as the number of quality features under monitoring is very large (order of thousands) and the number of samples available quite low (order of dozens). In this work, we propose an efficient approach for addressing the on-line and at-line monitoring of this process, addressing two hierarchically related problems: i) detection of faulty units (PCB's); ii) given that a faulty unit was detected, find a candidate set of SPD's responsible for the anomaly. Our methodology is based on a latent variable framework for effectively extracting the normal behavior of the process from the few reference samples available, and using it to classify the following samples as normal or abnormal and, in this case, analyze why it happens to be so. We have tested the proposed approach with real industrial data, and the results achieved illustrate its good discrimination ability, rendering it very promising for implementation in this class of scenarios.