Large-scale manufacturers aim to reduce the number of faulty products by finding tools or process factors that cause product faults through tool monitoring. The causes of faulty electronic components such as semiconductor chips and printed circuit boards (PCBs) include abnormalities in single tools and abnormalities caused by interactions between the tools of a specific process and a related process. Here, the tools exhibiting an interaction effect are called the fault-introducing tool group. This study presents a numerical association rule mining method for discovering the fault-introducing tool groups based on a genetic algorithm. A novel fitness function and rule pruning process are developed to identify the fault-introducing tool groups. The effectiveness of the method is verified using simulations and a case study of actual PCB production lines. The proposed method can discover fault-introducing tool groups better than machine learning algorithms. Additionally, the method can accurately identify fault-introducing tool groups in various manufacturing environments, such as those with highly skewed yield distributions or variations in yield distributions over time. In an actual PCB production line, the groups identified by the proposed method produced up to 36.5% more faulty chips than those identified by the comparison models.