## 3 Results
### Retro-Feedback for Controlling and Adjusting the Manufacturing Parameters  
As presented in Section 2.3, a system responsible for detecting anomalies must complement a system designed to optimize the process by eliminating the detected problems. Thus, the same section explains how this element of our system of systems completes the described digital twin, closing the loop and providing feedback to the plant to implement the proposed corrective actions.  
After the study conducted on anomaly detection based on predictions using machine learning models (see the previous section), we observed that detection works best in the primary coating stage. Nevertheless, the system was not modified, and all checks are still being performed. Thus, when any anomaly is detected in the first stage, attempts will be made to resolve it. In some cases, the issue may be corrected, while in others, the problem may persist. In the latter case, the current situation is continuously analyzed in subsequent detection and optimization steps. Otherwise, if no failures are found in that stage and the process advances to the next one, the digital twin will perform the checking operation again, continuing this cycle until all validation checkpoints have been passed.  
It should be noted that the importance of this area could change due to modifications in the depth of the learning dataset. Similarly, the recommendations generated could also change depending on the requirements at that time. Even so, the system will need to adapt to new production references and emerging trends. This concludes that the recommendation system must evolve and be adjusted to the changing cycle of a manufacturing process.  
The error rates of the production process where this technology has been deployed are low, not exceeding 12% of the produced parts. Considering the original number of faulty castings, the artificial intelligence-based detection system identified 84% of them in the first stage (primary coating). Practically all of these were subsequently resolved by the recommender system. Thus, in the following checks, the parts remained correct and successfully completed the manufacturing process. A small portion, less than 7% of the detections, progressed to the subsequent checkpoints, where some were detected again and corrected. The proposed corrections generated by the recommender system validated that the production limits defined by engineers were appropriate and that adjusting all parameters to those limits was sufficient to address the detected problems. However, in 2% of cases where a change was triggered, it was necessary to adapt the production ranges to optimize the expected manufactured parts. Consequently, for the same reference, different production levels or trends were required depending on the specific production parameters of each part.  
In the same way, and in an effort to evaluate the computational cost of the advisor system, we measured that the results are computed in less than 0.001 s. Thus, the combination of predictions with optimization does not exceed 1 second. This fact enables the complete proposed system to be used in a real-time investment casting production process.  
In summary, it is a promising system that can be modified in both knowledge and techniques, providing better performance. Nevertheless, the current development has reduced casting rejections to 8%. Moreover, at this moment, aluminum elongation hasimproved, increasing from 3.5% to 4.5%. Hence, despite the good results obtained, we must point out that since the accuracy of the prediction systems is not as high as desired, some faulty parts remain undetected. However, it is important to consider that the system is still in its early stages and does not yet have large volumes of data for training these learning processes. Improving the detection and prediction systems will directly lead to better early detection and more effective application of the corrective actions generated by our recommender system.