## 3 Results
### Primary and Secondary Coating Area Predictions  
As the second phase of the experiment for the ex ante predictive system in the investment casting process, following the same approach as with the classical classifiers, we concatenated the information from the primary and secondary coatings to perform elongation prediction. In this new test (shown in Table 9), we achieved accuracy ratios very similar to those obtained with simple classifiers. In fact, the best algorithm was the \"by vote\" method, which employs the mean of probabilities. Its accuracy was 76.5%, nearly matching the 76.95% achieved with the corresponding Bayesian network. Thus, in search of an even simpler method than the one that produced the best results, the majority voting method again performed comparably to the best meta-classification algorithm. Once again, grading proved to be the most stable method, as indicated by its precision percentages and error rates, all of which followed a consistent performance trend. \begin{table}
\begin{tabular}{l c c c c} \hline
**Classifier** & **Accuracy** & **MAE** & **RMSE** & **AUC** \\ \hline By vote (minimum probability) & 54.62 & 0.25 & 0.46 & 0.58 \\ By vote (maximum probability) & 68.75 & 0.43 & 0.45 & 0.67 \\ By vote (average of probabilities) & 72.32 & 0.37 & 0.44 & 0.70 \\ By vote (product of probabilities) & 54.62 & 0.25 & 0.46 & 0.58 \\ By vote (majority voting) & 71.52 & 0.28 & 0.52 & 0.58 \\ \hline Grading (meta: naive Bayes) & 71.50 & 0.28 & 0.52 & 0.59 \\ Grading (Bayes network–TAN) & 70.77 & 0.29 & 0.52 & 0.59 \\ Grading (meta: K-nearest neighbors with K = 1) & 71.07 & 0.29 & 0.52 & 0.59 \\ Grading (meta: K-nearest neighbors with K = 2) & 71.07 & 0.29 & 0.52 & 0.59 \\ Grading (meta: K-nearest neighbors with K = 3) & 70.39 & 0.30 & 0.53 & 0.57 \\ Grading (meta: K-nearest neighbors with K = 4) & 70.66 & 0.29 & 0.53 & 0.57 \\ Grading (meta: K-nearest neighbors with K = 5) & 70.80 & 0.29 & 0.53 & 0.57 \\ Grading (C4.5) & 70.84 & 0.29 & 0.53 & 0.57 \\ \hline Stacking (meta: naive Bayes) & 61.87 & 0.38 & 0.58 & 0.71 \\ Stacking (Bayes network–TAN) & 69.73 & 0.40 & 0.47 & 0.56 \\ Stacking (meta: K-nearest neighbors with K = 1) & 66.12 & 0.35 & 0.55 & 0.61 \\ Stacking (meta: K-nearest neighbors with K = 2) & 72.39 & 0.34 & 0.49 & 0.63 \\ Stacking (meta: K-nearest neighbors with K = 3) & 69.12 & 0.35 & 0.47 & 0.65 \\ Stacking (meta: K-nearest neighbors with K = 4) & 73.82 & 0.36 & 0.46 & 0.64 \\ Stacking (meta: K-nearest neighbors with K = 5) & 72.12 & 0.36 & 0.45 & 0.64 \\ Stacking (C4.5) & 69.18 & 0.34 & 0.49 & 0.62 \\ \hline
**Multi-scheme (Bayes network–TAN)** & 75.62 & 0.28 & 0.42 & 0.76 \\ \hline \end{tabular}
\end{table} 
Table 8: Results predicting the porosity apparition when we applied a combination of classical machine learning methods through a meta-classifier using data extracted only from the primary coating area. The best meta-classifier, marked in gray, was the multi-scheme method using a TAN Bayesian network with an accuracy level (percentage of correctly classified instances) of close to 75%. Subsequently, performing the same experiment but now focusing on detecting the appearance of shrinkages, we observed that the theoretical basis described in Section 2.2 was correct. The results shown in Table 10 illustrate how the meta-classifiers approximate the performance of the best single classical classifier. The \"by vote\" method (using the mean of probabilities) achieved almost the same performance as the kNN classifier in the original experiment. Moreover, methods such as majority voting, a simple union model, practically match these results, offering a success rate of 70%. Although it achieved a slightly lower accuracy, grading remained the most stable method. In contrast, stacking did not perform as well as the other methods, suggesting that it is not well suited for this specific case.