## 2 Materials and Methods
### Limit-Data Generating Process
#### 2.2.1 Synthetic Minority Oversampling Technique-Nominal Continuous (SmoteNC)
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Method** & **Recall Rate** & **Accuracy** & **Balanced Accuracy** \\ \hline CatBoost (non-oversampling) & 0.0000 & **0.9979** & 0.5000 \\ SmoteNC + CatBoost & 0.2857 & 0.8615 & 0.5742 \\ ctGAN + CatBoost & 0.0000 & 0.9882 & 0.4951 \\ SmoteNC + ctGAN + CatBoost & **0.8571** & 0.4206 & **0.6384** \\ \hline \hline \end{tabular}
\end{table} 
Table 16: Prediction results obtained for the RNF diagnosis using other methods used for processing limited data. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Method** & **Recall Rate** & **Accuracy** & **Balanced Accuracy** \\ \hline CatBoost (non-oversampling) & 0.4857 & **0.9942** & 0.7427 \\ SmoteNC + CatBoost & 1.0000 & 0.9579 & 0.9787 \\ ctGAN + CatBoost & 1.0000 & 0.9715 & 0.9856 \\ SmoteNC + ctGAN + CatBoost & **1.0000** & 0.9758 & **0.9877** \\ (The proposed method) &
\begin{tabular}{c} **1.0000** \\ \end{tabular} & 0.9758 & **0.9877** \\ \hline \hline \end{tabular}
\end{table} 
Table 13: Prediction results obtained for the OSF diagnosis using the confusion matrix. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Method** & **Recall Rate** & **Accuracy** & **Balanced Accuracy** \\ \hline CatBoost (non-oversampling) & 0.5833 & **0.9952** & 0.7915 \\ SmoteNC + CatBoost & 0.9722 & 0.9870 & 0.9797 \\ ctGAN + CatBoost & 0.9722 & 0.9742 & 0.9732 \\ SmoteNC + ctGAN + CatBoost & **1.0000** & 0.9615 & **0.9805** \\ (The proposed method) & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 14: Prediction results obtained for the OSF diagnosis using other methods used for processing limited data. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Method** & **Recall Rate** & **Accuracy** & **Balanced Accuracy** \\ \hline CatBoost (non-oversampling) & 0.4857 & **0.9942** & 0.7427 \\ SmoteNC + CatBoost & 1.0000 & 0.9579 & 0.9787 \\ ctGAN + CatBoost & 1.0000 & 0.9715 & 0.9856 \\ SmoteNC + ctGAN + CatBoost & **1.0000** & 0.9758 & **0.9877** \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Prediction results obtained for the PWF diagnosis using other methods used for processing limited data. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Method** & **Recall Rate** & **Accuracy** & **Balanced Accuracy** \\ \hline CatBoost (non-oversampling) & 0.4857 & **0.9942** & 0.7427 \\ SmoteNC + CatBoost & 1.0000 & 0.9579 & 0.9787 \\ ctGAN + CatBoost & 1.0000 & 0.9715 & 0.9856 \\ SmoteNC + ctGAN + CatBoost & **1.0000** & 0.9758 & **0.9877** \\ \hline \hline \end{tabular}
\end{table} 
Table 13: Prediction results obtained for the OSF diagnosis using the confusion matrix. The results presented in Tables 14-17 indicate that CatBoost classified most data into the normal category and, thus, exhibited a recall rate of 28.68%. SmoteNC + CatBoost exhibited high accuracy in the multicategory prediction but had a relatively low recall rate. ctGAN + CatBoost exhibited a recall rate of 83.05%. Finally, SmoteNC + ctGAN + CatBoost exhibited a recall rate of 90.68% and a balanced accuracy of 88.83%. ## 4 Discussion

Given that the failure data accounted for only 3.4% of the total data and were divided into five failure modes (i.e., 0.5%, 0.9%, 1.2%, 1.0%, and 0.2% of the data were classified into the TWF, HDF, PWF, OSF, and RNF minority classes, respectively), the data were highly imbalanced, which increased the difficulty in failure prediction. The experiment's results indicated that the proposed method was superior to the other methods in the five-category failure classification. Although the proposed method exhibited a high false positive rate, from the equipment diagnosis perspective, the cost of sudden machine downtime considerably exceeds that of system misdiagnosis. ### The Focus of Prediction Is to Detect Equipment Failure, Not Normal Operation

From the perspective of equipment failure prediction, the cost of false negatives considerably exceeds that of false positives. Therefore, this study aimed to increase the possibility of false positives and, thus, reduce the possibility of false negatives.