## 2 Materials and Methods
### Limit-Data Generating Process
#### 2.2.1 Synthetic Minority Oversampling Technique-Nominal Continuous (SmoteNC)
The experiment results revealed that prior to oversampling, the recall rate of the proposed method was approximately 0. This result suggests that the equipment exhibits normal operation; thus, the possibility of equipment failure can be ignored. The experiment results for RNF prediction revealed that most methods did not exhibit favorable prediction results. Despite achieving a recall rate of 85.71%, the proposed method generated an excessive number of false alarms, possibly due to the insufficient scope of data collection. To overcome this problem, an IoT sensor can be attached to the equipment, or the collected data can be expanded. In the future, the authors of this study will analyze the reason for the aforementioned problem and collect operation data according to the identified reason. Finally, the multicategory prediction results revealed that some categories of equipment failure correlated. Due to the overlap of the categories, they could not be effectively separated. This problem is commonly encountered in equipment failure prediction. To solve this problem, a new failure category can be established to relabel correlating failure categories, thereby increasing the failure prediction accuracy of the proposed method. ### Necessity of Processing Data with Hybrid Features in Limited Data Sets

The categorical data features of a product include product type. This information is crucial to the prediction of equipment failure. Different product types require drastically different allocations of production resources and sensor values. Therefore, processing data with hybrid features in limited data sets is essential. ### Interpretability of the Equipment Failure Prediction Results

In this study, a tree-based model was selected for failure prediction. This model has a certain degree of interpretability and can be used for problem analysis, correctly predicting failures, and analyzing the causes of failures. The results of equipment failure \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Recall Rate** & **Accuracy** & **Balanced Accuracy** \\ \hline CatBoost (non-oversampling) & 0.2868 & **0.9687** & 0.6423 \\ SmoteNC + CatBoost & 0.7881 & 0.9670 & 0.8809 \\ ctGAN + CatBoost & 0.8305 & 0.9082 & 0.8708 \\ SmoteNC + ctGAN + CatBoost & **0.9068** & 0.8712 & **0.8883** \\ (The proposed method) & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 17: Results obtained using different methods in multicategory fault diagnosis. prediction can be interpreted using tree algorithms to determine the reason for failure and to implement preventive measures accordingly [33]. Moreover, these results can be interpreted using GAN algorithms [34] to analyze the reason for each minority data class. The aforementioned analysis overcomes the overfitting problem of GAN algorithms. ## 5 Conclusions

In this paper, a method is proposed for predicting limited failure data with high accuracy to overcome the limitations associated with the processing of limited data with hybrid features. The experimental results indicate that the proposed method can improve 6.45% compared to similar methods when equipment failure data account for less than 1% of the total data. The proposed model can simultaneously handle imbalanced data with continuous and categorical features and can fulfill the demand of a ctGAN for considerable training data; thus, the proposed model provides a solution for equipment fault diagnosis by using limited failure data. Moreover, given the interpretability of the tree-based structure used in the proposed method, its results can be easily interpreted, and the reason for failure can be easily determined, thereby improving the maintenance efficiency. Given that equipment deterioration is a time-series problem, failure data might be sequential in nature. Future studies can employ time-series production and prediction models in the failure data generation process to increase the accuracy of the generated data.