## 6 Conclusions  
In this paper, we have proposed a DCGAN-based model as an effective way to augment defect patterns to improve the WBM defect pattern classification performance in WBM data where class imbalance in datasets is extremely severe. To confirm the effectiveness of the proposed method, the WBMs generated through two augmented methods trained using real-world data generated in the semiconductor manufacturing process were compared in terms of the pattern classification accuracy and the effectiveness of each augmented method. We have proposed a new quantitative index called the PGI to compare the effects of the augmented models. We have also proposed a masking process as a method for solving the problem of the quality degradation of augmented WBMs due to the tendency to augment by focusing on the defect pattern characteristics on wafers rather than absolute coordinates, which is one of the drawbacks of DCGAN-based models. In the masking process, the augmented WBMs were refined using a masking wafer. We experimentally confirmed that DCGAN-based models can be applied to address the extreme data imbalance problem which is common in industrial data. The experimental results show that the accuracy of each defect pattern of the classifier trained using WBMs generated by the DCGAN-based model was always higher than that of the classifier trained using WBMs generated by the CAE-based model, on average about 14.26% higher for all defect patterns. Furthermore, the experiments show that WBMs augmented with CAE-based models are fully classified into defect patterns by classifiers trained with DCGAN-based augmented wafers, while some of the WBMs augmented with DCGAN-based models are not accurately classified by the classifier trained with CAE-based models. These results intuitively demonstrate that the DCGAN-based model formed various defect patterns which were better than the CAE-based model. Furthermore, we quantitatively evaluated the improvement efficiency of each augmentation model through the proposed evaluation index. The proposed evaluation index, PGI, does not require a pre-trained model such as Inception v3 to calculate the index. In addition, the PGI has the advantage that calculation is simple and intuitive, as well as relatively free from the demand for a large amount of original sample data, as required for index evaluation such as FID. The PGI can be used as an evaluation index for image generation models specialized for specific domains, such as industrial data, where it is difficult to use a pre-trained model based on the ImageNet dataset. The proposed index is expected to be used for a quantitative evaluation of augmentation models in cases such as extremely small and imbalanced industrial data, for which it is difficult to use existing evaluation indicators such as FID or IS. Through experimental results, we have shown that the proposed DCGAN-based augmentation model produced a better performance than the CAE-based augmentation model. However, the PGI has the following issues:  
* When \(N_{Defect}=1\), the PGI cannot exceed 1. In this case, it is difficult for the PGI to reflect how various defect patterns can be formed by the augmentation model. * When \(PGI=N_{Defect}/N_{Augment}\), it is difficult for the PGI to indicate how many more diverse defect patterns the augmented model can form. In this case, the PGI can be considered to have a value greater than or equal to at least \(N_{Defect}/N_{Augment}\). * The PGI depends on the performance of the classification model. When images generated from the same augmentation model are used to train classification modelscomposed of different structures, PGIs may differ depending on the structure of the classification model. Therefore, in order to compare the PGIs of different augmentation models, the results calculated from the same classification model should be used. Nevertheless, due to the aforementioned advantages, the PGI is an effective quantitative evaluation metric for generative models.