## 4 Experimental Results
### Performance Evaluation
#### 4.3.3 Comparison of PGI  
Table 10 shows the PGI for each augmentation method calculated according to the results of Tables 6 and 7 in Section 4.3.1, above. The selection rate in Table 10 refers to the ratio of WBM used for augmentation to the number of original WBMs for each defect pattern. As shown in Table 10, the DCGAN-based model had the same or higher PGI compared to \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Actual** & **Predicted** & **Center** & **Donut** & **Edge-Loc** & **Edge-Ring** & **Loc** & **Near-Full** & **Random** & **Scratch** & **None** \\ \hline Center & \begin{tabular}{c} 500 \\ (100\%) \\ \end{tabular} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\  & 0 & \begin{tabular}{c} 500 \\ (100\%) \\ \end{tabular} & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\  & 0 & \begin{tabular}{c} 500 \\ (100\%) \\ \end{tabular} & 0 & 0 & 0 & 0 & 0 & 0 & (0\%) \\  & 0 & \begin{tabular}{c} 500 \\ (100\%) \\ \end{tabular} & 0 & 0 & 0 & 0 & 0 & 0 & (0\%) \\  & 0 & \begin{tabular}{c} 500 \\ (100\%) \\ \end{tabular} & 0 & 0 & 0 & 0 & 0 & 0 & (0\%) \\  & 0 & \begin{tabular}{c} 500 \\ (100\%) \\ \end{tabular} & 0 & 0 & 0 & 0 & 0 & 0 & (0\%) \\  & 0 & \begin{tabular}{c} 0 \\ (100\%) \\ \end{tabular} & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\  & 0 & \begin{tabular}{c} 0 \\ (100\%) \\ \end{tabular} & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\  & 0 & \
\begin{tabular}{c} 0 \\ (100\%) \\ \end{tabular} & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\  & 0 &
\begin{tabular}{c} 0 \\ (99.6\%) \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Confusion matrix of the classifier trained with data augmented by DCGAN-based model when using data augmented by CAE-based model as a validation dataset. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  
the case of the CAE-based model for all defect patterns. Notably, there was no correlation between the PGI and the proportion of the original WBMs used for augmentation. There are several limitations of the PGI when the quantity of the original data is highly scarce. First, as seen in the 'donut' defect pattern, the PGI cannot exceed 1 when \(N_{Defect}=1\), where \(N_{Defect}\) is the number of WBMs used to generate each defect pattern. In this case, it is difficult to use the PGI as an indicator reflecting how many distinct defect patterns the augmentation model can form. Moreover, it is difficult for the PGI to reveal how many more diverse defect patterns can be formed by augmented models, even when augmented results using only some defect patterns can generate accurately classifiable data for all original defect patterns not used for augmentation, as in the case of 'near-full' patterns. In other words, the PGI cannot be regarded as a true PGI. In this case, PGI may be considered to have a value of PGI \(>N_{Defect}/N_{Augment}\). To alleviate the problem of PGI not reflecting a true PGI, we recommend referring to the results produced via verifying each augmented data entry using classification models trained using different augmented models, such as those in the experiments outlined in Tables 8 and 9. Despite the limitations of the PGI listed above, it remains an effective index for the performance evaluation of augmented models. The PGI has the following advantages: first, it is simple and intuitive to calculate. As mentioned in Section 3.6, FID and IS are the typical metrics used to evaluate the performance of GAN-based generative models. However, these calculations require pre-trained models, such as the Inception v3 model. The PGI does not require an additional model for calculation. A large amount of sample data is required to evaluate the FID. Due to the nature of industrial sites, it is difficult to obtain a true FID because it is difficult to obtain sufficient abnormal data. Therefore, it may be difficult to use the FID as an evaluation index of the generation model. The calculation of the PGI uses relatively fewer sample data compared to FID.