## 3 Analysis and Discussion  
The GRA is conditioned by the data results, which was inducted out following the previous step. First, based on the target of the response output, in this study, normalization was presented according to the \"smaller is better\" approach. Second, divergence from the relation list was computed. Next, the GRC of each experiment were computed. Finally, the mean value of the GRG for the surface roughness, uncut fiber, and delamination were computed using Equations (3)-(9). The result is illustrated in Table 4.  
The GRG with highest value was always yearned. It was presented that the drilling parameter of the 25 th experiment had the highest, with a grey relation grade of 0.923, as shown in Table 4 and  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{\begin{tabular}{c} **Exp.** \\ **no.** \\ \end{tabular} } & \multicolumn{3}{c}{**Parameter Input**} & \multicolumn{3}{c}{**Measurement Output**} & \multicolumn{3}{c}{**Grey Relation Coefficient**} & \multicolumn{3}{c}{**Grey Relation Grade**} \\ \cline{2-11}  & **L** & **T** & **F** & **U\({}_{\text{c}}\)** & \begin{tabular}{c} **Surface** \\ **Roughness (R\_)** \\ \end{tabular} & \(\text{D}_{\text{L}}\) & \
\begin{tabular}{c} **Uncut** \\ **Fiber (U\({}_{\text{c}}\))** \\ \end{tabular} & \(\text{R}_{\text{a}}\) &
\begin{tabular}{c} **Delamination** \\ **(D\({}_{\text{L}}\))** \\ \end{  
==WARNING: Truncated because of repetitions==
Matrix Y=\(\left(w_{v}p_{nr}\right)_{m\text{\tiny{CM}}}\)**} \\ \cline{2-10}  & \multicolumn{3}{c}{**GRC**} & \multicolumn{3}{c}{**Attribute**} & \multicolumn{3}{c}{**Attribute**} \\ \cline{2-10}  & \(\mathbf{U_{c}}\) & \(\mathbf{R_{a}}\) & \(\mathbf{D_{L}}\) & \(\mathbf{U_{c}}\) & \(\mathbf{R_{a}}\) & \(\mathbf{D_{L}}\) & \(\mathbf{U_{c}}\) & \(\mathbf{R_{a}}\) & \(\mathbf{D_{L}}\) \\ \hline  
+++  
The S/N ratio data and raw data provided the same optimal level by drawing the main effects plot. The result is illustrated in Figure 9.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Experiment No** & \(F_{U}^{+}\) & \(F_{U}^{-}\) & \(C_{u}\) & **Rank** \\ \hline  
\hline \hline \end{tabular}
\end{table}
Table 7: Nearness coefficient values and alternative ranking.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Level** & \multicolumn{3}{c}{**Parameter**} \\ \cline{2-4}  & **Lubrication** & **Twist Angle** & **Feed Rate** \\ \hline
1 & \(-\)18.250 & \(-\)11.321 & \(-\)6.992 \\
2 & \(-\)10.881 & \(-\)16.334 & \(-\)10.487 \\
3 & \(-\)3.069 & \(-\)4.545 & \(-\)14.721 \\ Delta & 15.180 & 11.789 & 7.729 \\ Rank & 1 & 2 & 3 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Main response table of correlation to the ideal solution (\(C_{u}\)).  
Analysis of variance (ANOVA) was applied to verify the essential level of the parameter input influencing the multi-response output of the CFRP drilling process. The referred confidence and significance level were 0.95 and 0.05, respectively.  
As shown in Table 9, the lubrication, twist angle, and feed rate were remarkable factors, and the interaction of the lubrication and twist angle also had significant value. The lubrication had the highest contribution ratio at 52.88%. Therefore, the cryogenic gas had the most significant impact on the quality of the drilling hole based on the preferred criterion output. The contribution ratio of the twist angle and feed rate was at 26.10% and 8.43%, respectively. R squared was observed at 96.88%, which means this linear regression model was suitable for the data set at 96.88%.