## 3 Results  
### DoE Results  
The full factorial experiment was performed by adding one center point to the third level with two factors. The total number of test points is nine, and the total number of tests is 81, which can be obtained by extracting three samples per test point and repeating them thrice. Table 2 represents the level and range of the input variables. In this study, statistical software (Minitab 18) was used for the analysis of the base of RSM as previously described in Equations (1)-(4) (see Section 2.5). Based on the experimental results, the analysis of variance (ANOVA) of the response surface custom design was conducted to understand how the selected IVs influence the ORVs. The results of the analysis are shown in Table 3. If the \(p\)-value is less than 0.05, it is considered statistically significant; R\({}^{2}\) represents the coefficient of regression, which is deemed better as it increases in value. In the case of Y1 (TDD), Y2 (SZD), and Y3 (yield), the \(p\)-value of the model was less than 0.05, which was significant. In addition, the R\({}^{2}\) value was  
Figure 3: Overview of Robust Optimization Approach. over 80%, so the regression model was highly explained. On the other hand, in the case of Y4 (solid flour), the \(p\)-value of the model was 0.11, indicating no significant effect. In addition, we analyzed the variances generated by repeated experiments. In all results, the \(p\)-value was greater than 0.05, indicating that it was not statistically significant. In conclusion, based on the ANOVA results, Y1 (TDD), Y2 (SZD), and Y3 (yield) were optimized except for Y4 (solid flour), which were not statistically significant. To derive DS, first, fix the two factors of IVs to the X-axis and Y-axis. Next, we analyze all cases of overlapping with one remaining factor and various levels. Then, after confirming that a designable area that satisfies the upper and lower limits of the output response variable is derived, the final overlap contour plot is also derived. The derivation of DS in this study used the statistical software Design Expert Version 12. Figures 4-6 show the contour plots of X1, X2, and X3, respectively. In Figures 4-6, there is no case where a designable area is derived when all three levels (\(-1\), \(0\), \(+1\)) overlap. This is because there are many upper and lower limits to be satisfied due to a multitude of output response variables, as well as large variances in the experiment. To improve this condition, it was decided to set the X3 (filter paper size) to \(-1\) level and set the X- and Y-axes to X1 (extraction temperature) and X2 (circulation velocity), respectively. Figure 7 shows the overlapping contour plots derived by applying the 95% confidence interval. The yellow area is the designable area and the gray area is outside the upper and lower limits. In Figure 7, there is a yellow area, but it is overlaid by the gray area, which means that there is no designable area. The reason for this appeared to be due to the variance of the experimental results. \begin{table}
\begin{tabular}{c c c c} \hline \multirow{2}{*}{**Level**} & \multicolumn{3}{c}{**Input Factors**} \\ \cline{2-4}  & \multicolumn{1}{c}{\(\mathbf{X_{1}}\)} & \(\mathbf{X_{2}}\) & \(\mathbf{X_{3}}\) \\  & \multicolumn{1}{c}{**(Extraction Temperature)**} & \multicolumn{1}{c}{**(Circulation Velocity)**} & **(Filter Paper Size)** \\ \hline \(-1\) & 5 & 0 & 2.5 \\ \(0\) & 25 & 100 & 6 \\ \(+1\) & 45 & 200 & 8 \\ \hline \end{tabular}
\end{table} 
Table 2: Level and range of IVs. Figure 4: Contour plot with X1 (extraction temperature) fixed at \(-1\), \(0\), \(+1\) levels. \begin{table}
\begin{tabular}{c c c c} \hline \multicolumn{2}{c}{**ORVs**} & \multicolumn{1}{c}{_p-Value_} & **R2** \\ \hline Y1 (TDD) & AU & 0.00 & 84.87\% \\  & Area & 0.03 & 42.05\% \\ \hline Y2 (SZD) & AU & 0.00 & 87.42\% \\  & Area & 0.03 & 47.35\% \\ \hline Y3 (Yield) & 0.00 & 86.40\% \\ \hline Y4 (Solid flour 60\%) & 0.11 & 28.36\% \\ \hline \end{tabular}
\end{table} 
Table 3: Response surface analysis result.