## 3 Results and Discussion
### Optimization of Processing Conditions for Bread Prepared with Flour-Bran Blends at 30% Bran
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{1}{c}{**Response**} & \multicolumn{1}{c}{**Factor (\({}^{1}\))**} & \multicolumn{1}{c}{\(p\)**-Value**} & \multirow{2}{*}{**Model**} \\ \hline \multirow{3}{*}{Bread height} & Water & 0.3747 & \\  & MT & 0.0360 & Quadratic \\  & FT & 0.0844 & \\ \hline \multirow{3}{*}{Bread volume} & Water & 0.0281 & \\  & MT & 0.0287 & Quadratic \\  & FT & 0.5639 & \\ \hline \multirow{3}{*}{Bread firmness} & Water & 0.0030 & \\  & MT & 0.0148 & Quadratic \\ \cline{1-1}  & FT & 0.3919 & \\ \hline \hline \end{tabular} \({}^{(1)}\) MT: mixing time; FT: fermentation time.  
\end{table} 
Table 5: Fitted model and significant factor identified based on \(p\)-values for the three representative quality characteristics of bread prepared with flour–bran blend at 30% bran. the gluten was diluted and led to form \"weak dough,\" resulting in reduced volume [37]. Therefore, in this study, the volume of bread can be increased by controlling the water and mixing time. The bread firmness was 8.6-30.0 N. The firmness was the lowest at the center point: 65 g of water, 3.5 min of mixing, and 70 min of fermentation time, where the bread height and volume were the largest. The firmness of bread is related to the moisture content of bread, the degree of air cell development, and the bread volume. The firmness of bread decreased as the moisture content of bread was high, the air cell was well developed, and the volume increased [50]. On the other hand, the highest firmness value was observed at 55 g of water, 5 min of mixing time, and 50 or 90 min fermentation time because of low air cell development and small bread volume led by a small water amount. ANOVA analysis showed that the bread firmness was significantly affected by the amount of water and the mixing time (\(p<0.05\)) (Table 5). The representative characteristics of bread (bread height, volume, and firmness) were quadratic models (Table 5). For bread height, only the mixing time showed a significance at \(p<0.05\). For bread volume and firmness, water and mixing time showed significance at \(p<0.05\). Among the three factors, fermentation time did not significantly  
All three bread characteristics were found to have the highest significance with volume \(p\) < 0.05, height \(p\) < 0.01, and firmness \(p\) < 0.01. R\({}^{2}\) referred to the degree of model fit, and confirmed the suitability in the height of 0.911, volume of 0.888, and firmness of 0.912 (Table 6). For optimizing formula and processing conditions for bread prepared with flour-bran blend at 30% bran, the volume and height were set as the maximum value, and the firmness was set as the minimum value. With the determined reaction equations, the desirability analyzed by Design Expert Software was 0.960, and the identified optimum conditions were 68.1 g water, 4.0 min mixing time, and 67.3 min fermentation time. For verifying the predicted values based on the models, actual values based on experiments are shown in Table 7.  
The optimized formula and processing conditions were verified well. Compared with the bread height obtained from the previous test for the effect of bran blending ratio, bread formulated with optimum conditions showed a height of 64.7 mm, which was close to the height of the bread (65.4 mm) with 10% bran. The results demonstrated a significant improvement in bread quality by controlling the formulation of basic ingredients and processing conditions without adding additional dough improvers.