## Appendix A Appendix A Appendix A.1 Data from the Coating Experiment [49] \begin{tabular}{l l l l l l} \hline
**Run** & **Speed** & **Pressure** & **Distance** & \
\begin{tabular}{l} **Mean,** \\ \(\mathbf{y_{1}}\) \\ \end{tabular} &
\begin{tabular}{l} **Standard** \\ **Deviation, \(\mathbf{y_{2}}\)** \\ \end{tabular} \\ \hline
1 & \(-1\) & \(-1\) & \(-1\) & 24 & 12.5 \\
2 & 0 & \(-1\) & \(-1\) & 120.3 & 8.4 \\
3 & \(+1\) & \(-1\) & \(-1\) & 213.7 & 42.8 \\
4 & \(-1\) & 0 & \(-1\) & 86 & 3.5 \\
5 & 0 & 0 & \(-1\) & 136.6 & 80.4 \\
6 & \(+1\) & 0 & \(-1\) & 340.7 & 16.2 \\
7 & \(-1\) & \(+1\) & \(-1\) & 112.3 & 27.6 \\
8 & 0 & \(+1\) & \(-1\) & 256.3 & 4.6 \\
9 & \(+1\) & \(+1\) & \(-1\) & 271.7 & 23.6 \\
10 & \(-1\) & \(-1\) & 0 & 81 & 0.0 \\
11 & 0 & \(-1\) & 0 & 101.7 & 17.7 \\
12 & \(+1\) & \(-1\) & 0 & 357.0 & 32.9 \\
13 & \(-1\) & 0 & 0 & 171.3 & 15.0 \\
14 & 0 & 0 & 0 & 372.0 & 0.0 \\
15 & \(+1\) & 0 & 0 & 501.7 & 92.5 \\
16 & \(-1\) & \(+1\) & 0 & 264.0 & 63.5 \\
17 & 0 & \(+1\) & 0 & 427.0 & 88.6 \\
18 & \(+1\) & +1 & 0 & 730.7 & 21.1 \\
19 & \(-1\) & \(-1\) & \(+1\) & 220.7 & 133.8 \\
20 & 0 & \(-1\) & \(+1\) & 239.7 & 23.5 \\
21 & \(+1\) & \(-1\) & \(+1\) & 422.0 & 18.5 \\
22 & \(-1\) & 0 & \(+1\) & 199.0 & 29.4 \\
23 & 0 & 0 & \(+1\) & 485.3 & 44.7 \\
24 & \(+1\) & 0 & \(+1\) & 673.7 & 158.2 \\
25 & \(-1\) & \(+1\) & \(+1\) & 176.7 & 55.5 \\
26 & 0 & \(+1\) & \(+1\) & 501.0 & 138.9 \\
27 & \(+1\) & \(+1\) & \(+1\) & 1010.0 & 142.4 \\ \hline \end{tabular}   
_Appendix A.2. Evaluation of the RSM Models for \(y_{Ra}\), Ra Surface Roughness [28]_ \begin{tabular}{l l l l} \hline
1. \(y_{\text{Ra}}=0.210-0.0138x_{1}+15.133x_{2}-0.166x_{3}+0.0000308{x_{1}}^{2}+ 32.24{x_{2}}^{2}\) \\ \((0.403)\) (0.490) (0.541) (0.245) (0.468) \\ \(+0.419{x_{3}}^{2}-0.0268x_{1}x_{2}+0.000110x_{1}x_{3}+1.375x_{2}x_{3}\) \\ \((0.059)\) (0.192) (0.773) (0.031) \\ \(\text{R}^{2}=0.982\), \(\text{R}^{2}_{\text{adj}}=0.954\), s = 0.174, PRESS = 2.470 \\ \end{tabular}   
Delete \(x_{1}x_{3}\) and recalculate the equation. \begin{tabular}{l l l l l}
2. \(y_{\text{Ra}}=0.297-0.141x_{1}+15.102x_{2}-0.0827x_{3}+0.0000307{x_{1}}^{2}+ 33.310x_{2}^{2}\) \\ \((0.358)\) (0.457) (0.559) (0.210) (0.433) \\ \(+0.0418{x_{2}}^{2}-0.0268x_{1}x_{2}+1.375x_{2}x_{3}\) \\ \((0.041)\) (0.159) (0.020) \\ \hline \end{tabular}   
_Appendix A.3. Evaluation of the RSM Models for \(y_{Ra}\), Ra Surface Roughness [28]_ \begin{tabular}{l l l l l} \hline
1. \(y_{\text{Ra}}=0.210-0.0138x_{1}+15.133x_{2}-0.166x_{3}+0.0000308{x_{1}}^{2}+ 32.24{x_{2}}^{2}\) \\ \((0.403)\) (0.490) (0.541) (0.245) (0.468) \\ \(+0.419{x_{3}}^{2}-0.0268x_{1}x_{2}+0.000110x_{1}x_{3}+1.375x_{2}x_{3}\) \\ \((0.059)\) (0.192) (0.773) (0.031) \\ \(\text{R}^{2}=0.982\), \(\text{R}^{2}_{\text{adj}}=0.954\), s = 0.174, PRESS = 2.470 \\ \end{tabular}   
Delete \(x_{1}x_{3}\) and recalculate the equation. \begin{tabular}{l l l l l}
2. \(y_{\text{Ra}}=0.297-0.141x_{1}+15.102x_{2}-0.0827x_{3}+0.0000307{x_{1}}^{2}+ 33.310x_{2}^{2}\) \\ \((0.358)\) (0.457) (0.559) (0.210) (0.433) \\ \(+0.0418{x_{2}}^{2}-0.0268x_{1}x_{2}+1.375x_{2}x_{3}\) \\ \((0.041)\) (0.159) (0.020) \\ \hline \end{tabular}   
_Appendix A.4. Evaluation of the RSM Models for \(y_{Ra}\), Ra Surface Roughness [28]_  
\begin{tabular}{l l l l l} \hline
1. \(y_{\text{Ra}}=0.210-0.0138x_{1}+15.133x_{2}-0.166x_{3}+0.0000308{x_{1}}^{2}+ 32.24{x_{2}}^{2}\) \\ \((0.403)\) (0.490) (0.541) (0.245) (0.468) \\ \(+0.419{x_{3}}^{2}-0.0268x_{1}x_{2}+0.000110x_{1}x_{3}+1 Delete \({x_{2}}^{2}\) and recalculate the equation. \[ \begin{split} 3.\ \mathrm{y_{Ra}}=-0.863-0.0177x_{1}+30.425x_{2}-0.06 06x_{3}+0.0000366{x_{1}}^{2}+0.0463{x_{3}}^{2}\\ (0.222)\ (<\)0.001) (0.652) (0.115) (0.018)\\ -0.0268x_{1}x_{2}+1.375x_{2}x_{3}\\ (0.147)\ (0.015)\end{split}  \tag{10}\]  
Delete \({x_{1}}{x_{2}}\) and recalculate the equation. \[ \begin{split} 4.\ \mathrm{y_{Ra}}=1.022-0.0239x_{1}+22.228x_{2}-0. 0599x_{3}+0.0000366{x_{1}}^{2}+0.463{x_{3}}^{2}\\ (0.120)\ (<\)0.001) (0.680) (0.137) (0.023)\\ +1.372x_{2}x_{3}\\ (0.020)\end{split}