## 2 Experimental Research
### Main Experiment and Analysis of Obtained Results
The unbiased estimate of the variance is the mean square deviation of the residual, which is 15.42, while the standard error (deviation) is the root of the variance and is 3.9268. Expression 1 describes the regression model for the dependence of coating thickness on the input variables (Factor A--current, Factor B--voltage, Factor C--material). The \begin{table}
\begin{tabular}{c c c c c c} \hline
**Source** & **Sum of Squares** & \begin{tabular}{c} **Number of Degrees** \\ **of Freedom** \\ \end{tabular} & \
\begin{tabular}{c} **Mean Square** \\ **Deviation** \\ \end{tabular} &
\begin{tabular}{c} **Value of the** \\ **F-Test** \\ \end{tabular} & \(p\)**-Value** \\ \hline Model & 6987.22 & 11 & 635.20 & 41.20 & \textless{}0.0001 \\ A—Current & 318.34 & 1 & 318.34 & 20.65 & 0.0002 \\ B—Voltage & 4058.39 & 1 & 4058.39 & 263.21 & \textless{}0.0001 \\ C—Material & 1203.26 & 2 & 601.63 & 39.02 & \textless{}0.0001 \\ AB & 10.60 & 1 & 10.60 & 0.6877 & 0.4163 \\ AC & 53.15 & 2 & 26.58 & 1.72 & 0.2027 \\ BC & 7.72 & 2 & 3.86 & 0.2502 & 0.7809 \\ A\({}^{2}\) & 248.87 & 1 & 248.87 & 16.14 & 0.0006 \\ B\({}^{2}\) & 1306.79 & 1 & 1306.79 & 84.75 & \textless{}0.0001 \\ Residual & 323.79 & 21 & 15.42 & & \\ Lack of Fit & 279.86 & 15 & 18.66 & 2.55 & 0.1275 \\ Pure Error & 43.93 & 6 & 7.32 & & \\ Cor Total & 7311.01 & 32 & & & \\ \hline \end{tabular}
\end{table} 
Table 6: Analysis of variance of the regression model for coating thickness. values of the mentioned variables are coded for high factor levels as +1 and for low factor levels as -1, according to Table 3. Expression 2 describes a regression model with actual factor values, where factor C (material) is carbon steel. Expression 3 refers to a regression model with actual factor values, where factor C is galvanized steel, and expression 4 refers to a regression model with actual factor values, where factor C is aluminum. \[ \begin{split}\text{{Cating thickness}}=61.03+3.64\times A+13.00 \times B+7.69\times C1-7.06\times C2+0.9400\times AB+\\ 1.81\times AC1-1.84\times AC2+0.1098\times BC1-0.7428\times BC2-3.83 \times A^{2}-8.78\times B^{2}\\ \text{{Cating thickness}}=-23.19563+0.697016\times\text{{Current}}+1.7 1055\times\text{{Voltage}}+0.001175\times\\ \text{{Current}}\times\text{{Voltage}}-0.004791\times\text{{Current}}^{2}-0.0 10978\times\text{{Voltage}}^{2}\\ \text{{Cating thickness}}=-28.40584+0.568151\times\text{{Current}}+1.6 8041\times\text{{Voltage}}+0.001175\times\\ \text{{Current}}\times\text{{Voltage}}-0.004791\times\text{{Current}}^{2}-0.0 10978\times\text{{Voltage}}^{2}\\ \text{{Cating thickness}}=-28.86534+0.634377\times\text{{Current}}+1.7 2905\times\text{{Voltage}}+0.001175\times\\ \text{{Current}}\times\text{{Voltage}}-0.004791\times\text{{Current}}^{2}-0. 010978\times\text{{Voltage}}^{2}\\ \end{split}  \tag{1}\]  
\[ \begin{split}\text{{Cating thickness}}=-23.19563+0.697016\times\text{{Current}}+1.7 1055\times\text{{Voltage}}+0.001175\times\\ \text{{Current}}\times\text{{Voltage}}-0.004791\times\text{{Current}}^{2}-0. 010978\times\text{{Voltage}}^{2}\\ \end{split}  \tag{2}\]  
\[ \begin{split}\text{{Cating thickness}}=-28.40584+0.568151\times\text{{Current}}+1.6 8041\times\text{{Voltage}}+0.001175\times\\ \text{{Current}}\times\text{{Voltage}}-0.004791\times\text{{Current}}^{2}-0. 010978\times\text{{Voltage}}^{2}\\ \end{split}  \tag{3}\]  
\[ \begin{split}\text{{Cating thickness}}=-28.86534+0.634377\times\text{{Current}}+1.7 2905\times\text{{Voltage}}+0.001175\times\\ \text{{Current}}\times\text{{Voltage}}-0.004791\times\text{{Current}}^{2}-0. 010978\times\text{{Voltage}}^{2}\\ \end{split}  \tag{4}\]  
Figures 5-7 provide graphic presentations of the models, showing how the coating thickness behaves when influenced by changes in current and voltage. The dependence of the coating thickness on the input parameters is shown by the figures below when the coating is applied to carbon steel (Figure 5), galvanized steel (Figure 6), and aluminum (Figure 7). Figure 5: Response surface for the regression model of the dependence of coating thickness for carbon steel.