## 4 Results  
### Results to Minimize Surface Roughness  
The results shown in Table 4 were obtained from the measurements taken for each of the 19 mm and 25 mm specimens to know their surface roughness. The two different thicknesses were considered noise factors, implying that the process had to be as insensitive as possible to the thickness of the plate being machined. Together with the mean, the table shows the signal-to-noise ratio (S/N) using a smaller-the-better quality response. A high S/N ratio represents an experiment where the combination of factors and levels provides a more robust response, meaning that the surface roughness changes less from one replicate to the next. A low mean represents a less coarse, better surface roughness. \begin{table}
\begin{tabular}{l l l l l l l l l l l l l l l l l} \hline \hline \multirow{2}{*}{**RUN**} & \multirow{2}{*}{**Ton**} & \multirow{2}{*}{**Toff**} & \multirow{2}{*}{**SV**} & \multirow{2}{*}{**WT**} & \multirow{2}{*}{**WS**} & \multirow{2}{*}{**V**} & \multicolumn{4}{c}{**Surface Roughness (\(\mu\)m)**} & \multicolumn{4}{c}{**Surface Roughness (\(\mu\)m)**} & \multicolumn{4}{c}{**S/N (dB)**} & \multicolumn{1}{c}{**Mean (\(\mu\)m)**} \\  & & & & & & & & & &  
The average response plots of the S/N ratio and the mean for the surface roughness are shown in Figures 6 and 7, respectively. These graphs show the effect of each cutting parameter on the response. To determine the optimal values for each cutting parameter, it is necessary to consider both graphs, remembering that higher values of the signal-to-noise ratio and lower mean values are better. From both average response plots, two things stand out. First, the values for each factor that maximized the S/N ratio and minimized the mean were the same. These values are summarized in Table 5. Second, the pulse on-time and the voltage factors caused the most variation in the surface roughness. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**RUN**} & \multirow{2}{*}{**Ton**} & \multirow{2}{*}{**Toff**} & \multirow{2}{*}{**SV**} & \multirow{2}{*}{**WT**} & \multirow{2}{*}{**WS**} & \multirow{2}{*}{**V**} & \multicolumn{3}{c}{**Surface Roughness (\(\mu\)m)**} & \multicolumn{3}{c}{**Surface Roughness (\(\mu\)m)**} & \multirow{2}{*}{**S/N (dB)**} & \multirow{2}{*}{**Mean (\(\mu\)m)**} \\  & & & & & & & & & & & **Plate with 19 mm Thickness** & & & **Plate with 25 mm Thickness** & & \\ \hline
15 & 13 & 14 & 48 & 40 & 7 & 9 & 3.16 & 3.16 & 3.33 & 2.99 & 3.30 & 3.19 & 3.12 & 3.10 & 3.10 & 3.09 & \(-\)9.978 & 3.153 \\
16 & 1  
The statistical significance of the factors and their contribution on the response can be verified by an analysis of variance. Tables 6 and 7 show the analysis of variance (ANOVA) for the model considering the S/N ratio and the mean, respectively, for the surface roughness. From the results, both S/N ratio and the mean had a similar behavior. The pulse on-time (Ton) and the voltage were the only significant factors, with a \(p\)-value of less than 0.001. They were also the only factors that were relevant for the analysis, as both factors accounted for more than 90% of the contribution to the response and all the other factors had a contribution of less than 1.2%. Considering pulse on-time and the voltage as the more important factors, Figures 8 and 9 are contour plots showing the behavior of the S/N ratio and the mean for the surface roughness within the limits studied. The contour plots exhibit how both the S/N ratio and the mean improve as the pulse on-time and the voltage decrease.