# Parametric Investigation of Die-Sinking EDM of Ti6 Al4V Using the Hybrid Taguchi-Rams-RATMI Method
## 4 Results and Discussions
### Infuential Factors  
Figure 4 displays the main effect plot of means for the RATMI majority index (E\({}_{\rm i}\)) with respect to four machining parameters (A (pulse-on time (Ton), \(\rm\mu s\)); B (duty cycle, %); C (peak current, Amp); and D (voltage, V)). Since the RATMI majority index (E\({}_{\rm i}\)) must be maximized, the maximum value fetched in the factor configuration is to be considered. Hence, according to the plot, the Ton of 500 \(\rm\mu s\), duty cycle of 8%, peak current of 40A, and voltage of 20V can be considered for optimizing the machining characteristics. The ANOVA findings for the RATMI majority index (E\({}_{\rm i}\)) are shown in Table 7 in order to examine the impact of the EDM settings on the machining output characteristics. The p-value of less than 0.05 (95% confidence interval) indicates that all four machining parameters are important and have an impact on obtaining the intended result. Among all, the peak current was found to be a more significant and influential parameter with 51.77% influence followed by pulse-on time, duty cycle, and voltage with a contribution of 30.89%, 9.30%, and 3.13%, respectively, which can help in achieving the desired machining output characteristics where MRR and the depth of cut can be maximized while surface roughness and TWR can be minimized. R\({}^{2}\) of 95.09% indicates that the model's data fit the data well. However, after adjusting for the number of predictors in the model in relation to the number of observations, the adjusted R\({}^{2}\) value of 92.91% indicates the variance in the response that is explained by the model. The predicted R\({}^{2}\) value of 88.96% determines the fitness of the model for predicting the response to the observations. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Factors** & **DoF** & **Adj SS** & **\% Contribution** & **Adj MS** & **F-Value** & **\(p\)-Value** \\ \hline Ton, A & 2 & 0.71058 & 30.89 & 0.355289 & 56.67 & 0.000 \\ Duty cycle, B & 2 & 0.21391 & 9.30 & 0.106957 & 17.06 & 0.000 \\ Peak current, C & 2 & 1.19068 & 51.77 & 0.595339 & 94.97 & 0.000 \\ Voltage, D & 2 & 0.07200 & 3.13 & 0.035998 & 5.74 & 0.012 \\ Error & 18 & 0.11284 & 4.91 & 0.006269 & & \\ Total & 26 & 2.30001 & & & & \\ R-sq & 95.09\% & R-sq(adj) & 92.91\% & R-sq(pred) & 88.96\% & \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Analysis of variance. Figure 4: The main effect plot for the RATMI majority index (E\({}_{\rm i}\)). The residual plot for the RATMI majority index (E\({}_{i}\)) is displayed in Figure 5. The points fall close to the straight line, suggesting that the normal distribution fits the data well. The assumption that the residuals are randomly distributed and have constant variance is confirmed by the residuals versus fit plots. When you have around 20 or more data points, the residuals histogram helps you evaluate if the data are skewed or contain outliers despite the fact that the bell curve on the histogram indicates the sample distribution. The independent residuals do not display any trends or patterns in time order as the residuals versus the order graphic demonstrates. Nevertheless, given that the residuals fall randomly about the center line, patterns in the points may imply a correlation between the residuals, proving that they are not independent. Figure 6 shows the contour plot of E\({}_{i}\) vs. pulse-on time and duty cycle. It signifies that the majority index is reduced during medium-level settings for machining (dark red area) while the majority index increases when there is a lower-level setting for machining (purple area). In the experimental runs, it can also be seen that such factor setting causes lower MRR and high surface roughness values. Similar phenomena can be interpreted from Figure 7, which depicts the surface plot of E\({}_{i}\) vs. pulse-on time and duty cycle where E\({}_{i}\) decreases and increases according to a deeper area and a higher area, respectively. Figure 8 shows the contour plot of the RATMI majority index (E\({}_{i}\)) vs. pulse-on time and peak current.