## 3 Description, Implementation and Results of Experiments
### Application Results of GRA and ANOVA Methods  
The experimental data were normalized for the response parameters of flank wear and diameter deviation according to Equation (1) and are shown in Table 4. From the normalized data set in Table 5 the GRC relation coefficients using Equation (2) was calculated. We chose the value of the identification coefficient 0.5 because equal weight was given to response parameters. The statement is based on experience from various tests. The lower the wear value of the cutting part of the tool, the better the quality of the response parameter of the machined surface. The results are shown in Table 4. Next, the GRG was determined using Equation (3) and the GRC results. The GRG result is shown in Table 5.  
Figure 10: Main effect plot of diameter deviation \(\Delta_{d}\) and flank wear \(VB_{B}\). The optimal combination of input factors is selected based on higher mean GRG values according to Table 6. A higher GRG value expresses stronger correlation with the reference sequence, i.e., the optimal factor setting for several output parameters is the combination of factors \(a_{p}\) 4-\(f\) 4-\(v_{c}\) 1, i.e., cutting depth 0.5 mm, feed 0.4 mm per revolution, and cutting speed 70 m/min. The higher values of the average GRG (according to Figure 12) express the minimum values of the wear of the flank side of the cutting insert \(VB_{B}\) and the deviation of the diameter \(\Delta_{d}\). Table 6 shows the GRG values as differences between the maximum and minimum values of the four levels for each factor. This result can be interpreted to mean that cutting speed (0.3321) has the greatest influence on several output parameters compared to depth of cut (0.1276) and feed (0.1216) according to Table 6, when turning steel C45. The significance of each process input factor on the response parameters can be stated in the order of cutting speed \(>\) depth of cut \(>\) feed. Table 7 formulates the analysis of variance in terms of GRG. This table shows the significance of the process factors on several output parameters. Table 7 shows that cutting speed is a significant process factor affecting several output parameters, as its \(p\)-value is less than 0.05 at 95% confidence level. No significance was demonstrated for the feed and depth of cut factors with respect to multiple parameters simultaneously. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Factors**} & \multicolumn{3}{c}{**Mean Grey Relational Grade**} & \multirow{2}{*}{**Max-Min**} & \multirow{2}{*}{**Rank**} \\ \cline{2-2} \cline{5-6}  & **Level 1** & & & & & \\ \hline \(a_{p}\) & 0.6107 & 0.5536 & 0.4831 & 0.6367 & 0.1276 & 2 \\ \hline \(f\) & 0.5060 & 0.5760 & 0.5537 & 0.6276 & 0.1216 & 3 \\ \hline \(v_{c}\) & 0.7566 & 0.5774 & 0.5048 & 0.4245 & 0.3321 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Main effect on mean grey relational grade (total mean 0.5677). Figure 12: Main effect plot of mean grey relational grade. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Source** & **DF** & **Seq SS** & **Adj SS** & **Adj MS** & **F-Value** & \(p\)**-Value** & **Remarks** \\ \hline \(a_{p}\) & 3 & 0.0205 & 0.0205 & 0.0068 & 0.6286 & 0.6231 & Insignificant \\ \hline \(f\) & 3 & 0.0329 & 0.0329 & 0.0110 & 1.0075 & 0.4521 & Insignificant \\ \hline \(v_{c}\) & 3 & 0.2463 & 0.2463 & 0.0821 & 7.5460 & 0.0181 & Significant \\ \hline Error & 6 & 0.0653 & 0.0653 & 0.0109 & & & \\ \hline Total & 15 & 0.3650 & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Results of ANOVA on grey relational grade. At the end of the applied methods, confirmatory tests must be performed to determine the improvement in GRG from the initial setting of input factors to the optimum factors obtained when turning steel C45 while measuring the machined surface with LTS. The predicted GRG can be calculated using Equation (4). For the optimal setting of the input factors \(a_{p}\) 4-_f_ 4-\(v_{c}\) 1, GRG has a value of 0.7473, which is very close to the expected value, i.e., 0.8855.