## 3 Results and Discussion
### Analysis of Variance  
The Taguchi methodology does not directly provide the impact of process parameters on specific outputs. Therefore, statistical tools are especially required to calculate the relative importance and effects of each process parameter on specific outputs. The effectiveness of each parameter was evaluated using analysis of variance (ANOVA). This method can clearly identify how much each process parameter influences the response and determine the contribution of each parameter. The ANOVA analysis was conducted at a 95% confidence level. The importance of process parameters was determined by comparing the \(p\)-values. The lower the \(p\)-value, the greater the effect of that parameter on the response. Generally, if the \(p\)-value is less than 0.05, it indicates that the parameter has a significant effect on the process response [24]. Furthermore, it is necessary to verify whether assumptions such as independence and homogeneity of variance are met for ANOVA [25; 26; 27]. In this context, the Shapiro-Wilk test was used to check the normality of the samples for the analyses conducted in this study. Table 6 shows the ANOVA results for the safety factor of the autofret tagged cylinder without machining. When examining the ANOVA results, it is observed that the \(p\)-values for the \(S_{y}\) and \(T\) parameters are less than 0.05. Therefore, since the \(p\)-value is less than 0.05 at a 95% confidence level, it is concluded that the factors are statistically significant in their effect on the response. Additionally, the contribution of each material parameter was calculated by dividing each individual sum of squares by the total sum of squares. The contributions of the \(S_{y}\), \(E\), and \(T\) parameters to the response are 98.20%, 0.41%, and 1.29%, respectively. Yield strength is the most influential factor on the safety factor of the machined autofret tagged cylinder, while the effects of \(E\) and \(T\) are very low. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Source** & **DF** & **Adj SS** & **Adj MS** & **F-Value** & \(p\)**-Value** \\ \hline Regression & 3 & 0.553602 & 0.184534 & 1188.37 & 0.000 \\ \hline \(S_{y}\) & 1 & 0.544380 & 0.544380 & 3505.73 & 0.000 \\ \hline \(E\) & 1 & 0.002220 & 0.002220 & 14.30 & 0.013 \\ \hline \(T\) & 1 & 0.007001 & 0.007001 & 45.09 & 0.001 \\ \hline Error & 5 & 0.000776 & 0.000155 & & \\ \hline Total & 8 & 0.554378 & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Results of ANOVA for the safety factor of the autofret tagged cylinder without machining under working pressure of 400 MPa. Figure 9: Main effects plots for S/N ratios of the safety factor of the autofret tagged cylinder with only external machining under working pressure of 400 MPa. Table 7 displays the ANOVA results for the safety factor of the autofrettaged cylinder with only internal machining. Upon examining the ANOVA results, it is observed that the \(p\)-values for all material parameters are less than 0.05. Therefore, since the \(p\)-value is less than 0.05 at a 95% confidence level, the factors are statistically significant in their effect on the response. The contributions of the \(S_{y}\), \(E\), and \(T\) parameters to the response are 98.20%, 0.4%, and 1.26%, respectively. Yield strength is the most influential factor on the safety factor of the autofrettaged cylinder with only internal machining, while the effects of the other two factors are very low. Table 8 shows the ANOVA results for the safety factor of the autofrettaged cylinder with only external machining. Upon examining the ANOVA results, it is observed that the \(p\)-values for the \(S_{y}\) and \(T\) parameters are less than 0.05. Therefore, since the \(p\)-value is less than 0.05 at a 95% confidence level, it is concluded that the factors have a statistically significant effect on the response. The contributions of the \(S_{y}\) and \(T\) parameters to the response are 98.19% and 1.39%, respectively.