## 3 Results and Discussion  
### Taguchi Analysis  
In this study, the safety factor for three different scenarios of an autofrettaged cylinder was investigated: without machining, with only internal machining at a thickness of 5 mm, and with only external machining at a thickness of 5 mm. The effect of the factors listed in Table 1 was examined using the Taguchi \(L_{9}\) (3\({}^{3}\)) orthogonal array design. The experimental matrix created using the Minitab 19 statistical software is presented in Table 2. The safety factor for the operating pressure of autofrettaged cylinders without machining, with only internal machining, and with only external machining was taken as the response parameter. Since the goal is to maximize each response parameter, a type of S/N ratio where larger is better was considered. FE Analyses were conducted for each set of parameters specified in Table 2 of the experimental matrix. Subsequently, the calculated simulation responses were transformed into signal-to-noise (S/N) ratios using the Minitab 19 software. Regardless of the objective function, a larger S/N ratio corresponds to better performance characteristics. The calculated signal-to-noise (S/N) ratio values (mean) for the safety factor of the autofrettaged cylinder without machining are provided in Table 3 and graphically \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Factors**} & \multicolumn{3}{c}{**Levels**} \\ \cline{2-4}  & **1** & **2** & **3** \\ \hline Yield Strength (\(S_{y}\), MPa) & 700 & 1000 & 1300 \\ \hline Young’s Modulus (\(E\), GPa) & 100 & 200 & 300 \\ \hline Tangent Modulus (\(T\), GPa) & 0 & 10 & 20 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Material parameters and levels. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{1}{c}{**Order**} & **Young’s Modulus (GPa)** & **Tangent Modulus (GPa)** & **Yield Strength (GPa)** \\ \hline
1 & 100 & 0 & 0.7 \\ \hline
2 & 200 & 20 & 0.7 \\ \hline
3 & 300 & 10 & 0.7 \\ \hline
4 & 100 & 10 & 1 \\ \hline
5 & 200 & 0 & 1 \\ \hline
6 & 300 & 20 & 1 \\ \hline
7 & 100 & 20 & 1.3 \\ \hline
8 & 200 & 10 & 1.3 \\ \hline
9 & 300 & 0 & 1.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: [PERSON]’s \(L_{9}\) orthogonal array. The analysis of Figure 5 reveals that an increase in the yield strength of the material undergoing the autofrettage process without machining can enhance the S/N ratio by 4 to 5 times, irrespective of the Young's modulus value. Conversely, at a tangent modulus value of 0, the S/N ratio rises proportionally with the increase in Young's modulus. Notably, the optimal S/N ratios are observed with the maximum levels of yield strength and tangent modulus within the examined range, along with the lowest value of Young's modulus. The maximum effectiveness ranks were calculated based on delta values representing the variability between the highest and lowest average response values for each factor. According to the delta values in Table 3, the most influential parameter on the response for the autofrettaged cylinder with only internal machining is \(S_{y}\). It is clearly seen from the graphical data (Figure 4) that the average S/N ratio increases as \(S_{y}\) and \(T\) increase. This indicates that the safety factor of the autofrettaged cylinder without machining increases as \(S_{y}\) and \(T\) increase. However, the safety factor decreases as \(E\) values increase. The dashed line in Figure 4 represents the overall average of all S/N ratios. The calculated S/N ratio values (average) for the safety factor of the autofrettaged cylinder with only internal machining applied are provided in Table 4 and presented graphically in Figure 6. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Level** & \(S_{y}\) & \(E\) & \(T\) \\ \hline
1 & 1.140 & 1.462 & 1.407 \\ \hline
2 & 1.438 & 1.434 & 1.439 \\ \hline
3 & 1.742 & 1.424 & 1.475 \\ \hline Delta & 0.602 & 0.038 & 0.068 \\ \hline Rank & 1 & 3 & 2 \\ \hline \hline \end{tabular}
\end{table}