## 3 Results  
### Tensile Strength Evaluation  
Table 4 presents the tensile test results (average of three repetitions) after the experimental series from the combination of parameters exhibited in Table 3 was conducted (DOE). The analysis begins by explaining and interpreting the tensile test results because they serve as the starting point for the microstructural analysis of the samples and the further investigation of fracture behavior. Also, the ultimate tensile strength is an indicator or reference for the study of the Taguchi DOE and ANOVA. As a reference, we measured the tensile strength of the as-received alloy, which was found to be 274 MPa with a standard deviation (SD) of 10 MPa. Although a mechanical strength of 290-310 MPa is often mentioned in the literature as a typical value for 6061-T6 alloy, the ASTM B209 standard [32] specifies a minimum UTS value of 42 ksi (approximately equivalent to 289 MPa). Then, our measured UTS of 274 MPa (SD = 10 MPa) for the as-received material is, to some extent, slightly below this minimum specification. However, it is important to note that we purchased the commercial plate from a local supplier and assumed inherent variations as accounted for in the ASTM E8 standard, particularly Table X1.1 in [30], where a repeatability and reproducibility (R&R) value of 12.1 MPa is reported, indicating variability due to sampling. Given this context, our measurement of 274 MPa falls within the acceptable range when considering the reported tolerance value and our measurement precision. Furthermore, the UTS of 293.7 MPa (SD = 1.5 MPa) obtained from our best condition after the heat treatment study indeed shows an improvement compared to the original strength of the as-received alloy. This result emphasizes the main point of our research: the significant influence of solutionizing and aging parameters on the mechanical properties of the alloy, from a Taguchi DOE perspective. Thus, UTS was chosen as the primary output response, and a criterion of the larger-the-better approach was selected. The signal-to-noise (S/N) ratio for each run is calculated as the negative logarithm of the reciprocal of the squared output value. The average S/N ratio for a particular factor level combination is then determined as follows:  
\[\frac{S}{N}=-10 log_{10}\left(\frac{1}{m}\sum_{i=1}^{m}\frac{1}{y_{i}^{2}}\right) \tag{10}\] \begin{table}
\begin{tabular}{c c c c c c} \hline
**Run** & **Level Combination** & \begin{tabular}{c} **UTS** \\ **(MPa)** \\ \end{tabular} & \begin{tabular}{c} **Young Modulus** \\ **(GPa)** \\ \end{tabular} & \
\begin{tabular}{c} **Yield Strength** \\ **(MPa)** \\ \end{tabular} &
\begin{tabular}{c} **Signal-to-Noise Ratio** \\ **(dB)** \\ \end{tabular} \\ \hline
1 & 1-1-1-1 & 193.7 (8.7) & 57.20 (2.46) & 157.7 (32.7) & 45.723 \\
2 & 1-2-2-2 & 219.0 (3.5) & 45.00 (2.33) & 176.0 (27.2) & 46.807 \\
3 & 1-3-3-3 & 281.7 (5.0) & 52.47 (4.91) & 134.7 (19.4) & 48.992 \\
4 & 2-1-2-3 & 246.3 (3.1) & 51.37 (4.30) & 187.0 (21.1) & 47.829 \\
5 & 2-2-3-1 & 270.0 (0.0) & 61.07 (3.29) & 191.3 (58.0) & 48.627 \\
6 & 2-3-1-2 & 223.3 (3.2) & 55.23 (3.97) & 138.0 (5.0) & 46.977 \\
7 & 3-1-3-2 & 293.7 (1.5) & 57.87 (2.87) & 180.7 (28.0) & 49.357 \\
8 & 3-2-1-3 & 252.7 (3.1) & 58.33 (2.87) & 217.0 (44.2) & 48.050 \\
9 & 3-3-2-1 & 248.7 (4.7) & 56.07 (0.90) & 221.3 (10.8) & 47.909 \\ \hline \end{tabular}
\end{table} 
Table 4: Tensile test results after executing the DOE. Values in parenthesis are the standard deviation of three repetitions. The probability \(p\)-value is an approach for making decisions in hypothesis tests. One way to report the results of a hypothesis test is to state that the null hypothesis (usually denoted \(H_{o}\)) was or was not rejected at a specified \(\alpha\)-value or significance level; this \(\alpha\)-value is typically 0.05. The \(p\)-value is the probability that the test statistic will take on a value that is at least as extreme as the observed value of the statistic when the null hypothesis \(H_{o}\) is true [33].