## 3 Results and Discussions  
### Modeling of Tensile Strength by ANOVA and RSM  
The results of the tensile strength test were collected and used to generate a representative mathematical model. Statistical processing and ANOVA were adopted to obtain reliable mathematical models based on the previously described procedures and experimental data, obtained by the CCCD. The significance of the model and the members of the response polynomial was determined with ANOVA. Table 6 presents the data of the initial ANOVA analysis, with a recommendation for selection of the appropriate model for the tensile strength \(R_{m}\) prediction. A quadratic model for the tensile strength (\(R_{m}\)) prediction was proposed, based on the recommendation for the selection of the appropriate model. The cubic model has more terms than the number of unique points in the design, because some terms were aliased, and the model was aliased. By reducing the number of terms in the cubic model (eliminating insignificant terms), the adequate reduced cubic model was found to have the best Lack of Fit \(p\)-value, R\({}^{2}\), Adjusted R\({}^{2}\), and Predicted R\({}^{2}\) values compared to the other \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Source** & **Lack of Fit** & **R\({}^{2}\)** & **Adjusted** & **Predicted** & **Remarks** \\  & \(p\)**-Value** & & **R\({}^{2}\)** & **R\({}^{2}\)** & **R\({}^{2}\)** & **Remarks** \\ \hline Linear & 0.0103 & 0.7502 & 0.7102 & 0.6137 & \\
2 FI & 0.0096 & 0.8137 & 0.7157 & 0.6012 & \\ Quadratic & 0.0460 & 0.9298 & 0.8643 & 0.6237 & Suggested \\ Cubic & 0.8003 & 0.9929 & 0.9708 & 0.9040 & Aliased \\ Reduced Cubic & 0.6037 & 0.9860 & 0.9663 & 0.9000 & Selected \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Model summary statistics. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Exp. No. ** & \multicolumn{4}{c}{**Process Parameters**} & \multicolumn{1}{c}{**Tensile Strength (MPa)**} \\ \cline{2-5}  & **A** & **B** & **C** & **D** & \\ \hline
1. & 0.25 & 70 & 30 & 1.7 & 58.07 \\
2. & 0.1 & 80 & 45 & 1.4 & 73.93 \\
3. & 0.2 & 80 & 45 &  
three considered models (linear, 2 FI and quadratic). Table 7 presents the ANOVA analysis of the selected reduced cubic model. The Model F-value of 49.84 implies the model's significance. There is only a 0.01% chance that an F-value this large could occur due to noise. In this study, \(p\)-values less than 0.0500 indicate that the model's terms are significant enough. In this case, A, B, C, D, AC, AD, BC, BD, A\({}^{2}\), B\({}^{2}\), C\({}^{2}\), D\({}^{2}\), ABD, A\({}^{2}\)C, and AB\({}^{2}\) are significant model terms. Terms AB and CD were retained, due to the model's hierarchy. The Lack-of-Fit \(p\)-value of 0.6037 implies that the lack of fit is not significant relative to the pure error. There is a 60.37% chance that a lack-of-fit \(p\)-value this large could occur due to noise. The calculations of the basic statistical parameters for the selected reduced cubic model are given in Table 8. The values of R\({}^{2}\), adjusted R\({}^{2}\), and predicted R\({}^{2}\) indicate a strong relationship between the model and the experimental data. Adequate precision is a measure of the predicted response range in relation to the error, i.e., it represents the signal-to-noise ratio. In this case, a ratio of 27.556 indicates an adequate signal. Figure 3 presents the normal probability plot of residuals, and the predicted values vs. actual plot for tensile strength. It is evident that all the residuals are clustered in a straight line, implying that the errors are normally distributed. Additionally, since the points are clustered around a straight line, the predicted values are in close adherence to the actual values. For an analyzed response, the mathematical model is generated according to the reduced cubic model, as given below in Equation (1):