## 1 Introduction
The number of studies with each experimental methodology, as determined using Google Scholar, is listed in Table 1.  
Table 1 presents the number of papers employing the three statistical experimental techniques from 2019 to 2024, as determined by a Google Scholar search. It can be seen that the number of papers using central composite design is the largest, followed by full factorial design, while Box-Behnken design is the least frequent. The number of papers using the central composite design is about 10 times that of paper using Box-Behnken design. However, upon examining the increasing trend, it can be seen that the number of papers using central composite design and full factorial design has been decreasing year by year. The number of papers using Box-Behnken design is increasing year by year. The experimental matrices in the three methods for RSM design can be found in various publications and textbooks [1,2]. The number of required experiments for the experimental methods is 27, 22, and 13 or more for FFD, BBD, and CCD, respectively. Many criteria have been proposed to evaluate the regression models' fitting agreement and predictive ability. The essential procedure in regression analysis is to find the significant effect of certain variables on the response. To evaluate the fitting agreement of a proposal model, the criteria include the F-value of ANOVA, coefficient of determination R\({}^{2}\), adjusted R\({}^{2}\) (R\({}^{2}\)adj), lack-of-fit test, etc. To assess the significant effect of one variable on the response, the criterion is the \(t\)-value or \(p\)-value of the coefficients of this variable. The criteria to evaluate the predictive ability are the predicted residual error sum of squares (PRESS) and predicted R-squared (R\({}^{2}\)pred) [17; 18; 19]. After the evaluation, the appropriate equation (RSM model) establishes the relationship between the response value and the influencing factors as a mathematical function. Among the graphical methods, contour plots and three-dimensional surface response plots are particularly popular among researchers [1,3,20]. The studied techniques are described in detail in this paper [21]. The accuracy and predictive power of the RSM model determine whether it can effectively find the factors that actually affect the response value. However, engineers often do not care about the suitability of the regression equations they use. Many researchers directly use commercial software to calculate the RSM model. [PERSON] et al. [22] emphasize the importance of the model's validity and accuracy in the context of RSM application, as well as the validity of the RSM model itself [22]. Compared with other experimental design methods, the most prominent feature of the response surface method is that it graphically represents the relationship between the influencing factors (variables) and the response value. Contour maps are used to present two-dimensional space. These contour maps illustrate the changes in response value under various influencing factors. Three-dimensional surface response maps represent information in three-dimensional space, with the response value as the z-coordinate and the x- and y-coordinates as the two influencing factors. Suppose the quadratic polynomial relationship does not exist. In that case, this type of contour plot will be drawn as a straight line, and the three-dimensional surface response plot will appear as a stable plane. If the \begin{table}
\begin{tabular}{l l l l} \hline
**Year** & **Full Factorial** & **Box–Behnken** & **Central Composite** \\
**Design (CFD)** & **Design (BBD)** & **Design (CCD)** \\ \hline
2019 & 145,000 & 7250 & 218,000 \\
2020 & 151,000 & 8450 & 235,000 \\
2021 & 147,000 & 9860 & 224,000 \\
2022 & 132,000 & 12,400 & 207,000 \\
2023 & 114,000 & 13,600 & 159,000 \\
2024 & 88,300 & 16,500 & 113,000 \\ \hline \end{tabular}
\end{table} 
Table 1: The number of studies using each experimental methodology, determined using Google Scholar. quadratic polynomial relationship is significant, both graphs will be represented by curves.