## 1 Introduction  
The industry urgently needs technology to seek optimization to improve system efficiency, increase quality, save energy, and reduce carbon emissions. A system's output or response is usually affected by several factors. Finding the optimum levels of these factors is called optimization. A simple method is to test the optimal levels of a factor and keep the other factors constant. This technique is impractical because of the interaction of other factors. To assess the effect of several factors on the response, the response surface methodology (RSM) is usually adopted to simultaneously assess the optimum conditions for several factors [1,2]. RSM has been a popular experimental design in the industry. RSM is a special experimental design used to improve the utilization of processing and develop processes for new products. Statistical techniques help evaluate the factors influencing the process and confirm the optimum conditions for different factors [1; 3]. RSM's special function is to test the experimental run for several factors with fewer samples. As the data are collected, the relationship between the system's response and its influencing factors can be established by regression analysis. Then, the effect of factors on the response is graphed. Researchers can observe the relationship through the linear or curved distributions of these figures. This graphical function led to \"response surface methodology\" being widely used [1; 2; 3]. The relationship between the response (y) and the input factors (x\({}_{1}\), x\({}_{2}\), \(\ldots\), x\({}_{k}\)) is expressed as  
\[\mathrm{y}=\mathrm{f}(\mathrm{x}_{1},\mathrm{x}_{2},\ldots,\mathrm{x}_{k})+\varepsilon \tag{1}\]  
where y is the response, f is the unknown function in the response, x\({}_{1}\), x\({}_{2}\), \(\ldots\), and x\({}_{k}\) are the independent variables, also called influencing factors, k is the number of factors, and \(\varepsilon\) is the model's error. The mathematical model also includes linear, quadratic, and interaction effects. If the process system involves two factors, x\({}_{1}\) and x\({}_{2}\), the form of the RSM equation is  
\[\mathrm{y}=\mathrm{b}_{\mathrm{o}}+\mathrm{b}_{1}\mathrm{x}_{1}+\mathrm{b}_ {2}\mathrm{x}_{2}+\mathrm{b}_{11}\mathrm{x}_{1}{}^{2}+\mathrm{b}_{22}\mathrm{ x}_{2}{}^{2}+\mathrm{b}_{12}\mathrm{x}_{1}\mathrm{x}_{2}+\varepsilon \tag{2}\]  
In the three-process-variable condition, x\({}_{1}\), x\({}_{2}\), and x\({}_{3}\), the mathematical equation of the RSM is  
\[\mathrm{y}=\mathrm{b}_{\mathrm{o}}+\mathrm{b}_{1}\mathrm{x}_{1}+\mathrm{b}_ {2}\mathrm{x}_{2}+\mathrm{b}_{3}\mathrm{x}_{3}+\mathrm{b}_{11}\mathrm{x}_{1} {}^{2}+\mathrm{b}_{22}\mathrm{x}_{2}{}^{2}+\mathrm{b}_{33}\mathrm{x}_{3}{}^{ 2}+\mathrm{b}_{12}\mathrm{x}_{1}\mathrm{x}_{2}+\mathrm{b}_{13}\mathrm{x}_{1} \mathrm{x}_{3}+\mathrm{b}_{23}\mathrm{x}_{2}\mathrm{x}_{3}+\varepsilon \tag{3}\]  
For the four-factor cases, x\({}_{1}\), x\({}_{2}\), x\({}_{3}\), and x\({}_{4}\), the RSM equation is  
\[\mathrm{y}=\mathrm{b}_{\mathrm{o}}+\mathrm{b}_{1}\mathrm{x}_{1}+\mathrm{b}_ {2}\mathrm{x}_{2}+\mathrm{b}_{3}\mathrm{x}_{3}+\mathrm{b}_{4}\mathrm{x}_{4}+ \mathrm{b}_{11}\mathrm{x}_{1}{}^{2}+\mathrm{b}_{22}\mathrm{x}_{2}{}^{2}+ \mathrm{b}_{33}\mathrm{x}_{3}{}^{2}+\mathrm{b}_{44}\mathrm{x}^{2}+\mathrm{b}_ {12}\mathrm{x}_{1}\mathrm{x}_{2}+\mathrm{b}_{13}\mathrm{x}_{1}\mathrm{x}_{3}+ \mathrm{b}_{14}\mathrm{x}_{1}\mathrm{x}_{4}+\mathrm{b}_{23}\mathrm{x}_{2} \mathrm{The experimental matrices in the three methods for RSM design are easily found in a textbook [1]. The number of tests required for the three test methods with three factors and three levels is 27 for the FFD method, 22 for the BBD method, and 13 for the CCD method. The replicates of the center ports for CCD may influence the sample numbers. The criteria to evaluate the fitting agreement and predictive ability of the selection of models are essential aspects of regression analysis. The key is to find the variables' significant effect on the response. Many criteria have been used.