## 1 Introduction  
The results or responses of an engineering system or its process are often affected by many factors. Finding the optimal level of these factors is called optimization. In research evaluating the impact of multiple factors on one or more response values, the most common method to evaluate the most appropriate conditions of multiple factors is the response surface methodology (RSM) [1, 2]. RSM is a special experimental design that can be used to establish process operations for new products, improve the utilization rate of operating processes, and reduce resource waste. Through the use of appropriate statistical techniques,it is possible to evaluate the factors that have a significant impact on the process and thus determine the optimal conditions for these factors [1; 3]. The special feature of RSM in experimental design is that this method can test multiple factors with a small number of samples. After completing the data collection, regression analysis is used to establish the mathematical relationship between the system response value and its influencing factors. These models are then used to create graphs that illustrate the impact of various factors on the response. Researchers can use these linear or curvilinear distribution graphs to observe this relationship. Due to this unique graphical observation capability, the response surface methodology has been widely used in industry [1; 2; 3; 4]. Two excellent textbooks introduce the RSM concept, two- and three-level factorial design, experimental design for fitting the response surface, and some special topics of RSM [1; 2]. [PERSON] and [PERSON] [4] proposed an essential concept about RSM. [PERSON] et al. [3] introduced the historical background of RSM. These review papers related to engineering applications involved processing in machinability [5], manufacturing [6], biofuel [7; 8], energy [9; 10], agro-industrial processes [11], and polymers [12]. In an experimental design, an experimental system includes the response of this system and is combined with different levels of the influencing factor. These factors serve as the independent variables for the regression analysis. Experimental runs represent a series of tests for the experiment. The response or output of the experiments is used as the dependent variable for further analysis. The relationship between the response (\(y\)) and the input factors (\(x_{1}\), \(x_{2}\), \(\ldots\), \(x_{k}\)) of the RSM can be expressed as  
\[y_{i}=f(x_{1},x_{2},\ldots,x_{k})+\varepsilon_{i} \tag{1}\]  
where \(y\) is the response of the RSM model and is called the dependent variable; \(x_{1}\), \(x_{2}\), \(\ldots\), and \(x_{k}\) are the influencing variables and are called independent variables in regression; k is the number of factors; and \(\varepsilon_{i}\) is the model's error. The mathematical model of the RSM model includes linear, interaction, and quadratic terms effects. If the process system involves three process variables, \(x_{1}\), \(x_{2}\), and \(x_{3}\), the form of the RSM equation is  
\[y=b_{0}+b_{1}x_{1}+b_{2}x_{2}+b_{3}x_{3}+b_{11}{x_{1}}^{2}+b_{22}{x_{2}}^{2}+b _{33}{x_{3}}^{2}+b_{12}x_{1}x_{2}+b_{13}x_{1}x_{3}+b_{23}x_{2}x_{3}+\varepsilon \tag{2}\]  
If four factors are used, \(x_{1}\), \(x_{2}\), \(x_{3}\), and \(x_{4}\), the RSM equation is  
\[y=b_{0}+b_{1}x_{1}+b_{2}x_{2}+b_{3}x_{3}+b_{4}x_{4}+b_{11}{x_{1}}^{2}+b_{22}{x_ {2}}^{2}+b_{33}{x_{3}}^{2}+b_{44}{x_{4}}^{2}+b_{12}x_{1}x_{2}+b_{13}x_{1}x_{3} +b_{14}x_{1}x_{4} \tag{3}\]  
If the RSM equation includes all variables, as in Equations (2) and (3), it is called a full RSM equation. The relationship between the response variable, the independent variable, and the dependent variable can be established through regression analysis techniques. This regression model is an empirical equation, not a theoretical equation. The major experimental methodologies used for the response surface methodology are the full factorial design (CFD), Box-Behnken design (BBD), and central composite design (CCD) [1; 6; 13; 14; 15; 16].