# Response Surface Methodology Using Observational Data: A Systematic Literature Review
## 2 RSM Overview for Response Optimization
### Classic RSM  
As mentioned above, classical RSM works by integrating three tools in a sequential analysis (Figure 1). In the first stage, classic RSM implements the DoE. In this step, the DoE plays a role in experiment planning, data collection, analysis, and interpretation and ensures that the experiment fulfills its purpose. Orthogonality fulfillment in the DoE matrix ensures that the predetermined process parameters can be estimated independently among others. Second, classic RSM applies a specific mathematical model to fit the data obtained by the DoE. This model captures the relationship between factors or parameters as inputs and responses as outputs. Classic RSM usually prefers to adopt a linear model because of its simple interpretation and formal statistical inference of all its required assumptions during the modeling stage. Third, the optimization stage works by finding the factor (or parameter) setting to optimize the response. Standard optimization tools, such as mathematical optimization and desirability functions [21], are preferred in classic RSM, along with some theoretical approaches. As the required assumptions in RSM are fulfilled for each stage, this methodology has become the best choice rather than any modification.  
In addition, an essential prestage in RSM involves determining the factors involved in the analysis. As the DoE is applied, researchers should subjectively select the factors in RSM. They need to find the factors with more minor or significant effects on the response based on previous research, considering the scope and knowledge domain of the researchers.  
Figure 1: Overview of RSM (adopted from [19]).  
As an established methodology for designed, experimentally-based optimization, the classic RSM has been successfully applied for years in many research fields. Starting with the concept proposed by [22], more than 48,000 Scopus-indexed papers applied classic RSM. Figure 2 shows that the general engineering fields dominate the percentage of RSM applications, followed by chemical engineering, chemistry, biological sciences, and other applied sciences. It means that RSM plays an important role as an optimization methodology in many research fields, and there are also considerable developments in RSM to accommodate recent research issues.  
Many improvements to classic RSM have been performed, mainly when optimization of the target by standard RSM procedures provides dissatisfactory results. Some papers on RSM improved the linear model to increase its performance in capturing the causality between factors and responses by replacing it with nonlinear versions. For example, [23; 24] applied neural networks and support vector regression for RSM modeling to optimize surface roughness, respectively, in the milling and turning process. Other researchers [25] provided a similar approach that uses the RSM neural network model to optimize iron extraction from food. The complexity of these modified RSM models requires advanced optimization techniques and adopt a meta-heuristics method; for example, the authors of [26; 27] successfully adopted a genetic algorithm for injection-molding and CNC process optimization.  
Classic RSM can be improved by some modifications in order to enhance the performance of the process being investigated. However, all the methodological improvements of classic RSM should consider the basic concept of RSM, its stages, and the final purpose of the RSM, i.e., process optimization.