# Response Surface Methodology Using Observational Data: A Systematic Literature Review
## 5 Synthesis and Discussion
### Comparative Analysis  
Several approaches to handling observational data for RSM were proposed, and rationales were provided for each based on specific references. Figure 13 represents the combination of tools or methods applied to RSM-OD, and the maps based on the stages in classic RSM analysis are shown in Figure 1. By reading from the left side, each box in the figure represents the tools or methods used in RSM-OD, and the lines denote the other tools/methods at each stage of the RSM analysis. Various modifications in RSM-OD in the reference papers still obeyed the basic principles of classical RSM, and any RSM improvement should not be much different. Figure 12: Optimization stage. Figure 13: Combination of the methods adopted in RSM-OD. The method combinations started with the identification of nondesigned-experimental data (Code A). Several papers referred to observational data from this type of continuous process, and others referred to previous experimental data or conducted an actual nondesigned experiment. Code B categorizes the recorded variables that will be the factors in RSM. Primarily, the studied process records its equipment parameters, the composition of the materials, or both. Code C represents how the provided data will be treated by considering all observations or selecting its subset. Code D categorizes the standard DoE adopted while treating the provided data within the RSM analysis. Code E shows the RSM model adopted, and Code F represents the optimization technique. The combinations of Code A-F provided many options. However, the main concept of the three-stage RSM became the focus of grouping each paper. As is shown in Table 6, based on Codes C (stage 1: treating data), E (Stage 2: RSM model), and F (Stage 3: optimization), only seven types of approaches, which were represented by seven clusters, were obtained, and the references are shown in Table 6.  
\begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline \multirow{2}{*}{**Clusters**} & \multicolumn{4}{c}{**Three Stages of RSM**} & \multicolumn{4}{c}{**Additional Stage**} & \multirow{2}{*}{**References**} \\ \cline{2-2} \cline{4-7}  & **Stage 1** & **Stage 2** & **Stage 3** & & & & \\  & **(Code C)** & **(Code E)** & **(Code F)** & **Code A** & **Code B** & **Code D** & **Code D** \\ \hline \hline \multirow{8}{*}{ \begin{tabular}{l} Cluster 1: \\ subset—Linear model—local search \\ (12.05\%) \\ \end{tabular}  } & \multirow{8}{*}{C1} & \multirow{8}{*}{E1} & \multirow{8}{*}{A1} & \multirow{8}{*}{B1} & \multirow{8}{*}{D1} & \multirow{8}{*}{[44]} \\ \cline{1-1} \cline{5-7}  & & & & & & D3 & [2] \\ \cline{1-1} \cline{5-7}  & & & & & & D2 & [45] \\ \cline{1-1} \cline{5-7}  & & & & & & B2 & D2 & [35] \\ \cline{1-1} \cline{5-7}  & & & & & & & D1 & [46] \\ \cline{1-1} \cline{5-7}  & & & & & F4 & & & D3 & [11]  
The most preferred was cluster 4, with 55.42% relativity to all the selected reference papers; it used all observations as the input to the linear RSM model and applied the ordinary local search optimization method. It is similar to standard RSM, but risks may arise during the analysis by selecting all observations. Cluster 1, which was similar to Cluster 4, had the second highest value: 12.05%; the difference is that this cluster selected a subset of observations that fulfilled a particular DoE and guaranteed interfactor orthogonality. Next, Cluster 5 (10.84%) was similar to Cluster 4 but replaced the local optimization method with a metaheuristic technique. A more complex RSM model with all observations as the input became the rationale for this replacement. Cluster 6 (8,43%) applied other optimization techniques, such as Taguchi S/N ratio, linear programming, and the Monte Carlo method [2,44,45]. In Clusters 2 and 7, the linear model was replaced with neural networks to handle the nonlinearity of the observational data, all observations, or the subset data. Moreover, such a complicated black-box neural-network model applied the metaheuristics method to find the optimum.