## 2 Experimental and Statistical Methods  
Various methodologies were employed to advance and refine new predictive models, with a particular emphasis on statistical analysis methods. Within this study, statistical techniques were utilized to analyze available data from the factory lab in order to uncover the correlation between formulations and final color discrepancies. These methods are summarized as follows:  
* Number mining, involving the selection of diverse formulations and processing parameters linked to color discrepancies based on historical data. * RSM experiments, which are employed when a few significant factors are involved in optimization. Various types of RSM designs, such as full factorial design, central composite design (CCD), Box-Behnken design (BBD) and D-optimal design, were utilized. RSM serves as a practical tool for evaluating the impact of multiple variables and their interactions on either single or multiple response variables. Moreover, the study juxtaposed RSM with alternative optimization methods, including artificial neural networks (ANNs) [15]. Moreover, advanced statistical analysis was conducted using RSM and microstructural examination via scanning electron microscopy (SEM) to optimize the process [16]. The statistical analysis in this study is focused on scrutinizing the thermal gelation tendencies of two known reactants employing RSM; partially hydrolyzed polyacrylamide (PHPA) and polyethyleneimine (PEI). The significance of the model was validated against experimental data with a confidence level of 95% through analysis of variance (ANOVA) [17]. An experimental design approach was employed to optimize the rheological properties of the HPAM polymer. This involved examining the impacts of three key parameters: the size of polystyrene microspheres, their concentration and the test temperature, on the zero-shear viscosity of HPAM polymer solutions. The findings illustrated a strong alignment between the anticipated results derived from the RSM method and the actual experimental observations [18]. Multiple techniques of design were implemented, including the following:  
* Box-Behnken Design (BBD)  
Design of experiments (DOE) is extensively employed in diverse scientific fields owing to its capacity to reduce the number of necessary experiments. It was utilized to pinpoint the variables crucial for the effective establishment of a process window model. The experimental design incorporated both the utilized level and the extruder FR, S and T. It considered the same three process parameters and represented each factor with three different levels coded as \(-\)1, 0 and +1, as depicted in Table 1.  
Table 2 presents the selected experimental design levels for the three process parameters: temperature, feed rate and screw rpm. These parameters were varied across 12 different treatments, with an additional 5 center points introduced to assess the variables' impact on color. The extra center points were included to estimate experimental error. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Processing**} & \multirow{2}{*}{**Parameters**} & \multicolumn{3}{c}{**3 Code Levels**} \\ \cline{3-5}  & & \(-\)**1.0** & **0.0** & **+1.0** \\ \hline T & degrees Celsius (\({}^{\circ}\)C) & 230 & 255 & 280 \\ \hline S & revolutions per minute (rpm) & 650 & 750 & 850 \\ \hline FR & kilograms per hour (kg/h) & 11 & 19 & 27 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: In the actual coding unit, three levels and parameters’ experimental design. The RSM employed also a DOE based on the BBD with the same objective: examining the influence of varied processing conditions on the output color of a compounded plastic grade during extrusion. Compared to the full factorial design, this approach offers a design space comprising 17 runs and a wider range of input parameters. It is more precise, cost-effective and time-efficient than the 3-level full factorial design.