## 3 Response Models
### Model Fitting
The regression results when the Full CCD is used are presented in Table 8 for the response variable D-flow, as an example, due to length limitations. For more details, see reference [18]. To the best of our recollection, similarly to the previous research by [18], here, all the axial points were excluded in the multiple fit of the D-flow regression model. Thus, the quadratic model given by Eq. 1 was not able to explain the response outside the hypercube space. The regression model fit with Fractioned Plan A also presented some difficulties. A couple of runs were excluded based on the normal plot of the residuals. In the case of Fractioned Plan A for the D-flow, to reach a non-significant lack of fit, the mixtures CC1 (Std#16 Run), F17 (Std#8 Run) and CC7 (Std#22 Run) were excluded (see Figure 2). For the T-funnel, after applying an inverse transformation, one axial mixture still had to be excluded (see Figure 3). Table 9 summarises the actions undertaken for fitting the D-flow and T-funnel models for Fractioned A. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Full** & **Fitting Model Action** & **Mix Nr.** & **Value** & **Reason for Action** \\ \hline \multirow{8}{*}{D-flow} & & CC1 & 168.00 \\ \cline{3-4}  & & CC2 & 342.00 \\ \cline{3-4}  & & CC3 & 330.50 \\ \cline{3-4}  & & CC4 & 337.00 \\ \cline{3-4}  & First action: exclude all axial mixtures & CC5 & 295.00 \\ \cline{3-4}  & & CC6 & 368.50 \\ \cline{3-4}  & & CCT & 398.00 \\ \cline{3-4}  & & CC8 & 169.50 \\ \cline{3-4}  & & CC9 & 338.00 \\ \cline{3-4}  & & CC10 & 330.50 \\ \hline \multirow{4}{*}{T-funnel} & First action: apply inverse transform & - & - & Optimisation of properties of residuals. \\ \cline{2-4}  & Second action: exclude one factorial mixture & F15 & 26.33 \\ \cline{1-1} \cline{2-4}  & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Model fit results for D-flow and T-funnel—Full plan. Figure 3: Fractioned Plan A: Residuals versus predicted values for T-funnel. \begin{table}
\begin{tabular}{l l c c c} \hline \hline
**Fractioned A** & **Fitting Model Action** & **Mix Nr.** & **Value** & **Reason for Action** \\ \hline \multirow{8}{*}{D-flow} & First action: exclude one & \multirow{4}{*}{FC1} & \multirow{4}{*}{168.00} & Inappropriate normal plot; \\  & axial mixture & & & Residual versus predicted \\ \cline{3-5}  & & & plot out of range. \\ \cline{3-5}  & \multirow{4}{*}{Second action: exclude one & \multirow{4}{*}{F17} & \multirow{4}{*}{330.00} & Inappropriate normal plot; \\  & & & Residual versus predicted \\ \cline{3-5}  & & & plot out of range; \\ \cline{3-5}  & \multirow{4}{*}{D-flow} & Second action: exclude one & \multirow{4}{*}{F17} & \multirow{4}{*}{330.00} & Inappropriate normal plot; \\  & & & & Residual versus predicted \\ \cline{3-5}  & & & plot out of range. \\ \cline{3-5}  & \multirow{4}{*}{Third action: exclude one & \multirow{4}{*}{CC7} & \multirow{4}{*}{398.00} & Inappropriate normal plot; \\  & & & Residual versus predicted \\ \cline{3-5}  & & & plot out of range; \\ \cline{3-5}  & & & & high leverage point. \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Model fit results for D-flow and T-funnel—Fractioned Plan A.  
Figure 2: Normal plots of D-flow residuals for Fractioned Plan A: (**a**) all runs; (**b**) CC1 (Stdd#16 Run) excluded. In the case of Fractioned Plan A for the T-funnel, in addition to the inverse transformation, we excluded the sample CC6 (Std#21 Run--Figure 2), which was enough to prevent the model from exhibiting a significant lack of fit. Figure 3 shows graphically the T-funnel residuals versus the predicted values for Fractioned Plan A before excluding the CC6 mixture. In case of Fractioned Plan B for the D-flow, the other half of the Full Plan, to obtain a non-significant lack of fit, two axial points were dismissed: CC1 (Std#17 Run) and CC7 (Std#23 Run) (see Figure 3). In addition, a power transform was applied to the data. Figure 4 presents the Cook's distance before and after removing these two runs. The inverse square root transformation was necessary for the T-funnel to fit the model.