## 3 Results  
### Initial Data Screening  
The data screening process begins with tiled Q-plots for each replicate dataset and quality characteristic. As shown in Figure 2, all nine datasets appear symmetrically distributed and fit closely around their centerlines. On the other hand, exploring replicate shape patterns by violin plot screening [74] reveals several instances of skewed motifs (Figure 3). Median locations are maintained uniform across different replicates. However, the distribution shapes within each quality characteristic may also vary for different settings. For example, in the case of the average permeate flux, the \"bulging pattern\" of the data distribution and its orientation are not uniform; the mode of the second and third settings bottoms toward \(\rm{J_{P}}\) values (Figure 3A). Tail effects are more exaggerated in the second replicate. Similar comments may be extended to the COD rejection rate behavior, only this time, it is the first replicate dataset that exhibits stronger skewness, while the third replicate is more balanced (Figure 3B). Therefore, it is not clear whether a propensity is present and whether it is co-operative across all characteristics. Finally, the cumulative flux decline data are more consistently concentrated toward lower values (Figure 3C); skewness tendencies are more uniform for this quality characteristic. At first glance, there is no indication that the three quality characteristics might share parallel trends.  
Figure 3: \(Cont.\)  
Figure 2: QQ-plot replicate screening of the three quality characteristics: (1) average permeate flux (\(\rm{J_{P}}\)), (2) COD rejection rate (COD), and (3) cumulative flux decline (SFD).  
To probe potential relationships among characteristic responses, the pairwise correlations of the three quality characteristics have been tabulated in Table 1; the upper and lower confidence intervals were set at 95% (IBM SPSS v.29). Prior to estimating their respective correlations, the data from the three replicates were consolidated into a single group for each quality characteristic. It can be observed that there is a strong positive correlation between the average permeate flux and the cumulative flux decline. This positive correlation is expected, given the underlying physical principles of permeate flux and flux decline. Their correlation coefficient is estimated to have a value of 0.83; the 95% confidence interval ranges from 0.66 to as high as 0.92. This implies that the factorial modeling may be simplified by reducing the original three-response problem to a two-response problem. It can also be observed that there is a weaker negative correlation between the COD rejection rate and the cumulative flux decline since their estimated correlation coefficient value of \(-0.39\) is statistically significant (\(\alpha=0.05\)). To determine whether it was plausible to further simplify the model structure, a bagplot screening [75] was performed (Figure 4). It is clear that the only correlation worth retaining is indeed that between the average permeate flux and the cumulative flux decline (middle bagplot), which illustrates the \"sufficiently elongated\" bag effect.  
Figure 3: Violin plot replicate screening of the three quality characteristics: (**A**) average permeate flux (J\({}_{\rm p}\)), (**B**) COD rejection rate (COD), and (**C**) cumulative flux decline (SFD).  
It is observed that there are no outlier points beyond the bagplot fence. The zone between the loop and the fence is narrow--for all three bagplots--an indication that the formed bags solidly support the depth 2D median estimations.