## 4 Results And Discussion  
The VIFs of all the independent variables are shown in Table 1; all the values are less than 5, indicating no multicollinearity problem. The significance level \(\alpha\) was set equal to 0.10 and we applied the CPT illustrated above to the data in order to test the hypotheses defined in Equation (4). The global \(p\)-value of the test is equal to 0.0002, which indicates significance at the level \(\alpha=0.10\). The adjusted partial \(p\)-values on the significance of the coefficient estimates with the Bonferroni-Holm correction are shown in Table 2. \begin{table}
\begin{tabular}{c c} \hline
**Variable** & **VIF** \\ \hline d-block & 1.00 \\ d-page-c2 & 1.83 \\ d-page-c3 & 1.83 \\ d-page-c4 & 1.83 \\ d-page-c5 & 1.83 \\ d-page-c6 & 1.83 \\ d-page-c7 & 1.83 \\ d-page-c8 & 1.83 \\ d-page-c9 & 1.83 \\ d-page-c10 & 1.83 \\ d-page-c11 & 1.83 \\ d-page-c12 & 1.83 \\ d-tlcpage-1 & 1.33 \\ d-tlcpage-2 & 1.33 \\ PE-cycles & 1.00 \\ \hline \end{tabular}
\end{table} 
Table 1: Variance inflation factors of the explanatory variables. Looking at the adjusted _p_-values, the significance of the overall test can be limited to a few of the regression coefficients. In particular, it appears that the sum of the number of errors in Layers 0, 1, 2, and 3 is strongly affected by the variables _d-page-c6_, _d-page-c12_, _d-tlcpage-2_, and _PE-cycles_. A moderate effect on the dependent variable is seen with _d-page-c9_, _d-page-c10_, and _d-page-c11_. Finally, we found a weak significance of _d-page-c5_ on the sum of the number of errors. From an experimental standpoint, we were expecting to identify the _PE-cycles_ variable as one of the most significant in affecting the response variable of the model, given the experimental results of the endurance characterization provided in Figure 3. In addition, this finding is consistent with the expectation from the 3D NAND flash endurance test standards [33; 34]. Concerning the variable _d-tlcpage-2_, we were also expecting that most of the endurance failures would come from TLC pages associated with the CSB or MSB, as demonstrated in the experimental results section of this work. Regarding the dependency of the response variable on the topological position, we would like to refer to the work reported in [37], where it is shown that some 3D NAND flash memory blocks have some specific locations (due to manufacturing variability) that are more sensitive in the generation of corrupted bits (i.e., errors). Furthermore, the condition of normality of the model errors, typical of the classical parametric approach to regression analysis, is not satisfied. The normal probability plots that confirm this statement are shown in Figure 5, graphs (a) and (b). In accordance with the analysis of the residuals, marginal error distributions may be asymmetric (see graphs (c) and (d)). These results support the belief in the benefit of embracing a nonparametric approach, which does not require the assumption that the underlying distribution follows a certain family of probability laws, such as Weibull or others typically used in parametric approaches. Hence, this test, unlike its parametric competitors, is powerful regardless of the underlying probability distribution. Furthermore, the use of CPT allows us to test the validity of the model and to determine which explanatory variables affect the number of errors.