###### Abstract
A seminal work is that of [22], where the BER was modeled in different operating corners. A similar approach, although oriented to 3D NAND flash architectures was proposed in [23], where, for the first time, the authors introduced the use of the gamma-Poisson distribution for error modeling, and in [24], where a generalized Pareto distribution was used to model real disturb errors. Other interesting solutions have relied on machine learning algorithms for memory lifetime classification and prediction [13; 15; 16] and on deep neural networks [25; 26; 27]. However, some of the developed models require a huge characterization dataset and significant computing power to run the model training process or the creation of a dedicated computational framework based on neural networks to optimize the device characteristics, such as the case discussed in [28] though for a different technology. Some of these well-founded reliability models have a deep link with the failure mechanisms in the NAND Flash technology [29]. In general, the more precise and accurate the model, the lower the probability of incurring storage performance slowdowns due to improperly calibrated error correction techniques. In this work, we target the second category of models using for the first time, to the best of our knowledge, an approach based on non-parametric inference on the regression coefficients to characterize the FBC in 3D NAND flash memories tested with endurance stress. We focus here on the statistical testing of the model validity (goodness-of-fit test), where the full model, which includes all the considered explanatory variables, is compared to the null model, which lacks explanatory power. To this extent, a non-parametric approach is carried out. The proposed test, unlike the parametric approaches, does not require the assumption that the distribution of the responses follows a specific family of probability laws. Such a test is very powerful, especially (but not only) when the typical assumptions of the parametric approaches (such as the normality of data in the classic regression analysis) are not satisfied and the parametric tests are not reliable [30]. Furthermore, this method is more flexible and robust with respect to the parametric tests [31]. In this work, a permutation test on the goodness-of-fit of a multiple regression model is applied. In particular, we consider such a problem as a multiple test on the significance of the single regression coefficients (partial tests), and the proposed solution is based on the combination of the \(p\)-values of the partial tests. In other words, we study the performance of the 3D NAND flash memories in terms of the sum of the number of errors without assuming a specific probability distribution. In fact, we adopt a regression approach to analyze the relationship between the 3D NAND flash errors and some explanatory factors in order to determine whether such factors affect the number of errors and which factors produce a significant effect. This method is valid regardless of the assumed distribution of the errors. Hence, the main objective of the paper consists in proposing a robust and flexible method to test the validity of the model to predict the performance of the 3D NAND flash memories. Such a method is based on the permutation approach and it is preferable to the classic parametric approach because it is distribution-free and powerful regardless of the underlying data distribution.