###### Abstract  
Solid-state drives represent the preferred backbone storage solution thanks to their low latency and high throughput capabilities compared to mechanical hard disk drives. The performance of a drive is intertwined with the reliability of the memories; hence, modeling their reliability is an important task to be performed as a support for storage system designers. In the literature, storage developers devise dedicated parametric statistical approaches to model the evolution of the memory's error distribution through well-known statistical frameworks. Some of these well-founded reliability models have a deep connection with the 3D NAND flash technology. In fact, the more precise and accurate the model, the less the probability of incurring storage performance slowdowns. In this work, to avoid some limitations of the parametric methods, a non-parametric approach to test the model goodness-of-fit based on combined permutation tests is carried out. The results show that the electrical characterization of different memory blocks and pages tested provides an FBC feature that can be well-modeled using a multiple regression analysis. n _et al._[1]_[  
secondary correction schemes, like soft decoding [8], moving read references [6], and even RAID [9]. To this extent, storage designers have devised dedicated parametric statistical models [10; 11; 12; 13; 14; 15; 16] to capture the evolution of the memory's error distribution through well-known statistical frameworks (probability distributions), like Gaussian, binomial, Poisson, gamma, and so on. Concerning the model abstraction level, we identify two families: (_i_) statistical models of the flash channel (i.e., the cells' threshold voltage distributions) used to extrapolate the memory reliability characteristics; and (_ii_) statistical models or machine-learning-based approaches directly applied to the reliability features extracted from measurements. In the first set of models, many parametric continuous probability distributions (e.g., Weibull, lognormal, gamma) are proposed to represent the threshold voltage (\(V_{T}\)) distributions of flash cells and then extrapolate the memory reliability in different scenarios through the calculation of the number of corrupted bits per distribution. Reports in the literature suggest the use of the Gaussian function for its simplicity although it has been found that other mathematical functions exhibit a better fit and even that the tail regions of the \(V_{T}\) distributions in the flash memory are mainly exponential due to the random telegraph noise [17; 18; 19]. To further improve the fitting quality, previous works have proposed modeling \(V_{T}\) distributions with a mixture of Gaussian with data-dependent variances [10; 11; 12; 14], by using a normal-Laplace mixture model [19], developing tailored Monte Carlo models in the crossover regions between different distributions [20], or by relying on the physics-based model associated with the NAND flash architecture [21]. In some cases [11; 12], it is stated that the reliability features extracted from the models tend to be underestimated. Parameterized versions [19] for particular operating conditions, like endurance degradation, describe well the evolution of the model parameters as a function of the memory lifetime, though they rely on complex fitting procedures. For the first time, the authors in [18] discussed the possibility of considering non-parametric models for \(V_{T}\) distribution fitting, although few details were shared with the reader, limiting the model evaluation possibilities. The second set of models used in flash memory targets well-defined metrics for reliability evaluation either at the device or at the system level (i.e., in solid-state storage platforms), namely the bit error rate (BER) or the fail bits count (FBC). Both metrics indicate the number of corrupted bits in a precise location of the NAND flash memory due to specific physical mechanisms, like endurance wear, retention loss, and so on.