## 2 The 3D NAND Flash Endurance Reliability Case Study
### Data And Model  
The dataset employed was reduced from the original endurance characterization dataset retrieved from 3D NAND flash measurements. The new dataset used for modeling purposes consisted of 144 rows and 16 columns (variables). The variable denominated _sum-Errors_ is the model output and represents the FBC retrieved for each measured TLC-page in a memory block. A TLC-page consists of a 16 kB data readout plus the parity size used for ECC purposes. Since our experimental setup allows measuring 4 kB chunks (i.e., _Layer_), we measured the FBC per layer and summed them to calculate the FBC per page. The variable _Block_ is an identifier of the tested 3D NAND flash block. Further, the variable _Page_ was split into 12 clusters (one for each 32), and then 11 dummy variables were created based on the clusters. These clusters represent homogeneous topological areas of a memory block and were identified according to the device structure. The variable _TLC-Page_ indicates whether the read page in a block is associated with the LSB, CSB, or MSB. Finally, the variable _PE-cycles_ represents the endurance lifetime points where the FBC of the 3D NAND flash block was characterized (i.e., fresh device or at EoL). In this list, we report the variables of the model that consider both physical, topological, and logical features of the 3D NAND flash devices tested in this work:  
* _sum-Errors_, the dependent variable which represents the sum of the number of errors in Layer 0, 1, 2, 3 and for each TLC-Page;
* _d-block_, dummy explanatory variable which is 1 for block A and 0 for block B;
* _d-page-c2_, dummy explanatory variable which is 1 for cluster 2 of _Page_ and 0 for all the other clusters in the measured block;
* _d-page-c3_, dummy explanatory variable which is 1 for cluster 3 of _Page_ and 0 for all the other clusters in the measured block;
* _d-page-c4_, dummy explanatory variable which is 1 for cluster 4 of _Page_ and 0 for all the other clusters in the measured block;
* _d-page-c5_, dummy explanatory variable which is 1 for cluster 5 of _Page_ and 0 for all the other clusters in the measured block;  
Figure 3: FBC extracted during an endurance stress-test in different 3D NAND flash memory TLC pages as a function of the lifetime (\(N_{P/E}\)). The average behavior between pages has been reported as a guideline for general reliability considerations. * _d-page-c6_, dummy explanatory variable which is 1 for cluster 6 of _Page_ and 0 for all the other clusters in the measured block;
* _d-page-c7_, dummy explanatory variable which is 1 for cluster 7 of _Page_ and 0 for all the other clusters in the measured block;
* _d-page-c8_, dummy explanatory variable which is 1 for cluster 8 of _Page_ and 0 for all the other clusters in the measured block;
* _d-page-c9_, dummy explanatory variable which is 1 for cluster 9 of _Page_ and 0 for all the other clusters in the measured block;
* _d-page-c10_, dummy explanatory variable which is 1 for cluster 10 of _Page_ and 0 for all the other clusters in the measured block;
* _d-page-c11_, dummy explanatory variable which is 1 for cluster 11 of _Page_ and 0 for all the other clusters in the measured block;
* _d-page-c12_, dummy explanatory variable which is 1 for cluster 12 of _Page_ and 0 for all the other clusters in the measured block;
* _d-lclpage-1_, dummy explanatory variable which is 1 if the read Page is associated with Middle Page (CSB) and 0 otherwise;
* _d-lclpage-2_, dummy explanatory variable which is 1 if the read Page is associated with Upper Page (MSB) and 0 otherwise;
* _PE-cycles_, dummy explanatory variable representing the memory lifetime which is 1 for _PE-cycles_ = EoL and 0 for _PE-cycles_ = 0 (fresh device). From a descriptive point of view, the main effect plots of the explanatory variables are represented in Figure 4. The typical block-to-block, page-to-page, and TLC page error variability are expected as already confirmed in previous literature reports [35].