## 5 Conclusions  
In this paper, a novel two-tier approach was presented to select the most effective precursors to a failing HDD. These precursors were selected from an initial list of 42 SMART attributes, which were  
Figure 4: The receiver operating characteristic (ROC) curves for SVM and Naive Bayes Classifiers using different feature selection schemes.  
recorded in a commercial datacenter over a period of nine months for 21 different models with storage capacities ranging from 1.0 TB to 8.0 TB. The proposed two-tier approach evaluated the SMART attributes, both in combinations and individually. First, a GA was used to explore different feature subspaces in order to determine the best combination of features or SMART attributes. The quality of a feature subset was measured by determining how well clustered the samples of those features are for each of the two classes, i.e., healthy and failed HDD, and how well separated those clusters are from one another. This was done by calculating the ratio of intra-class compactness to inter-class separation for each subset of features, and finding the subset that minimized this ratio. The compactness of a class and the separation between two classes were measured using Euclidean distances. In the second tier, a new measure, i.e., significance score, was proposed to individually evaluate the features selected by the GA. The significance score measured the statistical contribution of a given feature towards disk failures. Features with statistical scores lower than a certain value were discarded. The final list of features selected by the proposed two-tier feature selection process comprised nine SMART attributes as opposed to the original 42, resulting in a shorter training time for the classifiers. These nine attributes were then used to train a generative classifier, the NB. The NB gave an FDR of 98.40% compared to 40.0% by the SVM, which is a discriminative classifier. To avoid overfitting by the classifier on the majority class data, the inherent class-imbalance problem in the failure data for HDD was addressed by under-sampling the majority class of healthy HDD. The proposed method correctly detected 185 of the 188 failed drives with only 1.2 false alarms on average.  
[PERSON] was involved in the conception of the idea and its implementation. [PERSON] was involved in the design of experiments. [PERSON]-[PERSON] and [PERSON] were involved in the analysis and interpretation of results. [PERSON] and [PERSON] prepared the manuscript. [PERSON]-[PERSON] and [PERSON] were involved in the revision of the manuscript. All authors have read and agreed to the published version of the manuscript.  
This work was supported by 2020 Research Fund of University of Ulsan.  
The authors declare no conflict of interest.  
The following abbreviations are used in this manuscript:  
AE Acoustic Emission  
AFR Annual failure rate  
ARR Annual (disk) replacement rate  
BIOS Basic input output system  
CRC Cyclic redundancy check  
DFP Disk failure prediction  
DMA Direct memory access  
FAR False alarm rate  
FC Fiber channel  
FDR Failure detection rate  
FPR False positive rate  
GA Genetic algorithm  
HDD Hard disk drive  
IT Information technology  
MTTF Mean time to failure  
MVM Multi-variate multi-nomial  
NB Naive Bayes  
SATA Serial advanced technology attachment  
SCSI Small computer system interface  
SMART Self monitoring, analysis and reporting technology  
SVM Support vector machine  
ROC Receiver operating characteristic  
TPR True positive rate