## 1 Introduction  
The annual shipments of tablet computing devices surpassed personal computers in 2013, making flash memory the predominant mode of data storage for digital consumers [1]. However, the size of the digital universe is expected to be around 40 trillion gigabytes, which is roughly 5200 gigabytes of data for every living person on earth [2]. For a long time to come, consumers of digital data would rely on relatively cheaper storage options for backup and archival purposes, i.e., local or cloud storage afforded by magnetic hard disk drives (HDD) [1]. HDD are generally regarded as reliable components as their mean time to failure (MTTF) typically lies between 1 million to 1.5 million hours, as per manufacturer specifications. This would suggest a maximum annual failure rate (AFR) of 0.88%; however, field observations indicate that annual disk replacement rates (ARR) of 2-4% are common and, in some systems, replacement rates of up to 13% have also been reported [3; 4; 5]. Moreover, HDD are the most frequently replaced hardware components in large-scale information technology (IT) infrastructure [6], and, in some large datacenters, 70-80% of the known failures have been causedby failing HDD [7; 8]. Thus, detecting a failing HDD is important to ensure data availability and to avoid permanent data loss. Hard disk drives are complex electromechanical devices and their failure can be caused by a number of factors, which may not always be easy to determine. A review of the available literature reveals that three approaches have been considered to determine the characteristics of failed HDD and then to use that knowledge to predict an impending failure. The first approach explores the use of external sensors, the second approach analyzes logs and replacement records of failed drives, whereas techniques based on the third approach utilize self-monitoring, analysis, and reporting technology (SMART) attributes that are internally recorded in all HDD. In [9], the use of accelerometers and acoustic emissions (AE) sensors has been investigated. However, the authors conclude that the degradation signatures obtained from the vibration acceleration and AE signals are weak, inconsistent, and do not follow a trend that is indicative of the degradation of the HDD. Moreover, the use of accelerometers and AE sensors is prohibitive in terms of the associated costs, given the number of sensors required to monitor large-scale IT infrastructure. Hence, they propose using three SMART attributes instead, to evaluate the condition of the HDD. In [3; 4; 6; 10], the authors analyze logs and replacement records of more than \(100,000\) hard disks that were determined to be faulty and hence replaced by the customers. However, these studies do not investigate the causes of disk failures; rather, they provide an analysis of the data from a reliability perspective, and hence do not offer any useful clues for predicting a failing HDD. Nevertheless, these studies do offer important conclusions. First, HDD failure rates are influenced by factors such as workloads, \"duty cycles\", \"powered-on-hours\", and the temperature and humidity of the environment they operate in. Second, the actual replacement rates for HDD are much higher than those suggested by manufacturer specifications, roughly by a factor of 2 to 10 for drives less than five years old, and by a factor of 30 for older drives. Third, the replacement rates for serial advanced technology attachment (SATA), small computer system interface (SCSI), and fiber channel (FC) drives are more or less the same. The majority of the techniques [7; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24] developed to detect failing HDD use the third approach, i.e., utilizing SMART attributes to detect impending disk failure. SMART was originally named drive failure prediction (DFP) and was adopted by the HDD industry in 1995 [11; 13].