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and so forth [20] . In addition to the bathtub curve model, some other studies have
also obtained results that contradict the constant disk failure rate model. For example,
one study [18] shows that populations of disks generally do not follow an exponential
failure distribution.
In addition to the exponential disk reliability and the bathtub disk reliability models,
there is another type of model that describes the failure pattern of disks in a discrete
fashion. For example, the International Disk Drive Equipment and Materials Associa-
tion (IDEMA) proposed a compromised presentation for disk failure rates that uses
discrete disk failure rates [38] . It divides the life span of each disk into four different
life stages, which are 0-3 months, 3-6 months, 6-12 months, and 1 year to the end-of-
design life (EODL), and disks have different failure rates at different life stages. The
discrete disk reliability models have fixed the inconsistency between the exponential
disk reliability models, which are of constant disk failure rates, and the variable disk
failure rate in reality. Moreover, such models greatly reduced the complexity of the
continuous disk reliability model based on the bathtub curve. Such a discrete disk fail-
ure rate model has been demonstrated to be feasible [20] , and a 9-month investigation
conducted by Google also obtained results consistent to this model [17] .
2.1.2 Other storage medias
This topic will primarily focus on storage media of disks. However, in addition to the
widely used disks as the dominating storage devices, there are also several other data
storage medias that need to be mentioned.
Magnetic tape: It is a data storage device that uses magnetic tapes in the form of cartridges
or cassettes for storing large amount of data with very low time requirements. Currently,
the highest capacity tape cartridges can reach 8.5 TB [39] , which is quite large. The biggest
advantage of magnetic tape data storage is that the storage cost can be signiicantly reduced
as tapes can be much cheaper than disks. Modern usage of magnetic tape storage is primar-
ily as a high-capacity medium for backups and archives. However, the poor random access
performance and high maintenance overhead of a tape library have limited its use. Little re-
search has been conducted on investigating the reliability pattern of magnetic tapes. Several
research studies committed to replacing magnetic tape data storage with disk storage have
been spotted in both academia and industry [40-42] .
Solid-State Drive (SSD): It is a data storage device that uses solid-state memory to store data.
SSDs were invented for the same purpose as disks and magnetic tapes, but they are made
of electronic storage units and do not have any mechanical parts. Unlike disks, SSDs do not
store data on spinning platters, but use lash memory instead, such features have eliminated
the possibility of storage failures caused by mechanical problems. Compared to disks, SSDs
have several beneits, such as much higher data read/write speed and lighter weight. How-
ever, this type of storage is more expensive per gigabyte of storage and has a lower storage
capacity. Each storage unit (memory cell) of SSDs has a strictly limited number of write
cycles. Therefore, under certain usage frequency, the failure rate of SSDs could be shown
in a continuously rising form, in which the magnitude of increment depends on the writing
frequency of SSDs. In addition, some research has also found that SSDs are more vulner-
able to power faults compared with other disks [43] . In order to enhance the data reliability
assurance for storing data on SSDs, RAID-based approaches have been investigated [44,45] .
 
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