Generic data reliability model in the cloud - Reliability Assurance of Big Data in the Cloud - page 33

4.1.3 Failure rate pattern of storage devices
As mentioned in Section 2.1 , there are three different styles of failure rate patterns
that have been applied in existing research studies and industry standards, which are
(1) the constant failure rate applied in reliability models strictly following exponential
distribution, (2) the continuous variable failure rate pattern applied in “bathtub” (and
extended models based on the bathtub theory) reliability models, and (3) the discrete
failure rate pattern applied in several research studies and industry standards. In this
book, we describe the disk failure rate pattern with discrete failure rates, which divides
the life span of disks into discrete life stages with discrete disk failure rates. By using
the discrete disk failure rate pattern, the constant disk failure rates in different disk
life stages and the trend of changes in disk reliability are well combined. Compared to
the continuous variable failure rate pattern, the discrete disk failure rate pattern could
greatly simplify the computational complexity of the reliability model, and hence re-
duce the computing overhead for calculating parameters in the data reliability model.
In addition, by using the discrete disk failure rate pattern, we could also apply existing
research results in industry to our research. In Chapter 6 , we conduct the evaluation
for our research based on the discrete disk failure rates provided by the International
Disk Drive Equipment and Materials Association (IDEMA) standards and Google's
9-month disk failure trend study.

4.2 Generic data reliability model

In this section we describe our generic data reliability model. The relationship be-
tween data reliability and the variable disk failure rate is demonstrated by presenting
data reliability with static disk failure rate and data reliability of a single replica with
variable disk failure rate respectively. Finally, a generic data reliability model is pre-
sented in detail. For easy description, we use the term “data file” to represent a Cloud
data storage unit, where actually any types of data storage unit, such as data object and
data block, are also applicable.

4.2.1 Data reliability with static disk failure rate
For many existing theories that assume disk reliability following the exponential dis-
tribution, the failure rate of each disk is a constant. In that case, the reliability of a disk
over period T can be expressed as equation (4.1) :

− λ T

(4.1)

RT e () =

In this equation, R ( T ) is the function of the disk reliability over period T. l is the
disk failure rate. The replicas stored in the disk should have the same reliability as the
disk. In other words, if a data center experiences 100 disk failures from 10,000 disks
for a year, the average disk failure rate is 1% per year, and thus the reliability of each
replica stored in the data center should be 99% per year. Therefore, equation (4.1) is