Information Technology Reference
In-Depth Information
(1=(1 10
15
))
9
disks
10
12
bytes
disk
8
bits
P
succeed recovery read
=
byte
0:9306
So, there is nearly a 7% chance that recovery will fail, and we
have
10
6
100
1
= 1:44 10
5
hours
MTTDL
disk+sector
=
1 0:9306
Notice that this rate of data loss is higher than the rate from double disk failures
calculated above. Of course, the relative contributions of each failure mode will
depend on disks' MTTF, size, and bit error rates as well as the system's MTTR.
Failure of two sectors sharing a redundant sector. In principle, it is also
possible to lose data because the corresponding sectors fail on different disks.
However, with billions of distinct sectors on each disk and small numbers of
latent failures per disk, this failure mode is likely to be a negligible risk for most
systems.
Overall data loss rate. If we assume independent failures and constant fail-
ure rates, then we can add the failure rates from the two significant failure
modes to estimate the combined failure rate:
FailureRate
indep+const
= FailureRate
twofulldisk
+ FailureRate
disk+sector
1
MTTDL
twofulldisk
+
1
MTTDL
disk+sector
=
N(G 1)MTTR
MTTF
2
+
N P
failrecoveryread
MTTF
=
MTTF
(
MTTR(G 1)
N
=
+ P
failrecoveryread
)
MTTF
The total failure rate is thus the rate that the first disk fails times the rate that
either a second disk in the group fails before the repair is completed or a sector
error is encountered when the disks are being read to rebuild the lost disk.
We label the above FailureRate
indep+const
to emphasize the strong assumptions
of independent failures and constant failure rates. As noted above, failures are
likely to be correlated in many environments and failure rates of some devices
