Information Technology Reference
In-Depth Information
will find one in a nearby sector or that you will to find a fault in another
sector soon.
Assuming uniform error rates. The relative contributions of different
causes of nonrecoverable read errors can vary across models and different
generations or production runs of the same model. For example, one
model of disk drive might have many of its sector read errors caused by
contaminants damaging its recording surfaces while another model might
have most of its errors caused by write interference where writes to one
track perturb data stored on nearby tracks. The first might see its error
rate rise over time, while the second might have an error rate that increases
as its write/read ratio increases.
Failure rates can even vary across different individual devices. If you
deploy several outwardly identical disks, some may exhibit tens of nonre-
coverable read errors in a year, while others operate flawlessly.
Example: Unrecoverable read errors.
Question: Suppose that the nearly-full 500 GB disk on your laptop has just
stopped working. Fortunately, you have a recent, full backup on
a 500 GB USB drive with an unrecoverable read error rate of 1
sector per 10
14
bits read. Estimate the probability of successfully
reading the entire USB backup disk when restoring your data to
a replacement laptop disk.
Answer: We need to read 500 GB, so the expected number of failures is
500 GB
810
9
bits
GB
1
error
10
14
bits
= 0:04 . The probability of encoun-
tering at least one failure might be a bit lower than that (since we
may encounter multiple failures as we scan the entire disk), but
there appears to be a chance of at least a few percent that the
restoration will not be fully successful.
We can approach the problem in a slightly different way by in-
terpreting the unrecoverable read rate as meaning that each bit
has a 10
14
chance of being wrong and that failures are inde-
pendent (both somewhat dubious assumptions, but probably OK
for a ballpark estimate). Then each bit has a 1-10
14
chance of
being correct, and the chance of reading all bits successfully is
P
S
= (1 10
14
)
850010
9
= 0:9608. Under this calculation, we
estimate that there is slightly less than a 4% chance of encoun-
tering a failure during the full-disk read of the backup disk.
As noted in the sidebar, these calculations ignore some impor-
tant factors, so the results may not be precise. But, even if they
are off by as much as an order of magnitude, then it is still rea-
sonable to conclude that the rate of nonrecoverable read errors
is likely to be non-negligible.
