On Thu, Jan 12, 2006 at 11:16:36AM +0000, David Greaves wrote:
> ok, first off: a 14 device raid1 is 14 times more likely to lose *all*
> your data than a single device.
No, this is completely incorrect. Let A denote the event that a single
disk has failed, A_i denote the event that i disks have failed.
Suppose P(A) = x. Then by Bayes's Law the probability that an n disk RAID
will lose all of your data is:
n_1 = P(A) = x
n_2 = P(A_2) = P(A) * P(A_1 | A) = x^2
n_3 = P(A_3) = P(A) * P(A_2 | A) = x^3
...
n_i = P(A_i) = P(A) * P(A_{i-1} | A) = x^i
ie, RAID1 is expoentially more reliable as you add extra disks!
This assumes that disk failures are independant - ie, that you
correctly configure disks (don't use master and slave on an IDE
channel!), and replace failed disks as soon as they fail.
This is why adding more disks to a RAID1 is rare - x^2 is going to be
a really low probability! It will be far, far more common for
operator error to break a RAID than for both devices to honestly fail.
--
Ross Vandegrift
ross@xxxxxxxxxxxx
"The good Christian should beware of mathematicians, and all those who
make empty prophecies. The danger already exists that the mathematicians
have made a covenant with the devil to darken the spirit and to confine
man in the bonds of Hell."
--St. Augustine, De Genesi ad Litteram, Book II, xviii, 37
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