From mboxrd@z Thu Jan 1 00:00:00 1970 From: ross@lug.udel.edu (Ross Vandegrift) Subject: Re: Date: Thu, 12 Jan 2006 12:20:38 -0500 Message-ID: <20060112172038.GA12426@lug.udel.edu> References: <20060111144943.93BAA396A20@mxo3.broadbandsupport.net> <43C63A94.2020702@dgreaves.com> Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Return-path: Content-Disposition: inline In-Reply-To: <43C63A94.2020702@dgreaves.com> Sender: linux-raid-owner@vger.kernel.org To: David Greaves Cc: bhess@patmedia.net, linux-raid@vger.kernel.org List-Id: linux-raid.ids 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@lug.udel.edu "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