On Monday 03 January 2005 18:46, maarten wrote: > On Monday 03 January 2005 12:31, Peter T. Breuer wrote: > > Guy <bugzilla@xxxxxxxxxxxxxxxx> wrote: > > Doing the math, the outcome is still (200% divided by four)= 50%. > Ergo: the same as with a single disk. No change. Just for laughs, I calculated this chance also for a three-way raid-1 setup using a lower 'failure possibility' percentage. The outcome does not change. The (statisticly higher) chance of a disk failing is exactly offset by the greater likelyhood that the raid system chooses one of the good drives to read from. (Obviously this is only valid for raid level 1, not for level 5 or others) Let us (randomly) assume there is a 10% chance of a disk failure. We use three raid-1 disks, numbered 1 through 3. We therefore have eight possible scenarios: A disk1 fail disk2 good disk3 good B disk1 good disk2 fail disk3 good C disk1 good disk2 good disk3 fail D disk1 fail disk2 fail disk3 good E disk1 fail disk2 good disk3 fail F disk1 good disk2 fail disk3 fail G disk1 fail disk2 fail disk3 fail H disk1 good disk2 good disk3 good Scenarios A, B and C are similar (one disk failed). Scenario's D, E and F are also similar (two disk failures). Scenarios G and H are special, the chances of that occurring are calculated seperately. H: the chance of all good disks is (0.9x0.9x0.9) = 0.729 G: the chance of all disks bad is (0.1x0.1x0.1) = 0.001 The chance of A, B or C (one bad disk) is (0.9x0.9x0.1) = 0.081 The chance of D, E or F (two bad disks) is (0.9x0.1x0.1) = 0.009 The chance of (A, B or C) and (D, E or F) occurring must be multiplied by three as there are three scenarios each. So this becomes: The chance of one bad disk is = 0.243 The chance of two bad disks is = 0.027 Now let's see. It is certain that the raid subsystem will read the good data in H. The chance of that in scenario G is zero. The chance in (A, B or C) is two-thirds. And for D, E or F the chance the raid system getting the good data is one-third. Let's calculate all this. [ABC] x 0.667 = 0.243 x 0.667 = 0.162 [DEF] x 0.333 = 0.027 x 0.333 = 0.008 [G] x 0 = 0.0 [H] x 1.0 = 0.729 (total added up is 0.9) Conversely, the chance of reading the BAD data: [ABC] x 0.333 = 0.243 x 0.333 = 0.081 [DEF] x 0.667 = 0.027 x 0.667 = 0.018 [G] x 1.0 = 0.001 [H] x 0.0 = 0.0 (total added up is 0.1) Which, again, is exactly the same chance a single disk will get corrupted, as we assumed above in line one is 10%. Ergo, using raid-1 does not make the risks of bad data creeping in any worse. Nor does it make it better either. Maarten - To unsubscribe from this list: send the line "unsubscribe linux-raid" in the body of a message to majordomo@xxxxxxxxxxxxxxx More majordomo info at http://vger.kernel.org/majordomo-info.html
