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More specifically, when referring to MTTF, MTTR, and MTTDL

I understand the disks sometimes "fail" so I was wondering what really constitutes a "disk repair"? And also, does anyone know what a repair "load" is, and how hot spares work in RAID architectures?

Basically, what else do file system researchers do besides using redundancy, in order to make disk repairs much faster and more reliable?

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This really depends on the component that's failed - these aren't solid state components. (Well, okay, solid state drives are, but the key is that even on those there are lots of discrete components.) For some idea of how much sense this makes, and it's maybe not the best metaphor, but imagine asking "I understand that cars sometimes stop working so I was wondering what really constitutes automotive repair?" You should really try to be familiar with the actual workings of a traditional mechanical hard drive - I'd point you at howstuffworks.com/hard-disk.htm – Shinrai Oct 26 '11 at 19:14
@Shinrai But HDD isn't a car! Unlike cars, most computer components ARE NOT repaired and are at best just fixed enough to get the data off the disk and then trashed. – AndrejaKo Oct 26 '11 at 19:45
@AndrejaKo - You're right. My point is, though, that a drive belt failure and a fuel injector failure have about as much in common as a drive controller failure and a read/write head jam in terms of how you'd attempt to get your data off the disk. It's an awfully broad question, and it's the reason you should be familiar with how a disk actually OPERATES as a start. – Shinrai Oct 26 '11 at 21:10
@Shinrai I agree with general idea, but in this case it's irrelevant. In the mean time data about which OP is talking about, repair time needs to be taken into account. This time needs to be specified as something and it would be good to know what is used as a "repair" in that context, since HDDs usually aren't repaired. – AndrejaKo Oct 26 '11 at 21:15
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Of course, when examining statistically generated data, the best idea would be to ask the data provider himself but often that's impossible so we need to have an idea how the data is created. – AndrejaKo Oct 26 '11 at 21:18
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Hard-disk have no more serviceable parts so are replaced by new ones when they fail.

Spares are disks waiting to be put on line to replace failed ones in redundant disk arrays.

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This is actually incorrect. There are laboratories which will repair drives if they're paid enough. – AndrejaKo Oct 26 '11 at 21:12
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They are not really repairing disks as that would made no sense economically or technically. What they do is "hacking" the disk with various techniques in order to recover some data and then copy it to a different media. – jlliagre Oct 26 '11 at 21:21
It is certainly possible, in theory, to replace components and get the exact same platters working again. It's just ridiculously impractical, so it's never done. :) – Shinrai Oct 26 '11 at 21:29
Indeed, that was my point. – jlliagre Oct 27 '11 at 5:25
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