I am reading about disk redudancy. I read the following: Suppose that the mean t

Question

I am reading about disk redudancy.
I read the following:

Suppose that the mean time to failure of a disk is 100,000 hours. Then the mean time to failure of some disk in an array of 100 disks will be 100,000/100 = 1000 hours

I don't understand this. Why isn't it 100,000^100 instead?
Then the same textbook says in the next paragraph concerning 2 mirrored disks:

If the mean time to failure of a single disk is 100,000 hours and the mean time to repair is 10 hours then the mean time to data loss is (100,000^2)/2*100

Now here it multiplies for the 2 disks but before the MTTF was divided.

Can anyone please help me figure out how we calculate this.
In case it matters the text book is Database Concepts from Silberschatz 4th edition paragraph 11.3.1 (Improvement of reliability via redundancy) page 403

Explanation / Answer

Think of it this way. A single disk fails on average after 100,000 hours. Now you have 100 disks. How long before one of them fails? It will almost certainly take much less than 100,000 hours for the first to fail, and much more than 100,000 hours for the last to fail. (This of course depends on the distribution of failures, which is assumed to be exponential here.)

Here is another example: if you keep throwing one die, it will show 6 after an average of 6 throws. Now suppose that you throw two dice. How long do you expect to wait until some 6 shows up? Certainly less than 6 throws. (In fact, 36/11?3.27 throws on average.)

In the second example, you need both disks to fail in order for data loss to occur. Not only this, but you also want both failure "events" to be within 10 hours of each, since otherwise the system will recover after repairing the faulty disk. Hopefully the book explains the calculation somewhere, if not, the book is useless and you should tell your instructor to use a different one (perhaps with less pictures but more content, and not nth edition, prepared to finance the publisher's new yacht).

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