Hey,

I just had a "D'oh!" moment I'm afraid, woke up this morning realising my 
previous post about the chances of failure was completely wrong.

You do need to multiply the chance of failure by the number of remaining disks, 
because you're reading the data of every one of them, and you risk loosing data 
from any one of them.  However, I'm not sure where the 8 is coming from in your 
calculations.  To my mind, the chance of failure on any one drive is:

amount of data reads / chance of failure
= 1TB / 10^14 
~ 10^12 / 10^14 or a 1 in 100 chance of failure

So then, once one of your 14 disks fail, you have 13 left and for raid-z you 
need to read the data of every single one of them to survive without errors, 
which means the calculation is now:

no of disks * amount of data reads / chance of failure

In this case approximately 13/100 or around 1 in 8 odds.

So with raid-z you have around a 1 in 8 chance of *some kind* of data error 
during the rebuild of the raid.  So your odds calculations weren't far off, but 
the key point is that you're not calculating entire drive failure here, you're 
calculating the odds of having a single bit of data fail.  Now that bit could 
be in a vital file, but it could just as easily be in an unimportant file, or 
even blank space.

And I can also give you the correct math for raid-z2.  Keeping in mind that 
these figures are for a *single piece of data*, not the entire drive, the 
chance of raid-z2 failing during the rebuild is very small.  I agree that the 
odds of having at least one piece of data fail during the raid-z2 rebuild are 
reasonably high (1 in 8), but for the rebuild to fail, you need two failures in 
the same place which means the calculation is for the failure rate for that 
particular bit, not for every bit on the drive:

no of disks / chance of failure

So the chance of your raid-z2 failing during the rebuild is approximately 12 in 
10^14.  Which I think you'll agree are much better odds :D

Ross
 
 
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