MTTF Calculations in "A Case for RAID"

[e(ho0n3]

Hi everyone,

 

I'm reading the paper "A Case for RAID" and I'm having difficulty understanding some of the calculations made. Example:

 

Since we assume that disk failures occur at a uniform rate, this average number of second failures during the repair time for the X first failures is

 

[math]\frac{X*\mbox{MTTR}}{\mbox{MTTF of remaining disks in the group}}[/math]

 

So as X gets larger the above gets larger. This makes sense because it will take more time to repair more disks so the average number of second failures will grow. However, I'm not exactly sure how the formula is derived. Can anyone shed some light on this?