Below is an excerpt from the book Database System Concepts, Seventh Edition, Chapter 12 - Storage Systems.
Suppose that the mean time to failure of a disk is 100,000 hours, or slightly over 11 years. Then, the mean time to failure of some disk in an array of 100 disks will be 100,000∕100 = 1000 hours, or around 42 days, which is not long at all!
Is this calculation even right? If yes, Can someone please explain the math behind this?
The failure of a device is often modeled with the exponential distribution. If the time to failure of the $i$th disk is an exponential random variable with mean $\frac{1}{\lambda} = 100000$, then the minimum of these $n=100$ independent exponential random variables turns out to also be an exponential random variable with mean $\frac{1}{n\lambda} = 1000$.