Equivalence of Redundant Systems With Respect to Time to Failure

The time to failure of an m out of n component system, with component failure times exponentially and identically distributed, is treated. This failure time is shown to be identically distributed to the failure time of an n - m + 1 component standby system, with component failure times exponentially but not identically distributed. The proof of this result is based on a recursion formula for the distribution of time to system failure.