Crossing properties of reliability functions

The authors give short proofs by total positivity arguments that: (1) the reliability function of a k-out-of-n system crosses an arbitrary coherent system reliability function at most once, and if a crossing does not occur, crosses from below for , and crosses the reliability function (alternatively, ) of a system of m independent components in series (alternatively, parallel) at most once, and if it does occur, it crosses from below, .