Let τk|n denote
the lifetime of a k-out-of-n system, where
the n components have independent lifetimes
Ti with completely arbitrary
distribution Fi, i = 1,..., n.
It is shown that τk+1|n
Tn, i = 1,..., n − 1;
Ti, i = 1,..., n − 1.
These results are available in the literature for the special case of
Fi's being absolutely continuous. Also,
even in this case, the proofs are often tedious and use the
concept of “totally positive of order infinity in differences
of k.” In contrast, the proofs given here are
simple and elegant and do not use the above concept.