Reliability Properties of $(n,f,k)$ Systems

In the present article we study several reliability properties of
$(n, f, k)$
systems. More specifically, for the special case
$k = 2$
, we deduce the generating function of a system's reliability, and discuss techniques for evaluating its signature vector and reliability function. In addition, for the general case
$(k \geq 2)$
, we establish some stochastic comparisons between reliability structures' lifetimes using their signatures, and present several results and applications pertaining to the lifetimes of
$(n, f, k)$
systems.