On comparisons of r -out-of- n systems having dependent components

An r-out-of-n system refers to a configuration where system functionality is contingent upon the survival of at least r out of the n components of the system. Series and parallel systems are particular instances of an r-out-of-n system. This article explores the comparison of lifetimes of two r-out-of-n systems with dependent and identically distributed components in relation to various stochastic orders. We derive the results under arbitrary distributions for component lifetimes and define the dependency structures by arbitrary copulas. As special cases, the applicability of the derived results is shown with Archimedean copulas and some other copulas as well, such as Farlie-Gumbel-Morgenstern (FGM) copulas. The results presented here generalize many established findings in the literature. This article also compares two series and parallel systems, each having dependent homogeneous components, with respect to some new class of aging faster orderings.