Stochastic comparisons of series and parallel systems with dependent log-logistic components

Abstract

This paper studies the usual stochastic, star, convex transform, and dispersive orders of both series and parallel systems comprised of dependent log-logistic components. We establish that, without any restriction on the parameters, the lifetime of a parallel or series system with dependent components is smaller than that with dependent homogeneous components in the sense of the dispersive orders. Sufficient conditions are established for the star ordering between the lifetimes of series and parallel systems consisting of multiple outlier dependent log-logistic distributed components. Under certain conditions on the Archimedean copula and the parameter, we also discuss convex transform order of series and parallel systems.