Stochastic comparisons of series-parallel and parallel-series systems with dependence between components and also of subsystems

In this paper, we consider series-parallel and parallel-series systems comprising dependent components that are drawn from a heterogeneous population consisting of $$ m $$ different subpopulations. The components within each subpopulation are assumed to be dependent, and the subsystems themselves are also dependent, with their joint distribution being modeled by an Archimedean copula. We consider a very general setting in which we assume that the subpopulations have different Archimedean copulas for their dependence. Under such a general setup, we discuss the usual stochastic, hazard rate and reversed hazard rate orders between these systems and present a number of numerical examples to illustrate all the results established here. Finally, some concluding remarks are made. The results established here extend the recent results of Fang et al. (2020) in which they have assumed all the subsystems to be independent.