Stochastic comparisons of series and parallel systems with dependent subsystems consisting of dependent and heterogeneous components under Archimedean copula

In this paper, we study series and parallel systems composed of m dependent subsystems consisting of dependent and heterogeneous components. The components of the system follow additive or multiplicative hazard models, and their dependence structure is modeled by Archimedean copula. We derive sufficient conditions for comparing two series (parallel) systems stochastically under three different scenarios. We first assume that the vector of the additive or multiplicative hazard parameters of the first system majorizes to that of the second one. Secondly, we assume that the vector of the number of components in each subsystem of the first system majorizes to that of the second one. Thirdly, we assume that two systems have different numbers of subsystems formed by different numbers of components. At the end, we provide some numerical examples to illustrate the developed results of this paper.