Stochastic comparisons of series and parallel systems with dependent heterogeneous extended exponential components under Archimedean copula

In this paper, we discuss the usual stochastic, star and convex transform orders of both series and parallel systems comprising heterogeneous (and dependent) extended exponential components under Archimedean copula. Sufficient conditions are established for the star ordering between the lifetimes of series and parallel systems consisting of such dependent components. Under certain conditions on the Archimedean copula and the parameters, we also discuss convex transform order between the series and parallel systems. These results generalize some existing results in the literature to the case of dependent components as well as to a general family of component lifetime distributions.