Abstract: In this paper, we assume that the k-out-of-n system comprised by each subsystem consists of a number of randomly assigned redundancies and a different component in parallel (series), the random lifetimes of redundancies and components are independent of each other, but the random lifetimes of redundancies in the same subpopulation are dependent, where the dependence of redundancies is modeled by the Archimedean copula tool. We use stochastic order theory to establish the main results based on selection probabilities, stochastic lifetime and allocation policies of redundancies. Finally, we present some numerical examples to illustrate the scientific validity of the conclusions.