Optimal grouping of heterogeneous components in series–parallel and parallel–series systems under Archimedean copula dependence

In this paper, we investigate series–parallel and parallel–series systems comprising n dependent components drawn from a heterogeneous population consisting of m different subpopulations. The components within each subpopulation are assumed to be dependent, while the subpopulations are independent of each other. We also assume that the subpopulations have different Archimedean copulas for their dependence. Under this setup, we discuss the system reliability for three different cases: first by fixing the number of subsystems and then presenting relationships between allocation vectors, second by studying the impact of changes in the number of subsystems, and the last by examining the influence of the selection probabilities or the distributions of subpopulations. We use the theory of stochastic orders and majorization to establish the main results, and present some numerical examples to illustrate all the results established here. Finally, some concluding remarks are made.