On reliability analysis in k-out-of-n systems under Archimedean copula dependence

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In this paper, we investigate k-out-of-n system with n independent parallel subsystems comprising 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 k-out-of-n systems reliability by comparing two selection probabilities or two allocation policies in the sense of majorization order. In addition, we present some numerical examples to illustrate all the results established here. Finally, some concluding remarks are made.