In this paper, we consider optimal components grouping in series–parallel and parallel–series systems composed of k subsystems. All components in each subsystem are drawn from a heterogeneous population consisting of m different subpopulations. Firstly, we show that when one allocation vector is majorized by another one, then the series–parallel (parallel–series) system corresponding to the first (second) vector is more reliable than that of the other. Secondly, we study the impact of changes in the number of subsystems on the system reliability. Finally, we study the influence of the selection probabilities of subpopulations on the system reliability.
