In this article we compare the minimums of two heterogeneous samples each following Weibull-G distribution under three scenarios. In the first scenario, the units of the samples are assumed to be independently distributed and the comparisons are carried out through vector majorization. The minimums of the samples are compared in the second scenario when the independent units of the samples also experience random shocks. The last scenario describes the comparison when the units have a dependent structure sharing Archimedean copula.

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