  In this paper we compare the minimums of two heterogeneous samples each
following Weibull-G distribution under three scenarios. In the Fifirst
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.
