In this paper, we consider two different systems consisting of independent components with inverse Weibull distributions whose characteristic life parameters are heterogeneous, but the shape parameters are common. It is shown that the survival function (hazard rate) of a series system is decreasing in the characteristic life parameter vector with respect to $p$-larger (majorization) ordering. It is also shown that the reversed hazard rate of a parallel system is decreasing (increasing) in characteristic life parameter vector with respect to majorization ordering if the common shape parameters are less (greater) than $1$. As a consequence, the simple upper bound on the survival function of the series (parallel) systems is built in terms of geometric (arithmetic) mean of the characteristic life parameters.