  Given a pair of non-negative random variables $X$ and $Y$, we introduce a
class of nonparametric tests for the null hypothesis that $X$ dominates $Y$ in
the total time on test order. Critical values are determined using
bootstrap-based inference, and the tests are shown to be consistent. The same
approach is used to construct tests for the excess wealth order. As a
byproduct, we also obtain a class of goodness-of-fit tests for the NBUE family
of distributions.
