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

Bootstrap-based tests for the total time on test order, the NBUE property, and the excess wealth order