The question is discussed when of two ordered sets of continuous distribution functions one shows less positive trend than the other. The resulting ordering has applications to power function monotonicity of isotonic rank tests, and is related to certain orderings in parametric models.
"A Note on Nonparametric Trend Conformity." Ann. Statist. 12 (2) 775 - 777, June, 1984. https://doi.org/10.1214/aos/1176346524