This paper introduces a Kolmogorov-type test for the shortfall order (also known in the literature as the right-spread or excess-wealth order) against parametric alternatives. In the case of the null hypothesis corresponding to the Negative Exponential distribution, this provides a test for the new better than used in expectation (NBUE) and for the new worse than used in expectation (NWUE) properties. Such a test is particularly useful in reliability applications as well as duration and income distribution analysis. The theoretical properties of the testing procedure are first established for uncensored data, and then for censored and truncated data. Simulation studies reveal that the test based on a bootstrap procedure performs well, even with moderate sample sizes. Applications to real data, namely chief executive officer (CEO) compensation data, flight delay data and throttle failure data, illustrate its empirical relevance.