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Methods for conducting accelerated vibration fatigue testing of structures, such as MIL-STD-810G, allow for the non-linear scaling of the test time with the inverse of the rms vibration amplitude based on the slope of the material S-N curve obtained from cyclic fatigue tests. The Fatigue Damage Spectrum (FDS) is used as a method to allow for different level scalings at different frequencies in a broadband vibration environment using the relative responses of resonances in the structure. A recent development in industry has been to mix impulses with random excitations to increase the vibration peak levels (as measured by the kurtosis), thereby accelerating the fatigue even more than would occur with a Gaussian excitation. This paper presents results from a study to determine the conditions under which high kurtosis, impulsive excitations actually produce high kurtosis responses in structural resonances thus increasing the level of the FDS.