This paper addresses the usage of inverse power laws in accelerated fatigue
testing under wide-band Gaussian random loading. The aim is not at predicting an
absolute value of fatigue life but assessing the fatigue damage relative
accumulation. The widely accepted inverse power scaling laws in fatigue damage
assessment is discussed, reviewing the engineering standards and pointing out
their inherent limitations. A physically consistent general scaling law is
obtained by rigorous mathematical analysis in the framework of random vibration
theory and the rules of safe-life fatigue analysis. Simplifications of the
general scaling rule are presented, highlighting conditions under which the
current standard practice could provide a correct an acceptable estimation of
the relative fatigue damage accumulation.