A new theory was developed to obtain an exact sinusoidal simulation of material fatigue life when subjected to a gaussian narrow band random loading. The theory was based upon duplicating the probability density distribution of peak amplitudes that is Rayleigh.An experimental investigation was conducted to obtain validity of this theory. The fatigue lives obtained under the two types of loadings compared within 10%. The statistical probability density distribution of input and output acceleration processes for both types of loading compared very well. It is believed that the approach of the theory described herein can be applied to any real loading time history where the probability density distribution of the actual field service peak amplitudes is known.