A technique for digitally generating random time histories having arbitrarily shaped power spectra is presented. Four random time histories having significantly different statistical and power spectral properties have been generated and analyzed to determine their mean and amplitude distributions. It was found that the distribution of means could be approximated by a normal distribution and that the distribution of amplitudes could be approximated by the sum of a Rayleigh distribution and a normal distribution. An attempt was made to relate the coefficients of the equations used to represent the distributions of means and amplitudes to the power spectral properties of the generated time histories. It was found that two of the coefficients could be related to the power spectral properties of the time histories. The remaining two coefficients were empirically determined since no apparent relationship was found between these coefficients and the power spectral properties of the generated random time histories. In addition a discussion of the applicability of results for estimating fatigue life under randomly varying loads or stresses is presented. / Master of Science