The vast majority of vibrations Encountered in the real Environment are random in nature. Such vibrations are intrinsically complicated, and this volume describes the Enabling process for simplification of the analysis required. and the analysis of the signal in the frequency domain. Power spectrum density is also defined, with the requisite precautions to be taken in its calculation described together with the processes (windowing. overlapping) necessary for improved results. A further complementary method, the analysis of statistical properties of the time signal. is described. This enables the distribution law of the maxima of a random Gaussian signal to be determined and simplifies calculation of fatigue damage to be made by the avoidance of the direct counting of peaks.