This research describes random process modeling of the accelerated aging process based upon the mechanical degradation in induction motors. In order to show this aging effect, vibration measurements are considered at the end of each aging cycle, which gradually cause to bearing damage in the motor. In this manner, the accelerated aging study comprises seven aging stage sequentially and collected data set is presented as seven aging cycles and one initial cycle. Hence total aging process is represented by a set of the sequential vibration signals for initial and aged cases. Since the vibration signals are random values which represent the Gaussian distribution character in each period of measurement and this character can be conveyed to the next stage with a scaling of the signal related to elapsed time, the process reminds the Brownian motion or the so-called random walk and it is expected that the degradation can be described as a Wiener process. Examining the collected data proves that in the statistical manner, this compact data set reflects the properties of a non-stationary random process and it is expressed by the Wiener Process Model (WPM) as a statistical approach. This property of the process will be helpful to estimate the residual useful life (RUL) of the bearings in induction motors with high accuracy.