Transportation is essential for many logistics systems and vibration is one of the most critic physical circumstances on road causing numerous possible damage sources. One of the primary sources of these damages is often the broadband random vibration. This effect cannot be handled with formal mechanical models; therefore, vibration test simulation is essential for packaging testing. The current vibration systems use Power Spectral Density (PSD) functions to control the intensity of random signal in laboratory based on Fast Fourier Transformation (FFT). Naturally, the PSD frequency does not contain time series data making it hard to determine how long a given simulation should be performed. In this paper, mathematical and probability methods are presented that can be used for representing real vibration circumstances.