The stationary gaussian assumption hypothesis is often used as the test condition for the traditional random vibration transportation test of packaging materials. The paper aims to study a method to quantify and characterize non-stationary random vibration, and to simulate non-stationary and non-gaussian characteristics in the actual transportation vibration environment of packaging, especially under harsh road conditions. This paper introduces the run test non-parametric statistical test method to quantitatively characterize the time-varying non-stationary process of the root mean square value. The amplitude modulation method of beta distributed random number, non-stationary and non-gaussian random processes were simulated. It is verified numerically that the beta distribution method can flexibly generate non-stationary non-gaussian random processes with different degrees of stability based on constraint conditions such as target kurtosis and power spectral density function. This method can be used to quantitatively characterize non-stationary features, and can be used to truly simulate the actual transportation vibration environment of the package, avoiding the occurrence of under-test and over-test problems.