Abstract: To solve the problem of traditional inductive method for measured random vibration data only applying to normal distribution data, the way for selecting the suitable curve in Johnson curves family was introduced, and the method of fitting measured non-normal random vibration data by Johnson curves family was researched. Then, power spectrum density(PSD)upper probability limit of measured non-normal random vibration data was given by using it. Based on these results, a new method for inducing reliability test vibration force was developed. Some product measured random vibration data induction result shows that the method can give a reasonable PSD upper probability limit of measured random vibration data with any distribution successfully. Furthermore, comparing with traditional normal-based data inductive method, the result of the method is more reliable for characterizing vibration environment condition.