A random variable with statistical property was built; by means of the statistical theory hypothesis testing,and using the sample data,the change rule of random variable distribution parameter was analyzed,the evaluation method of the pressure vessel burst pressure calculation formula precision was established. Based on 27 groups of steel thin-wall single-layer cylinder burst pressure measured data,related factors influence on the precision of mid-diameter formula and Faupel formula were studied. The research shows that:（ 1） For thin-wall single-layer cylinder,with the vessel materials yield ratio ranging from0. 488 9 to 0. 0. 966 0,and the diameter ratio ranging from 1. 010 to 1. 5,the yield ratio value is not obviously affect the standard deviation and mean value of mid-diameter formula corresponding to random variable; although yield ratio value is no significant effect on mean value of Faupel formula corresponding to random variable,but if experimental data of yield ratio was lower than0. 499 7,Faupel formula corresponding to random variable standard deviation is significant increase;（ 2） In above scope,middiameter formula corresponding to random variable coefficient of variation is less than Faupel formula ’s,and mid-diameter formula with higher concentration,for calculating steel thin-walled single layer cylinder burst pressures,mid-diameter formula is better than Faupel formula;（ 3） Adjust the materials yield ratio ranging from 0. 538 8 to 0. 966 0,and the diameter ratio ranging from 1. 013 3 to 1. 5 accordingly,the variation coefficient of Faupel formula corresponding to random variable is significantly decreased,and the concentration of Faupel formula is significantly improved.