In order to improve the design method of pressure vessels strength,applying the theory of statistical hypothesis testing,the precision comparison method for design formula expansion applied range was established. Based on 52 groups of measured burst pressure of steel wall single-layer cylinder,the precision of mid-diameter formula with the Tresca formula was compared,and the application of formulas was extended according to the principle of no precision reduction. The research shows that:（ 1） According to the design pressure,benchmark scope and plans to expand the scope of mid-diameter formula are determined,respectively.（ 2） According to the relationship between design pressure and burst pressure,sample test data of measured burst pressure of the benchmark scope and plans to expand the scope are definite,respectively.（ 3） At the saliency of0. 05,the ratio of the sample and mid-diameter formula calculated value is random variables with the normal distribution,respectively,which sample located in the benchmark scope and plans to expand the scope.（ 4） The precision of mid-diameter formula in plans to expand the scope and the benchmark scope is same basically; the precision of Tresca formula in plans to expand the scope is higher than the benchmark scope.（ 5） When suitable scope extended to the design pressure less than100 MPa,the precision of mid-diameter formula and Tresca formula is same basically.