The current researches mainly adopt "Guide to the expression of uncertainty in measurement (GUM)" to calculate the profle error. However, GUM can only be applied in the linear models. The standard GUM is not appropriate to calculate the uncertainty of profle error because the mathematical model of profle error is strongly non-linear. An improved second-order GUM method (GUMM) is proposed to calculate the uncertainty. At the same time, the uncertainties in diferent coordinate axes directions are calculated as the measuring points uncertainties. In addition, the correlations between variables could not be ignored while calculating the uncertainty. A k-factor conversion method is proposed to calculate the converge factor due to the unknown and asymmetrical distribution of the output quantity. Subsequently, the adaptive Monte Carlo method (AMCM) is used to evaluate whether the second-order GUMM is better. Two practical examples are listed and the conclusion is drawn by comparing and discussing the second-order GUMM and AMCM. The results show that the diference between the improved second-order GUM and the AMCM is smaller than the diference between the standard GUM and the AMCM. The improved second-order GUMM is more precise in consideration of the nonlinear mathematical model of profle error.
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