标准不确定度A类评定中极差法的深入讨论

One of the differences between the JJF 1059.1-2012《Evaluation and Expression of Uncertainty in Measurement》 and the GUM is the introduction of the range method in the type A evaluation of standard uncertainty.Under the assumption of normal distribution and uniform distribution,the range statistic and the range coefficient can be derived from the distribution density function of the sample range.Analysis reveals that although the range estimation of the population standard deviation is unbiased, the range estimation of the population variance is biased larger.As the result,the combined standard uncertainty of the measurement result is biased larger.On the other hand, JJF1059.1 only lists the range coefficients for normal distribution,they cannot be applied in all circumstances.As a comparison,whatever the population distribution, the estimation of the population variance based on the Bessel formula is always unbiased, thus will not bring theoretical error into the calculation of the combined standard uncertainty of the measurement result.Since the range method suffering with the principle error in mathematical statistics and the restriction on applicability, it should be prudently used in the type A evaluation of standard uncertainty.