标准不确定度A类评定中极差法的深入讨论

JJF 1059.1-2012《测量不确定度评定与表示》与GUM的区别之一是在标准不确定度的A类评定中引入了极差法。假设总体分别服从正态分布和均匀分布,则总体标准差的极差估计量,以及用于实际计算的极差系数可以从样本极差的分布函数导出。理论分析表明:虽然用极差法估计的总体标准差是无偏的,但是估计的总体方差偏大,这将导致最终测量结果的合成标准不确定度偏大。同时JJF 1059.1中仅提供了总体接近正态分布时的极差系数,并不适用于所有情况。作为比较,不论总体分布如何,使用贝塞尔公式估计的总体方差总是无偏的,不会给测量结果的合成标准不确定度带来原理性误差。由于极差法存在概率统计学上的原理性误差以及适用性限制,建议在标准不确定度A类评定中应审慎使用极差法。

The Further Discussion of the Range Method in the Type AEvaluation of Sstandard Uncertainty

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.