一元线性校准曲线不确定度评定与适用条件的讨论  

Discussion on Uncertainty Evaluation and Applicable Conditions of Univariate Linear Calibration Curve

作　　者：汪斌[1] 卢晓华[1] WANG Bin;LU Xiaohua(National Institute of Metrology,Beijing 100029,China)

机构地区：[1]中国计量科学研究院,北京100029

出　　处：《计量科学与技术》2022年第7期45-49,44,共6页Metrology Science and Technology

基　　金：国家重点研发计划(2017YFF0205804)。

摘　　要：线性校准曲线在化学测量领域具有广泛应用,但其适用性条件及不确定度计算方式需要进一步优化,在不满足适用前提的情况下贸然使用普通最小二乘法并不合理。本文以数据实例为基础,比较了普通最小二乘法与加权最小二乘法确定校准曲线的差异。应用不确定度传播规律,详细推导了线性校准曲线的不确定度计算公式,并与目前广泛使用的计算公式进行了比较。建议在确定校准曲线时首先要判断测量结果的不确定度是否满足方差齐性,若不满足方差齐性应采用加权最小二乘法;在计算校准曲线引入的不确定度时,应使用实际测量结果的不确定度而不要用校准溶液测量结果残差进行替代。Linear calibration curve is widely used in the field of chemical measurement, but its applicability conditions and uncertainty calculation method need to be further strengthened, and it is unreasonable to rashly use the ordinary least square method when the applicable premise is not met. Based on practical data examples, this paper compares the difference between the ordinary least square method and the weighted least square method. Applying the uncertainty propagation law,the uncertainty calculation formula of the linear calibration curve is derived in detail and compared with the widely used calculation method at present. It is suggested that when determining the calibration curve, whether the uncertainty of the measurement results meets the homogeneity of variance should first be considered, and if it does not, the weighted least square method should be used. When calculating the uncertainty introduced by the calibration curve, the uncertainty of the actual measurement results should be used instead of substituting the residual of the measurement results of the calibration solution.

关 键 词：校准曲线 一元线性 普通最小二乘法 加权最小二乘法 不确定度 

分 类 号：O6-0[理学—化学]