Volume 66 Issue 7
Aug.  2022
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WANG Bin, LU Xiaohua. Discussion on Uncertainty Evaluation and Applicable Conditions of Univariate Linear Calibration Curve[J]. Metrology Science and Technology, 2022, 66(7): 45-49, 44. doi: 10.12338/j.issn.2096-9015.2021.0636
Citation: WANG Bin, LU Xiaohua. Discussion on Uncertainty Evaluation and Applicable Conditions of Univariate Linear Calibration Curve[J]. Metrology Science and Technology, 2022, 66(7): 45-49, 44. doi: 10.12338/j.issn.2096-9015.2021.0636

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

doi: 10.12338/j.issn.2096-9015.2021.0636
  • Available Online: 2022-07-15
  • Publish Date: 2022-08-04
  • 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.
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  • [1]
    全国法制计量管理计量技术委员会. 通用计量术语及定义: JJF 1001-2011 [S]. 北京: 中国质检出版社, 2011.
    [2]
    邓勃. 关于校正曲线建立和应用中一些问题的探讨[J]. 中国无机分析化学, 2011, 1(3): 1-7. doi: 10.3969/j.issn.2095-1035.2011.03.0001
    [3]
    刘庆, 邵志新. 回归分析的直线拟合不确定度探讨[J]. 中国测试, 2009, 35(3): 41-44.
    [4]
    丘山, 丘丰源, 丘星初. 一元线性回归在镀液分析中的应用[J]. 电镀与涂饰, 2016, 35(12): 643-650.
    [5]
    宋春满, 师君丽, 逄涛. 色谱分析中校准曲线制作的探讨[J]. 光谱实验室, 2011, 28(5): 2562-2565. doi: 10.3969/j.issn.1004-8138.2011.05.099
    [6]
    颜巧丽, 李悟庆, 刘天一, 等. 电感耦合等离子体质谱法测定汞元素校准曲线线性探讨[J]. 安徽农业科学, 2020, 48(11): 202-204. doi: 10.3969/j.issn.0517-6611.2020.11.056
    [7]
    何晓群, 刘文卿. 浅谈加权最小二乘法及其残差图-兼答孙小素副教授[J]. 统计研究, 2006(4): 53-57. doi: 10.3969/j.issn.1002-4565.2006.04.012
    [8]
    刘明. 基于一元线性回归模型异方差对加权最小二乘法的考察[J]. 统计与决策, 2012(19): 11-14.
    [9]
    卜乐平, 毛骁峰, 陈鹏辉, 等. 基于数学模型算法预测计量标准稳定性的方法探讨[J]. 计量技术, 2020(6): 50-52.
    [10]
    毕瑞锋, 张发玲. 加权最小二乘法线性回归模型参数的理论推导与计算实例[J]. 计量与测试技术, 2016, 43(2): 67-68.
    [11]
    钱进, 吴金美, 凌晓冬. 线性回归模型加权最小二乘估计的权值计算方法[J]. 统计与决策, 2007(17): 4-6. doi: 10.3969/j.issn.1002-6487.2007.17.002
    [12]
    刘喆, 蒋兴鹏, 刘译文, 等. 基于线性回归的涡轮标准装置不确定度研究[J]. 计量技术, 2019(4): 45-48.
    [13]
    Martins R, Roesslein M, Josephwilliams N. Quantifying Uncertainty in Analytical Measurement[M]. 3rd Edition. London: EURACHEM CITAC, 2012: 60-72.
    [14]
    中国合格评定国家认可委员会. 化学分析中不确定度的评估指南: CNAS-GL006[R]. 北京: 中国合格评定国家认可委员会, 2018.
    [15]
    全国法制计量管理计量技术委员会. 测量不确定度评定与表示: JJF 1059.1-2012 [S]. 北京: 国家质检出版社, 2012.
    [16]
    师义民, 徐伟, 秦超英, 等. 数理统计[M]. 第四版. 北京: 科学出版社, 2015: 201-202.
    [17]
    International Organization for Standardization (ISO). Determination and use of straight-line calibration functions: ISO/TS 28037-2010[S]. Switzerland: ISO, 2010.
    [18]
    全国标准物质计量技术委员会. 标准物质选择与应用: JJF 1507-2015[S]. 北京: 国家质检出版社, 2012.
    [19]
    汤尧旭, 杨晓东, 张轩溥. 国家标准物质在不同化学发光免疫分析系统上换算系数的研究[J]. 计量学报, 2021, 42(7): 964-970. doi: 10.3969/j.issn.1000-1158.2021.07.20
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