核能 - 通过线性回归分析评估铀溶液中杂质的测量不确定性的指南

[中文适用范围]： 本文件提供了一种方法，用于评估铀溶液中杂质含量的测量不确定度，该不确定度是通过“最小二乘法”拟合的回归线确定的。该方法旨在供化学分析仪使用。简单线性回归，以下称为“基本回归”，定义为具有单个独立变量的模型，用于通过 n 个不同的数据点 (xi, yi) (i = 1,…, n) 拟合回归线，使得误差平方和（即数据点与拟合线之间的垂直距离平方）尽可能小。对于线性校准，通常使用“经典回归”或“逆回归”；然而，它们并不方便。相反，本文件[2] 中使用“反向逆回归”。反向逆回归将 y（参考溶液）视为响应，将 x（观察到的测量值）视为输入；这些值用于通过最小二乘法拟合 y 对 x 的回归线。这种回归与基本回归的区别在于，xi（i = 1，…，n）根据正态分布而变化，但 yi（i = 1，…，n）是固定的；在基本回归中，yi 会变化，但 xi 是固定的。按提及的顺序说明了回归线拟合、组合不确定度的计算、有效自由度的计算、扩展不确定度的计算、参考溶液的不确定度在评估结果中的反映以及偏差修正。附件 A 提供了不确定度评估的实际例子。附件 B 提供了显示不确定性评估步骤的流程图。此外，附件 C 解释了在逆逆回归中使用加权因子处理非均匀方差的方法。注 1：在经典回归的情况下，在实际样本测量之前先反转拟合的回归线[3]。在逆回归的情况下，x 和 y 的作用与变量 x 代表输入，而变量 y 代表响应的惯例不一致。出于这些原因，本文件不包括这两个回归。注 2 考虑到回归分析理论的历史，建议使用术语“逆向回归”。相反，最好使用其他术语，例如“伪基本回归”。 [外文原描述]： This document provides a method for evaluation of the measurement uncertainty arising when an impurity content of uranium solution is determined by a regression line that has been fitted by the "method of least squares". It is intended to be used by chemical analyzers. Simple linear regression, hereinafter called "basic regression", is defined as a model with a single independent variable that is applied to fit a regression line through n different data points (xi, yi) (i = 1,?, n) in such a way that makes the sum of squared errors, i.e. the squared vertical distances between the data points and the fitted line, as small as possible. For the linear calibration, "classical regression" or "inverse regression" is usually used; however, they are not convenient. Instead, "reversed inverse regression" is used in this document[2]. Reversed inverse regression treats y (the reference solutions) as the response and x (the observed measurements) as the inputs; these values are used to fit a regression line of y on x by the method of least squares. This regression is distinguished from basic regression in that the xi's (i = 1,?, n) vary according to normal distributions but the yi's (i = 1,?, n) are fixed; in basic regression, the yi's vary but the xi's are fixed. The regression line fitting, calculation of combined uncertainty, calculation of effective degrees of freedom, calculation of expanded uncertainty, reflection of reference solutions' uncertainties in the evaluation result, and bias correction are explained in order of mention. Annex A presents a practical example of uncertainty evaluation. Annex B provides a flowchart showing the steps for uncertainty evaluation. In addition, Annex C explains the use of weighting factors for handling non-uniform variances in reversed inverse regression. NOTE 1 In the case of classical regression, the fitted regression line is inverted prior to actual sample measurement[3]. In the case of inverse regression, the roles of x and y are not consistent with the convention that the variable x represents the inputs, whereas the variable y represents the response. For these reasons, the two regressions are excluded from this document. NOTE 2 The term "reversed inverse regression" was suggested taking into account the history of regression analysis theory. Instead, it can be desirable to use some other term, e.g. "pseudo-basic regression".