ISO 18315:2018 核能 用线性回归分析评价铀溶液中杂质测量不确定度的指南

标准编号：ISO 18315:2018

中文名称：核能 用线性回归分析评价铀溶液中杂质测量不确定度的指南

英文名称：Nuclear energy — Guidance to the evaluation of measurement uncertainties of impurity in uranium solution by linear regression analysis

发布日期：2018-11

标准范围

本文件提供了一种评估测量不确定度的方法，该测量不确定度是由“最小二乘法”拟合的回归线确定的。它将用于化学分析仪。简单线性回归，以下称为“基本回归”，定义为一个具有单个自变量的模型，该模型通过n个不同的数据点（xi，yi）（i=1，，，n）拟合回归线，使平方误差之和，i。e、 数据点和拟合线之间的垂直平方距离应尽可能小。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，本文件中使用了“反向回归”[2]。逆回归以y（参考溶液）为响应，x（观察到的测量值）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）根据正态分布变化，而yi（i=1，n）是固定的；在基本回归中，彝族各不相同，但习族是固定的。依次解释了回归线拟合、组合不确定度计算、有效自由度计算、扩展不确定度计算、参考溶液不确定度在评估结果中的反映以及偏差校正。附录A给出了一个不确定性评估的实例。附录B提供了显示不确定度评估步骤的流程图。此外，附录C解释了在处理非冲突事件时使用的加权系数-反向回归中的一致方差。注1:在经典回归的情况下，拟合回归线在实际样本测量之前倒置[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代表响应的约定不一致。由于这些原因，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“反向回归”一词。相反，可以使用其他术语，例如“伪基本回归”。

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".

标准预览图