化学计量不确定度评定研究进展

测量不确定度是表征合理地赋予被测量之值的分散性的参数。本文针对化学计量不确定度评定基础模型仅适用于线性模型、概率分布为正态分布或缩放位移t分布等局限,介绍了近年来不确定度评定的研究热点:蒙特卡罗方法(Monte Carlo Method,MCM),不确定度评定的来源、评定概念、评估方法及其发展过程,扩大了测量不确定度评定与表示的适用范围。     

蒙特卡洛法评定橡胶门尼黏度测量的不确定度

根据高聚物流变学原理,建立了门尼黏度测量模型,分析了模型中各个变量的概率分布,利用Mathcad软件进行了测量模型的门尼黏度模拟,给出了模拟最佳值、不确定度及其包含区间,实现了门尼黏度测量不确定度的蒙特卡洛法评定。与GUM法相比,蒙特卡洛法评定门尼黏度测量不确定度具有编程模式化,过程简单等优点,适合多变量测量模型的不确定度评价。     

MCM法和GUM法评定氨气检测仪示值误差不确定度的对比

氨气检测仪广泛应用于涉氨作业场所,为确保其测量结果准确可靠必须定期对其检定校准。针对其检定过程中示值误差的测量不确定度,对测量不确定度表示指南方法(GUM)和蒙特卡罗法(MCM)进行了对比研究。建立了氨气检测仪示值误差模型,分析了模型中各个变量的概率分布,利用MCM Alchimia软件进行了测量模型模拟计算,给出了模拟最佳值、不确定度及其包含区间,实现了氨气检测仪示值误差测量不确定度的蒙特卡洛法评定。与GUM法相比,蒙特卡洛法评定氨气检测仪示值误差测量不确定度具有通用性强、过程简单、结果可靠等优点,适合氨气检测仪示值误差的不确定度评价。     

电感耦合等离子体质谱法测定岩石中47种元素的不确定度评定

采用封闭酸溶电感耦合等离子体质谱(ICP-MS)法测定岩石样品,分别对47种元素的测量结果不确定度进行评定。通过分析测试方法和测量条件,得到测量结果的不确定度主要由样品称量、样品溶液定容和样品溶液中元素浓度测量引入。在实验室质控条件下,对各不确定度分量进行评定和计算,其中随机因素导致的不确定度采用期间精密度试验综合评价,即采用A类方法评定。共完成了16个岩石国家标准物质(GBW 07103~GBW 07123)47种元素测量结果的不确定度合成,并参照GB/T 6379.2-2004,建立了含量w与扩展不确定度U之间的关系模型,运用这一关系模型可得到测量结果的不确定度估计值,只要测量过程本身或所使用的设备未变化,就不需要再重复进行不确定度评估。     

气相色谱仪检测器的灵敏度和检测限测量结果不确定度的评定

依据JJF1059-1999《测量不确定度评定与表示》评定了气相色谱仪检测器的主要技术指标灵敏度和检测限测量结果的不确定度。分析了各不确定度分量，建立了评定灵敏度、检测限测量结果不确定度的数学模型，并计算了其测量结果的扩展不确定度。     

分光光度法测定血清中尿酸的不确定度评定

对分光光度法测定血清中尿酸含量的不确定度进行了评定。根据GUM和QUAM文件规定的不确定度评定指南,确定尿酸测量不确定度的来源主要为重复测定、工作曲线拟合、标准溶液配制、样本和试剂的移取、和反应时间等不确定度分量,其他测量因素引起的分量较小,可以不予考虑。通过合理选择不确定度分量,优化了评定过程,减少了评定环节,达到了对不确定度合理评定的目的。     

液相色谱仪检测器的最小检测浓度测量结果不确定度的评定

依据JJF1059-1999《测量不确定度评定与表示》,评定了液相色谱仪检测器最小检测浓度测量结果的不确定度。分析了各不确定度分量,建立了评定最小检测浓度不确定度的数学模型。检测器最小检测浓度测量结果的相对扩展不确定度为7.1%(k=2.53)。     

非均匀梯度尿液分析仪测量不确定度评定

对非均匀梯度尿液分析仪测量不确定度进行评定。分别采用对称区间不确定度评定方法、选择校准点左右两侧分辨力较大者进行不确定度评定的方法、不对称区间不确定度评定方法对非均匀梯度尿液分析仪测量不确定度进行评定。采用常规的对称区间不确定度评定方法所得出的置信区间左右对称，不符合这类仪器低浓度范围分辨能力高于高浓度范围分辨能力的特性。如果选择校准点左右两侧分辨力较大者进行不确定度评定，虽较为稳妥，但其置信区间宽，不确定度偏大，测量结果准确度偏低。而通过不对称区间不确定度评定方法所得出的置信区间，左侧比右侧窄，且与仪器梯度相符，适合用于非均匀梯度尿液分析仪测量不确定度的评定。     

冷原子吸收分光光度法测定电子电气产品中汞的不确定度评定

根据《测量不确定度评定与表示指南》,对冷原子吸收分光光度法测定电子电气产品中汞含量的测量不确定度进行了评定。分析了影响不确定度的因素,对各不确定度分量进行了计算,结果表明测量不确定度主要来源于标准曲线拟合和测量重复性,合成相对标准不确定度为1.61%。     

石墨炉原子吸收法测定虫草花中铅含量的不确定度评定

测量虫草花中铅元素含量并对其结果的不确定度进行评定,为准确测定虫草花中铅含量提供参考依据。依据GB 5009.12—2017《食品安全标准食品中铅的测定》和相关不确定度评定规范,建立了虫草花铅含量测量不确定度评定的数学模型,对各影响因素进行了系统的分析,比较全面的分析了其不确定度的来源。虫草花中铅含量为(0.425±0.012)mg/kg(k=2),测量不确定度评定分量数据显示,在虫草花中铅元素含量的测定过程中,测量重复性、标准溶液、样品处理引入的不确定度分量较大,是其不确定度来源的重要方面。控制测量过程,选择合适的重复次数、标准溶液配制方法以及消解方法可以减小测量结果的不确定度。     

蒙特卡洛法评定在线pH计示值误差的不确定度

以在线p H计为例,考察了在线酸度计示值误差不确定度的分布规律,利用蒙特卡洛法评定示值误差不确定度。对于0.01级的在线p H计,蒙特卡洛法与GUM法评定结果的差值为9.1%,小于不可靠性(20%);对于0.1级的在线p H计,蒙特卡洛法与GUM法评定结果的差值为3.8%,小于不可靠性(10%)。通过比较得出结论,采用GUM法验证了蒙特卡洛法(MCM)根据JJF 1547–2015评定在线p H计示值误差不确定度的方法是有效且适用的。尤其在测量模型非线性以及输出量的概率密度函数(PDF)较大程度地偏离正态分布或t分布等GUM法不适用的场合,蒙特卡洛法是评定在线分析监测仪器仪表示值误差不确定度的重要手段。     

Comparison of ISO-GUM and Monte Carlo methods for the evaluation of measurement uncertainty: application to direct cadmium measurement in water by GFAAS

The propagation stage of uncertainty evaluation, known as the propagation of distributions, is in most cases approached by the GUM (Guide to the Expression of Uncertainty in Measurement) uncertainty framework which is based on the law of propagation of uncertainty assigned to various input quantities and the characterization of the measurand (output quantity) by a Gaussian or a t-distribution. Recently, a Supplement to the ISO-GUM was prepared by the JCGM (Joint Committee for Guides in Metrology). This Guide gives guidance on propagating probability distributions assigned to various input quantities through a numerical simulation (Monte Carlo Method) and determining a probability distribution for the measurand.In the present work the two approaches were used to estimate the uncertainty of the direct determination of cadmium in water by graphite furnace atomic absorption spectrometry (GFAAS). The expanded uncertainty results (at 95% confidence levels) obtained with the GUM Uncertainty Framework and the Monte Carlo Method at the concentration level of 3.01 μg/L were ±0.20 μg/L and ±0.18 μg/L, respectively. Thus, the GUM Uncertainty Framework slightly overestimates the overall uncertainty by 10%. Even after taking into account additional sources of uncertainty that the GUM Uncertainty Framework considers as negligible, the Monte Carlo gives again the same uncertainty result (±0.18 μg/L). The main source of this difference is the approximation used by the GUM Uncertainty Framework in estimating the standard uncertainty of the calibration curve produced by least squares regression. Although the GUM Uncertainty Framework proves to be adequate in this particular case, generally the Monte Carlo Method has features that avoid the assumptions and the limitations of the GUM Uncertainty Framework.     

From GUM to alternative methods for measurement uncertainty evaluation

Since the advent of the Guide to the expression of Uncertainty in Measurement (GUM) in 1995 laying the principles of uncertainty evaluation numerous projects have been carried out to develop alternative practical methods that are easier to implement namely when it is impossible to model the measurement process for technical or economical aspects. In this paper, the author presents the recent evolution of measurement uncertainty evaluation methods. The evaluation of measurement uncertainty can be presented according to two axes based on intralaboratory and interlaboratory approaches. The intralaboratory approach includes “the modelling approach” (application of the procedure described in section 8 of the GUM, known as GUM uncertainty framework) and “the single laboratory validation approach”. The interlaboratory approaches are based on collaborative studies and they are respectively named “interlaboratory validation approach” and “proficiency testing approach”.     

A computer program for a general case evaluation of the expanded uncertainty

The ISO Guide to the Expression of Uncertainty in Measurement provides a uniform method for the evaluation of combined standard uncertainty of a measurand whose expectation and standard deviation are stable over the measurement period. However, the method provided for the evaluation of the expanded uncertainty is not complete. Particularly, it does not include the case where the contributing components are correlated. Also, the probability distribution of the combined uncertainty must be close to a Normal distribution otherwise other methods must be used. The method presented here, which is implemented in a computer program, is based on a combination of the ISO guide method and Monte-Carlo simulation.The Monte-Carlo Simulation can obtain the data needed for the evaluation of the expanded and standard uncertainties directly from the measurement equation (that defines the measurand in terms of the contributing components) or from a spreadsheet-like format. Some sample results obtained by the computer program using both methods are compared and discussed.     

From a single analyzer to multiple instruments—The GUM approach

Assessment and expression of analytical quality have become novel spotlights in medical laboratories since accreditation began in the early 1990s, in Europe. Evaluation of uncertainty of measurement by definition was launched in Finland when the Finnish Accreditation Service (FINAS) accredited the first medical laboratories in the mid 1990s. In spite of all the analytical and statistical knowledge which has been available in medical laboratories for years, evaluation of total uncertainty of measurement has not yet caught on. The concept is still unfamiliar to experts and, indeed, little guidance has been available. National and international activities, with good results, can be shown when the educational aspect is considered. The Guide to the Expression of Uncertainty in Measurement (GUM) remains the main document for uncertainty evaluation. Uncertainty of measurement together with target value of uncertainty can be used as a good measure for analytical quality in large or smaller laboratories over time, because it is a quantitative indication and the evaluation is easy to repeat as running practical tools are available.Presented at the 8th Conference on Quality in the Spotlight, 17–18 March 2003, Antwerp, Belgium     

Uranium assay determination using Davies and Gray titration: an overview and implementation of GUM for uncertainty evaluation

The International Organization for Standardization (ISO) Guide to the expression of Uncertainty in Measurement (GUM) was developed to meet the demand for a standardized way of evaluating and expressing uncertainties. The Davies and Gray (D&G) titrimetry method is routinely used in nuclear safeguards for uranium accountability measurement and a statement of the uncertainty that can reasonably be attributed to the measured assay value is therefore of importance. A mathematical model for an uncertainty evaluation of D&G measurements in compliance with ISO GUM is presented. This is illustrated by a numerical example and the utilization of the uncertainty budget is explored.     

Optimising uncertainty in physical sample preparation

Uncertainty associated with the result of a measurement can be dominated by the physical sample preparation stage of the measurement process. In view of this, the Optimised Uncertainty (OU) methodology has been further developed to allow the optimisation of the uncertainty from this source, in addition to that from the primary sampling and the subsequent chemical analysis. This new methodology for the optimisation of physical sample preparation uncertainty (u(prep), estimated as s(prep)) is applied for the first time, to a case study of myclobutanil in retail strawberries. An increase in expenditure (+7865%) on the preparatory process was advised in order to reduce the s(prep) by the 69% recommended. This reduction is desirable given the predicted overall saving, under optimised conditions, of 33,000 pounds Sterling per batch. This new methodology has been shown to provide guidance on the appropriate distribution of resources between the three principle stages of a measurement process, including physical sample preparation.     

氢化物发生-原子荧光法测定高温合金中痕量铋的测量不确定度评定

介绍氢化物发生–原子荧光光谱法(HG–AFS)测定高温合金中痕量铋(Bi)的不确定度评定方法,建立了数学模型,分析了测量过程中不确定度的来源,并对不确定度分量进行了量化。当高温合金中铋含量为0.00016%时,扩展不确定度为0.00002%(k=2)。     

On the use of the ‘uncertainty budget’ to detect dominant terms in the evaluation of measurement uncertainty

In the evaluation of measurement uncertainty, the uncertainty budget is usually used to identify dominant terms that contribute to the uncertainty of the output estimate. Although a feature of the GUF method, it is also recommended as a qualitative tool in MCM by using ‘nonlinear’ equivalents of uncertainty contributions and sensitivity coefficients. In this paper, the use of ‘linear’ and ‘nonlinear’ parameters is discussed. It is shown that when and only when the standard uncertainty of the output estimate is nearly equal to the square root of the sum of the squares of the individual uncertainty contributions, will the latter be a reliable tool to detect the degree of contribution of each input quantity to the measurand uncertainty.