Towards a new edition of the “Guide to the expression of uncertainty in measurement”

The “Guide to the expression of uncertainty in measurement” (GUM) is an extremely important document. It unifies methods for calculating measurement uncertainty and enables the consistent interpretation and comparison of measurement results, regardless of who obtained these measurements and where they were obtained. Since the document was published in 1995, it has been realised that its recommendations do not properly address an important class of measurements, namely, non-linear indirect measurements. This drawback prompted the initiation of the revision of the GUM in the Working Group 1 of the Joint Committee for Guides in Metrology, which commenced in October 2006. The upcoming revision of the GUM provides the metrological community with an opportunity to improve this important document, in particular, to reflect developments in metrology that have occurred since the first GUM publication in 1995. Thus, a discussion of the directions for this revision is important and timely. By identifying several shortcomings of the GUM and proposing directions for its improvement, we hope this article will contribute to this discussion. Papers published in this section do not necessarily reflect the opinion of the Editors, the Editorial Board and the Publisher.     

Mechanical behaviour analysis of the interface in single hemp yarn composites: DIC measurements and FEM calculations

The present work aims to investigate the local deformation mechanisms around a yarn in an eco-composite. Different hemp yarn orientations and two types of epoxy resin were tested. Full-field measurements were realised with the digital image correlation technique on specific single yarn composites, either on the face of the specimens, or on the edge. The tensile tests were performed under an optical microscope to give sufficient precision, and a numerical model was developed. The experimental results showed high heterogeneities in strain fields which increase with the applied stress level. The comparison with the underlying microstructure and the numerical model enabled us to study the influence of the yarn on the mechanical behaviour. The local constitutive behaviour of the different constituents of the specimens could be approached by these analyses. These results constitute a complete and original database on hemp/epoxy interface mechanical behaviour.     

Application of consistency checking to evaluation of uncertainty in multiple replicate measurements

Use of repeated measurements in quantitative chemical analysis is common but leads to the problem of how to combine the measurement values and produce a result with an uncertainty following the GUM. There is often confusion between repeated indications or observations of an input quantity, for whose uncertainty the GUM prescribes a type A evaluation, and complete measurements repeated on multiple sub-samples, as considered here. A solution for combining repeated measurement results and their individual uncertainties based on simple interval logic is proposed here. The individual measurement values and their uncertainties are compared with the calculated average value to see if this implies that another, possibly unknown, source of uncertainty is present. The model of the individual results is modified for this possible between-replicate effect so that the repeated measurements are consistent. Lack of consistency is a strong indication that the measurement is not fully under control and needs further development or investigation. This is not always possible, however and the method given here is proposed to ensure that the values of the repeated measurements agree with each other. A simple numerical example is given showing how the method can be implemented in practice.     

An uncertainty evaluation for multiple measurements by GUM, III: using a correlation coefficient

After a measurement, a measured value and a measurement uncertainty are produced as a measurement result. By a repeated measurement, another measurement result is produced. Between the individual results of the two measurements, it is shown that there may be a significant correlation. A correlation coefficient can be determined when a GUM-compliant uncertainty budget for a measurement is available. Utilizing the correlations between the N individual results, an equation is derived to combine the N individual uncertainties of N measurements. Using the newly derived equation including the correlation coefficient, three measurement uncertainties of three measurement results are combined as an example. The combined uncertainty is compared with the uncertainty of a measurement which treats the three individual measurements as one process. Papers published in this section do not necessarily reflect the opinion of the editors, the editorial board, or the publisher.     

Detection limits and goodness-of-fit measures for the two-component model of chemical analytical error

The utility of analytical chemistry measurements in most applications is dependent on an assessment of measurement error. This paper demonstrates the use of a two-component error model in setting limits of detection and related concepts and introduces two goodness-of-fit statistics for assessing the appropriateness of the model for the data at hand. The model is applicable to analytical methods in which high concentrations are measured with approximately constant relative standard deviation. At low levels, the relative standard deviation cannot stay constant, since this implies vanishingly small absolute standard deviation. The two-component model has approximately constant standard deviation near zero concentration, and approximately constant relative standard deviation at high concentrations, a pattern that is frequently observed in practice. Here we discuss several important applications of the model to environmental monitoring and also introduce two goodness-of-fit statistics, to ascertain whether the data exhibit the error structure assumed by the model, as well as to look for problems with experimental design.     

Improving the quality of potentiometric pH measurements

Like all experimentally determined physical and chemical properties, pH measurements are affected by the limited precision and accuracy of the measurement procedures. Fundamental studies of pH standards, based on measurement of the potential of an electrochemical cell without transference, known as the Harned cell, containing a platinum–hydrogen electrode and a silver–silver chloride reference electrode, indicate that vapour condensation phenomena on potentiometric cell walls not immersed in the thermostatic bath are a major source of error in assessment of pH values. In this work a study was conducted on phthalate buffer, 0.05 mol kg⁻¹ KHPhth, and results are reported for the effect of this phenomenon on the assignment of pH values and on their corresponding uncertainties. Identification and quantification of this effect constitute an original contribution to improvement of the primary method of pH measurement and, therefore, more rigorous pH (PS) values.     

Uncertainty of atomic absorption spectrometer

The uncertainty of the flame atomic absorption spectrometer was studied. Drift of signal, noise, and nonlinearity of the calibration curve were found to be main sources of uncertainty for the absorbance measurement, and factors affecting these sources of uncertainty were evaluated using Cd as a typical element. The combined uncertainty was 0.00133 absorbance units at a Cd concentration of 0.5 mg/l (0.078 absorbance units). The relationship between the flame conditions and the burner optics contributed strongly to the uncertainty. Therefore, the matrix effect of the sample must to be taken into consideration in actual analyses.     

有机分析研究进展——单原子、单分子、单细胞的分析进展

简要地对单原子、单分子、单细胞的分析方法和研究进展情况进行了评述 ,共引用文献 193篇     

原子吸收光谱法测定水溶液中银不确定度的评定

分析了影响原子吸收光谱法(AAS)测定水溶液中银的主要因素,并对其所引起的不确定度分量进行评估。对含银0．10～2．00 mg·L-1的水溶液,置信水平95％时,测量结果的扩展不确定度为0．020 mg·L-1,有效自由度为50。     

Uncertainty of measurement for summed masses: application to controlled substances

Because sentences for drug possession depend on the mass of the seized drug, testing laboratories must often determine the summed mass of numerous items submitted under a single case. One common practice for this purpose is to continue analyzing and weighing samples until a legal threshold is passed, at which point it is important to inform the court whether the summed mass is significantly above the threshold, or only marginally so. This paper develops a means for estimating the uncertainty of the summed mass for the common situation where the readability, d, of the balance dominates the uncertainty. It is seen that for all sample sizes the uncertainty, UM, is given by the remarkable simple expression UM = (d/2) × [N + SQRT(3N)] + N × CCE, where N is the number of items and CCE is the absolute value of the calibration check error. In most instances, this can be further simplified to UM = N × d.     

测量不确定度的研究和应用进展

综述了测量不确定度在国内外的研究及应用的进展，发现测量不确定度是现代误差理论的重要内容，是定量描述测量结果质量的重要指标。目前由ISO等七个国际组织提出的GUM(测量不确定度表述导则)已被各国广泛接受，国内外已有大量关于不确定度应用的文献。除GUM外，还存在其它几种不确定度评定模型。我国虽然对GUM存在重大疑义，并向有关国际组织提出了一些建设性的意见，但在方法的执行上目前仍然与国际社会保持了对GUM的一致态度。     

Comparison of different methods to estimate the uncertainty in composition measurement by chromatography

Natural gas is a mixture that contains hydrocarbons and other compounds, such as CO₂ and N₂. Natural gas composition is commonly measured by gas chromatography, and this measurement is important for the calculation of some thermodynamic properties that determine its commercial value. The estimation of uncertainty in chromatographic measurement is essential for an adequate presentation of the results and a necessary tool for supporting decision making. Various approaches have been proposed for the uncertainty estimation in chromatographic measurement. The present work is an evaluation of three approaches of uncertainty estimation, where two of them (guide to the expression of uncertainty in measurement method and prediction method) were compared with the Monte Carlo method, which has a wider scope of application. The aforementioned methods for uncertainty estimation were applied to gas chromatography assays of three different samples of natural gas. The results indicated that the prediction method and the guide to the expression of uncertainty in measurement method (in the simple version used) are not adequate to calculate the uncertainty in chromatography measurement, because uncertainty estimations obtained by those approaches are in general lower than those given by the Monte Carlo method.     

标准溶液测量不确定度的评定

对标准溶液测量不确定度进行合理评定，充分估计分析不确定度的来源，从量值检验时考虑到影响不确定度的各种因素，测量方法的不确定度．配制时考虑到影响不确定度的各种因素以及标准溶液的不均匀性和在有效期内的变动性所引起的不确定度等方面进行综合分析，得出其扩展不确定度。并以镍标准溶液为例作实际分析。     

分光光度计测铁矿石中钛的测量不确定度评定

紫外-可见分光光度计在化学分析中应用较为广泛。对于借助其进行化学分析测量不确定度的评定，目前较多见于溶液测定。实际应用中，测试样品多为固体，涉及到称样、溶解、稀释、定容等步骤。此文试从随机效应和系统效应的角度考虑，对紫外-可见分光光度计应用ISO4691：1985铁矿石中钛含量的测定——二安替比林甲烷分光光度法对铁矿石中钛的测量过程中的不确定度来源进行了较为全面的分析，并最终给出评定结果。     

Calibration lines passing through the origin with errors in both axes

Linear regression of calibration lines passing through the origin was investigated for three models of y-direction random errors: normally distributed errors with an invariable standard deviation (SD) and log normally and normally distributed errors with an invariable relative standard deviation (RSD). The weighted (weighting factor is x ² _i ), geometric and arithmetic means of the ratios y _i /x _i estimate the calibration slope for these models, respectively. Regression of the calibration lines with errors in both directions was also studied. The x-direction errors were assumed to be normally distributed random errors with either an invariable SD or invariable RSD, both combined with a constant relative systematic error. The random errors disperse the true, unknown x-values about the plotted, demanded x-values, which are shifted by the constant relative systematic error. The systematic error biases the slope estimate while the random errors do not. They only increase automatically the slope estimate uncertainty, in which the uncertainty component reflecting the range of the possible values of the systematic error must be additionally included. Received: 9 May 2000 Accepted: 7 March 2001     

Wide range pH measurements using a single H(+)-selective chromoionophore and a time-based flow method

A hydrophilic transparent triacetyl cellulose membrane was adopted as a pH optode by immobilizing highly selective and sensitive Nile blue indicator on the membrane. Contrary to the common procedure for determinations using optodes, in which a steady state response is measured, a new approach is introduced in which the dynamic response of the optode is used as the analytical signal. While in common procedures, pH optodes exhibit limited linear dynamic range (often 2–4 pH units only), it is shown that in a time-based flow method, an optode with only one acid-base indicator can be used for measurement in the pH range of 0–10. The procedure is simple, inexpensive and rapid.     

Appropriate rather than representative sampling, based on acceptable levels of uncertainty

Appropriate sampling, that includes the estimation of measurement uncertainty, is proposed in preference to representative sampling without estimation of overall measurement quality. To fulfil this purpose the uncertainty estimate must include contribution from all sources, including the primary sampling, sample preparation and chemical analysis. It must also include contributions from systematic errors, such as sampling bias, rather than from random errors alone. Case studies are used to illustrate the feasibility of this approach and to show its advantages for improved reliability of interpretation of the measurements. Measurements with a high level of uncertainty (e.g. 50%) can be shown to be fit for some specified purposes using this approach. Once reliable estimates of the uncertainty are available, then a probabilistic interpretation of results can be made. This allows financial aspects to be considered in deciding upon what constitutes an acceptable level of uncertainty. In many practical situations ”representative” sampling is never fully achieved. This approach recognises this and instead, provides reliable estimates of the uncertainty around the concentration values that imperfect appropriate sampling causes. Received: 28 December 2001 Accepted: 25 April 2002     

Thermophoresis of single stranded DNA

The manipulation and analysis of biomolecules in native bulk solution is highly desired; however, few methods are available. In thermophoresis, the thermal analog to electrophoresis, molecules are moved along a microscopic temperature gradient. Its theoretical foundation is still under debate, but practical applications for analytics in biology show considerable potential. Here we measured the thermophoresis of highly diluted single stranded DNA using an all‐optical capillary approach. Temperature gradients were created locally by an infrared laser. The thermal depletion of oligonucleotides of between 5 and 50 bases in length were investigated by fluorescence at various salt concentrations. To a good approximation, the previously tested capacitor model describes thermophoresis: the Soret coefficient linearly depends on the Debye length and is proportional to the DNA length to the power of 0.35, dictated by the conformation‐based size scaling of the diffusion coefficient. The results form the basis for quantitative DNA analytics using thermophoresis.     

Introducing the concept of uncertainty of measurement in testing in association with the application of the standard ISO/IEC 17025

ISO/IEC 17025 requests laboratories to estimate the overall uncertainty associated with a test result. In many cases this means a new requirement to laboratories. It is essential to understand the importance of the knowledge of the uncertainty of measurements as well as the principle that not always the smallest possible uncertainty is needed, but fitness for purpose has to be achieved. The paper suggests a policy on the implementation of the concept of uncertainty and guidance on how to proceed, taking into account the present state of the art of understanding the problem.     

Treatment of uncorrected measurement bias in uncertainty estimation for chemical measurements

Consistent treatment of measurement bias, including the question of whether or not to correct for bias, is essential for the comparability of measurement results. The case for correcting for bias is discussed, and it is shown that instances in which bias is known or suspected, but in which a specific correction cannot be justified, are comparatively common. The ISO Guide to the Expression of Uncertainty in Measurement does not provide well for this situation. It is concluded that there is a need for guidance on handling cases of uncorrected bias. Several different published approaches to the treatment of uncorrected bias and its uncertainty are critically reviewed with regard to coverage probability and simplicity of execution. On the basis of current studies, and taking into account testing laboratory needs for a simple and consistent approach with a symmetric uncertainty interval, we conclude that for most cases with large degrees of freedom, linear addition of a bias term adjusted for exact coverage ("U(e)") as described by Synek is to be preferred. This approach does, however, become more complex if degrees of freedom are low. For modest bias and low degrees of freedom, summation of bias, bias uncertainty and observed value uncertainty in quadrature ("RSSu") provides a similar interval and is simpler to adapt to reduced degrees of freedom, at the cost of a more restricted range of application if accurate coverage is desired.