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.     

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.     

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.     

Reflections regarding uncertainty of measurement, on the results of a Nordic fatigue test interlaboratory comparison

This paper presents the experiences of calculation and reporting uncertainty of measurement in fatigue testing. Six Nordic laboratories performed fatigue tests on steel specimens. The laboratories also reported their results concerning uncertainty of measurement and how they calculated it. The results show large differences in the way the uncertainties of measurement were calculated and reported. No laboratory included the most significant uncertainty source, bending stress (due to misalignment of the testing machine, incorrect specimens and/or incorrectly mounted specimens), when calculating the uncertainty of measurement. Several laboratories did not calculate the uncertainty of measurement in accordance with the Guide to the Expression of Uncertainty in Measurement (GUM) [1].     

Considering uncertainty of measurement when assessing compliance or non-compliance with reference values given in compositional specifications and statutory limits: a proposal

Considering the uncertainty of measurement (UOM) is mandatory when assessing compliance with reference values given in compositional specifications and statutory limits, but the matter is still open to question. Working in the signal or concentration domains and considering false negative together with false positive errors are the main points of debate. Frequently, the available approaches look too simplified for being accurate or too complex (since more rigorously formulated from a theoretical point of view) for being largely acceptable. In the Authors opinion, assessing compliance with reference values given in compositional specifications and statutory limits is a problem similar to that of estimating the limit of detection. This allows proposing a simple operational approach based on well-known and accepted assumptions and approximations. This proposal, described in the light of the most recent literature information, is aimed to stimulate a critical discussion in view of evaluating possible corrections to the generally accepted approach.Papers published in this section do not necessarily reflect the opinion of the Editors, the Editorial Board and the Publisher.     

Evaluation of measurement uncertainty for thermometers with calibration equations

The method recommended by Eurachem did not mention the effect of adequateness of calibration equations on the measurement uncertainty. In this work, the sources of measurement uncertainty for two types of thermometer were evaluated. Three calibration equations were adopted to compare its predictive performance. These sources of combined uncertainty include predicted values of calibration equation, nonlinearity and repeatability, reference source, and resolution source. The uncertainty analysis shows that the predicted uncertainly of calibration equations is the main source for two types of thermometer. No significant difference of the uncertainty was found between the classical method and the inverse method. However, the calculation procedure of the inverse method was simpler and easier than that of the classical method.     

A new terminology for the approaches to the quantification of the measurement uncertainty

A new terminology for the approaches to the quantification of the measurement uncertainty is presented, with a view to a better understanding of the available methodologies for the estimation of the measurement quality and differences among them. The knowledge of the merits, disadvantages and differences in the estimation process, of the available approaches, is essential for the production of metrologically correct and fit-to-purpose uncertainty estimations. The presented terminology is based on the level of the analytical information used to estimate the measurement uncertainty (e.g., supralaboratory or intralaboratory information), instead of the direction of information flow (“bottom-up” or “top-down”) towards the level of information where the test is performed, avoiding the use of the same designation for significantly different approaches. The proposed terminology is applied to the approaches considered on 19 examples of the quantification of the measurement uncertainty presented at the Eurachem/CITAC CG4 Guide, Eurolab Technical Report 1/2002 and Nordtest Technical Report 537. Additionally, differences of magnitude in the measurement uncertainty estimated by various approaches are discussed.     

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.     

Estimates of uncertainty of measurement from proficiency testing data: a case study

The results obtained by a laboratory over a number of proficiency testing/external quality assessment schemes (PT/EQAS) rounds can give information on the uncertainty of its measurements for a given test, provided that conditions such as full coverage of the routine analytical range, traceability, and small uncertainty of the assigned values (compared to the spread of the results) are met and provided that systematic deviations and any other sources of uncertainty are considered. As organisers of the Italian EQAS (ITEQAS) in occupational and environmental laboratory medicine, we tested this hypothesis using as model data from well-performing laboratories taking part in ITEQAS for lead in blood over the last 2 years. We also investigated how different PT/EQAS features (frequency of trials and number of samples) would affect a laboratory estimate of its uncertainty. Such information can be helpful in improving PT/EQAS organisation and define, for a given test: (a) the state of the art of the uncertainty of current measurement procedures, (b) identify needs for improvement of analytical methodologies and (c) set targets for acceptable uncertainty values.Presented at the Eurachem PT Workshop September 2005, Portorož, Slovenia.Papers published in this section do not necessarily reflect the opinion of the Editors, the Editorial Board and the Publisher.     

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.     

分析测试不确定度的评定与表示(Ⅰ)

就“不确定度”概念的来历和意义;基本术语;误差与不确定度;化学分析测量不确定度的来源;不确定度的评定;标准物质的不确定度;不确定度的评定实例等7个方面概述分析测试不确定度的评定与表示,介绍不确定度的基本知识与应用。     

Estimation of measurement uncertainty in organic analysis: two practical approaches

Estimation of measurement uncertainty has become a more regularly performed part of the whole analytical process. However, there is still much on-going discussion in the scientific community about ways of building up the uncertainty budget. This study describes two approaches for estimation of measurement uncertainty in organic analysis: one which can be used for single sets of measurements and the other based on validation studies. In both cases the main contributions to the uncertainty are presented and discussed for the analysis of PCBs in mussel tissue, but the approaches can be extended to other organic pollutants in environmental/food samples. The main contributions to the uncertainty budget arise from calibration, sample preparation, and GC–MS measurements. A comparison of the relevant sources and their contributions to the expanded uncertainty is presented.     

A simplified approach to the estimation of analytical measurement uncertainty

The present study summarizes the measurement uncertainty estimations carried out in Nestlé Research Center since 2002. These estimations cover a wide range of analyses of commercial and regulatory interests. In a first part, this study shows that method validation data (repeatability, trueness and intermediate reproducibility) can be used to provide a good estimation of measurement uncertainty.In a second part, measurement uncertainty is compared to collaborative trials data. These data can be used for measurement uncertainty estimation as far as the in-house validation performances are comparable to the method validation performances obtained in the collaborative trial.Based on these two main observations, the aim of this study is to easily estimate the measurement uncertainty using validation data.     

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     

Correlation between repeated measurements: bane and boon of the GUM approach to the uncertainty of measurement

With measurement uncertainty estimation accounting for all relevant uncertainty contributions, the results of measurements using the same procedure on different objects or samples may no longer be considered as being independent, and correlations have to be taken into account. For this purpose, a simple approximation for the estimation of covariances is derived and applied to the estimation of uncertainty for some basic combinations of two measurement results. This covariance estimate is also applied to the estimation of uncertainty for the mean value of the results of replicate measurements on the same object or sample.

HPLC法测定辣椒油中苏丹红染料的测量不确定度评定

建立了HPLC法分析辣椒油中苏丹红染料的不确定度模型,分析了方法中的不确定度分量及其来源,计算了各不确定度分量和合成标准不确定度。     

Estimation of measurement uncertainty for the determination of aflatoxin M1 in milk using immunoaffinity clean-up procedures

A measurement uncertainty estimated for aflatoxin M₁ determination in milk sample has been calculated using data generated from analytical method validation studies. The protocol adopted is described in detail in document LGC/VAM/1998/088. The uncertainty budget was based on precision, trueness and ruggedness data. The individual contributions are described in detail. The expanded uncertainty for aflatoxin M ₁ at a concentration of 20 ng L⁻¹ was estimated as 2.81 ng L⁻¹. This was calculated using a coverage factor of two which gives a level of confidence of approximately 95%. Presented at AOAC Europe / Eurachem Symposium March 2005, Brussels, Belgium     

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.