Attempts to include uncorrected bias in the measurement uncertainty

In ISO Guide it is strictly recommended to correct results for the recognised significant bias, but in special cases some analysts find out practical to omit the correction and to enlarge the expanded uncertainty for the uncorrected bias instead. In this paper, four alternatively used methods computing these modified expanded uncertainties are compared according to the levels of confidence, widths and layouts of the obtained uncertainty intervals. The method, which seems to be the best, because it provides the same uncertainty intervals as in the case of the bias correction, has not been applied very much, maybe since these modified uncertainty intervals are not symmetric about the results. The three remaining investigated methods maintain their intervals symmetric, but only two of them provide intervals of the kind, that their levels of confidence reach at least the required value (95%) or a larger one. The third method defines intervals with low levels of confidence (even for small biases). It is proposed a new method, which gives symmetric intervals just with the required level of confidence. These intervals are narrower than those symmetric intervals with the sufficient level of confidence obtained by the two mentioned methods. A mathematical background of the problem and an illustrative example of calculations applying all compared methods are attached.     

Accounting for bias in measurement uncertainty estimation

Generic issues and current approaches in the evaluation of bias studies with respect to estimation of measurement uncertainty are discussed, focusing on two main scenarios. In the first, for a within-laboratory assessment of a fully developed uncertainty budget, bias studies are carried out to verify the pre-established performance of a measurement procedure, and design corrective actions if necessary. In the second scenario, for an estimation of measurement uncertainty from within-laboratory validation data, bias studies are carried out to calibrate the whole measurement procedure and evaluate its performance, more specifically to estimate the uncertainty of measurement by combination of bias and precision estimates.

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Should non-significant bias be included in the uncertainty budget?

The bias of an analytical procedure is calculated in the assessment of trueness. If this experimental bias is not significant, we assume that the procedure is unbiased and, consequently, the results obtained with this procedure are not corrected for this bias. However, when assessing trueness there is always a probability of incorrectly concluding that the experimental bias is not significant. Therefore, non-significant experimental bias should be included as a component of uncertainty. In this paper, we have studied if it is always necessary to include this term and which is the best approach to include this bias in the uncertainty budget. To answer these questions, we have used the Monte-Carlo method to simulate the assessment of trueness of biased procedures and the future results these procedures provide. The results show that non-significant experimental bias should be included as a component of uncertainty when the uncertainty of this bias represents at least a 30% of the overall uncertainty. Received: 29 May 2001 Accepted: 10 December 2001     

Measurement uncertainty in analytical methods in which trueness is assessed from recovery assays

We propose a new procedure for estimating the uncertainty in quantitative routine analysis. This procedure uses the information generated when the trueness of the analytical method is assessed from recovery assays. In this paper, we assess trueness by estimating proportional bias (in terms of recovery) and constant bias separately. The advantage of the procedure is that little extra work needs to be done to estimate the measurement uncertainty associated to routine samples. This uncertainty is considered to be correct whenever the samples used in the recovery assays are representative of the future routine samples (in terms of matrix and analyte concentration). Moreover, these samples should be analysed by varying all the factors that can affect the analytical method. If they are analysed in this fashion, the precision estimates generated in the recovery assays take into account the variability of the routine samples and also all the sources of variability of the analytical method. Other terms related to the sample heterogeneity, sample pretreatments or factors not representatively varied in the recovery assays should only be subsequently included when necessary. The ideas presented are applied to calculate the uncertainty of results obtained when analysing sulphides in wine by HS-SPME-GC.     

Treatment of bias in estimating measurement uncertainty

Bias in an analytical measurement should be estimated and corrected for, but this is not always done. As an alternative to correction, there are a number of methods that increase the expanded uncertainty to take account of bias. All sensible combinations of correcting or enlarging uncertainty for bias, whether considered significant or not, were modeled by a Latin hypercube simulation of 125,000 iterations for a range of bias values. The fraction of results for which the result and its expanded uncertainty contained the true value of a simulated test measure and was used to assess the different methods. The strategy of estimating the bias and always correcting is consistently the best throughout the range of biases. For expansion of the uncertainty when the bias is considered significant is best done by SUMU(Max):U(C(test result))=ku(c)(C(test result))+ |delta(run)|, where k is the coverage factor (= 2 for 95% confidence interval), u(c) is the combined standard uncertainty of the measurement and delta(run) is the run bias.     

Approaches to uncertainty evaluation based on proficiency testing schemes in chemical measurements

Since the advent of the Guide to the Expression of Uncertainty in Measurement (GUM) founding the principles of uncertainty evaluation, numerous projects have been carried out to develop alternative practical methods when it is impossible to model technical or economical aspects of the measurement process. These methods can use all the experimental data available to the laboratories, such as repeatability, reproducibility, quality-control charts, etc. The studies presented in this paper compare the results obtained by the modelling method from GUM with the uncertainties found by applying alternative methods. They show two examples, one in the field of environmental monitoring, the other in the biomedical field, based on the exploitation of PT schemes results. Presented at BERM-11, October 2007, Tsukuba, Japan.     

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。     

Effect of insignificant bias and its uncertainty on the coverage probability of uncertainty intervals Part 1. Evaluation for a given value of the true bias

This paper investigates the coverage probability of the uncertainty intervals determined in compliance with the GUM and EURACHEM Guide, which are defined by expanded uncertainty U about the results uncorrected with the insignificant biases and corrected with the significant biases. This coverage probability can significantly fall below the chosen level of confidence in some cases as Maroto et al. discovered by using the Monte Carlo method. Their numerical results obtained provided that only the β errors have occurred in the test significance and findings that the coverage reduction depends on the mutual proportions of the magnitudes of the systematic error, overall uncertainty and bias uncertainty are confirmed in this paper by using probability calculus and numerical integration. This problem is also studied when all possible experimental biases, both significant and insignificant, are considered. From this point of view, the reduction of the coverage probability turns out to be less severe than from the previous one. The coverage probability is also investigated for some uncertainty intervals computed in different ways than the above mentioned documents recommend. The intervals defined by U about the results corrected with both significant and insignificant bias give always the same coverage probability equalling the chosen level of confidence. The intervals with some uncertainties modified or enlarged with the insignificant biases remove or moderate the coverage reduction.     

塑料中镉的测定不确定度评定

建立了用实验室内精密度和偏差的数据来评定塑料中镉的测定不确定度的方法. 通过研究不同基体和不同含量水平的样品, 考察了方法的精密度和回收率, 分别计算并合并了两者的测量不确定度. 结果表明精密度和回收率的相对不确定度分量分别为0.026和0.068, 合成不确定度为0.072, 扩展不确定度为0.14. 此评定过程为实验室评定测量不确定度提供了一种新的方法, 简单、合理, 计算结果可靠.     

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.     

Chemical metrology, chemistry and the uncertainty of chemical measurements

Chemical results normally involve traceability to two reference points, the specific chemical entity and the quantity of this entity. Results must also be traceable back to the original sample. As a consequence, any useful estimation of uncertainty in results must include components arising from any lack of specificity of the method, the variation between repeats of the measurement and the relationship of the result to the original sample. Chemical metrology does not yet incorporate uncertainty arising from any lack of specificity from the method selected or the traceability of the result to the original sample. These sources of uncertainty may however have much more impact on the reliability of the result than will any uncertainty associated with the repeatability of the measurement. Uncertainty associated with sampling may amount to 50–1000% of the reported result. Chemical metrology must be expanded to include estimations of uncertainty associated with lack of specificity and sampling. Received: 29 May 2001 Accepted: 17 December 2001     

An uncertainty evaluation for multiple measurements by GUM

An approach for uncertainty evaluation is proposed to determine the overall uncertainty by combining the uncertainties of the individual results from multiple measurements. It is accomplished by the separate combinations of the individual random and systematic components of the uncertainties of the individual results. The approach is useful when the individual results are not statistically different. It is recognized that, owing to the correlation, the uncertainty resulting from systematic effects is not reduced by multiple measurements. On the contrary, the uncertainty resulting from random effects can be reduced. Received: 3 May 2002 Accepted: 16 July 2002     

An electrical pumping approach to eliminate sample bias in capillary electrokinetic injection

A general pumping injection (PI), which involves the use of two capillaries with different diameters, was taken to evaluate systematically the effects on eliminating sample bias associated with the electrokinetic injection process in CE. One end of the separation capillary of the smaller diameter was inserted into another pumping capillary of larger diameter. When a high voltage was applied to the pumping capillary, the EOF generated inside will act as a pump to drive the solution stream in the separation capillary. The results have demonstrated that PI is suitable for both normal and reverse EOF situations. Second, the bias degree (BD) and SD of bias we presented were used to evaluate the degree of the bias under different conditions, and the factors of bias elimination have been investigated. Under optimal conditions, the bias was satisfactorily eliminated by PI. This EOF pumping system was successfully applied to the analysis of samples in CEC for a bias-free injection. Moreover, this two-capillary pumping system did not significantly affect the EOF, current, and the column efficiency of the separation process. Finally, a PI with grounded electrode was proposed and shown to be suitable for samples with low conductivity and ions with different mobility.     

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.     

Calibration in chemical measurement processes. II. A methodological approach

This article discusses the common terms related to chemical measurement processes, the different methodologies of calibration (which are not always well established) and the role of chemical standards. General classifications of reference materials and their use in the calibration process are clarified. Related features, such as recovery studies or screening and corrections of matrix systematic errors, are also considered, and guidelines concerning experimental design and verification of the calibration are given.     

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.

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.     

Effect of insignificant bias and its uncertainty on the coverage probability of uncertainty intervals: Part 2. Evaluation for a found insignificant experimental bias

This paper continues in studying the coverage probability of uncertainty intervals. It particularly investigates the uncertainty intervals determined in compliance with the GUM and EURACHEM Guide in case of the results uncorrected for the systematic error, since the experimental bias has been found insignificant. The problem is solved for known values of the experimental bias, its standard uncertainty and the overall standard uncertainty. The obtained findings given in graphs and tables show that coverage probability of the uncertainty intervals defined by expanded uncertainty about the uncorrected results can considerably fall below the chosen level of confidence; this depression depends only on the ratio of the bias and the overall uncertainty. The bias uncertainty does not directly influence this depression, it only determines whether the bias is significant or not and thereby determines whether the results will be corrected or not. The paper proposes three methods how to remove this coverage probability reduction: to apply a higher level of confidence in the significance test, to correct the results with the insignificant but too high biases and to compute the uncertainty intervals defined by some type of the uncertainties enlarged with the insignificant bias.     

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.