Estimation of uncertainty in electrochemical amperometric measurement of dissolved oxygen concentration

A procedure for the estimation of measurement uncertainty of dissolved oxygen (DO) concentration measurement based on the ISO approach is presented. It is based on a mathematical model that involves 14 input parameters. The uncertainty of DO concentration strongly depends on changes in experimental details (temperature difference between calibration and measurement, the time interval between calibration and measurement, etc.). The relative measurement uncertainty is, however, practically independent of the DO concentration itself. The uncertainty is the lowest if the calibration and the measurement are done at the same temperature and on the same day. A calculation tool is provided (in the form of a GUM Workbench file) for practitioners that can be used for uncertainty calculation of DO concentrations at very different experimental conditions.Electronic Supplementary Material The uncertainty calculation example is available as a GUM Workbench calculation file C_O2_meas.smu (GUM Workbench ver. 1.3.3, Metrodata GmbH) together with its data file Input_values.xls (MS Excel 97). For those users who do not have GUM Workbench, the full report of the GUM Workbench calculation is available as a PDF file C_O2_meas.pdf. This material is available via the Internet at .     

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.     

Model-based measurement uncertainty evaluation,with applications in testing

Basic concepts and implementations of the model-based approach to uncertainty evaluation are discussed. One implementation is that of the law of propagation of uncertainty with the use of the central limit theorem as recommended in the Guide to the expression of uncertainty in measurement (GUM). Another is the propagation of distributions, the subject of a supplemental guide to the GUM, which is at an advanced stage of development. It falls in the category of other analytical and numerical methods indicated in the GUM. Two testing applications are used to illustrate the principles: tennis-ball rebound and tensile strength.

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”.     

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.     

Uncertainty Budget for k0-NAA

The concepts of the Guide to the expression of Uncertainties in Measurements for chemical measurements (GUM) and the recommendations of the Eurachem document "Quantifying Uncertainty in Analytical Methods" are applied to set up the uncertainty budget for k ₀-NAA. The "universally applicable spreadsheet technique", described by Kragten, is applied to the k ₀-NAA basic equations for the computation of uncertainties. The variance components — individual standard uncertainties — highlight the contribution and the importance of the different parameters to be taken into account.     

ISO 5725 and GUM: comparison and comments

We compare the approach to measure uncertainties proposed in ISO 5725 and GUM from a statistician point of view. In particular we give some warnings to the application of the expanded uncertainty introduced in GUM when the input variables are few and we report some considerations on the relevant role of the interactions among the input variables in the measurement equation as well as the role of statistical design of experiments to measure uncertainties.

Implementing the GUM in the certification of reference materials: the revision of ISO Guide 35

The availability of certified reference materials, certified in accordance to the GUM is an important tool for the proper estimation of measurement uncertainty in routine analysis. Many CRMs may suffer from incomplete or wrongly estimated uncertainties, mainly due to lack of guidance on how to implement the GUM in the production of CRMs. In particular the inclusion of the impact of inhomogeneity and instability in the uncertainty budget is often missing. The ongoing revision of ISO Guide 35 aims to fill this gap in providing guidance how (batch) inhomogeneity and instability can be translated into measurement uncertainty. The structure of the current ISO Guide 35 has been maintained as far as possible, but major parts underwent revision to become better aligned with GUM and ISO Guide 34 (2000). Received: 9 April 2001 Accepted: 22 October 2001     

Call to participate in surveys on GUM and VIM

News and Announcements

Call to participate in surveys on GUM and VIM     

Uncertainty in photometric analysis: a case study

A procedure for estimation of measurement uncertainty of photometric analysis based on the ISO GUM method is presented. Two variations of the procedure—for the calibration graph and the standard addition method, respectively—are discussed. The variations are based on mathematical models involving 64 and 80 input quantities, respectively. The uncertainty of the result strongly depends on changes in experimental details. These dependencies are explored for a practical example of determination of the iron content of aluminum. The importance of taking uncertainty from sample preparation into account in uncertainty estimation is stressed. The number of effective degrees of freedom is calculated and discussed. The examples are available as GUM Workbench files in the Electronic Supplementary Material.Electronic Supplementary Material  Supplementary material is available for this article at .

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.     

Accreditation of reference material producers: Let's get it right!

The accreditation of testing and calibration laboratories to ISO/IEC 17025 is increasingly calling for the accreditation of reference material (RM) producers. Two international guides, ISO Guide 34 (2000) " General requirements for the competence of reference material producers" issued by the ISO Committee on Reference Materials and ILAC-G 12 " Guidelines for the requirements for the competence of reference material producers" issued by the International Laboratory Accreditation Cooperation (ILAC), are already in use for this purpose. Recently however initiatives have been launched to accredit RM producers to ISO 17025 as calibration laboratories and it has been suggested that a combination of ISO/IEC 17025 " General requirements for the competence of testing and calibration laboratories" and ISO Guide 34 may be the best option. This publication is an expression of the position of the ISO Committee on Reference Materials (ISO/REMCO) on the standards and guides currently in use in the accreditation of RM producers. The paper discusses the advantages and disadvantages of these standards and guides from the perspective of benefit to RM producers and RM users. In conclusion, the use of ISO Guide 34 alone or in combination with ILAC-G 12 is the preferred system for the accreditation of RM producers. Therefore ISO/REMCO strongly encourages all accreditation bodies to adopt ISO Guide 34.     

Evaluation of measurement uncertainty in analytical assays by means of Monte-Carlo simulation

The main limitations of the Guide to the expression of Uncertainty Measurement (GUM) approach for evaluating the measurement uncertainty of analytical assays are presented and explained. The advantages of using Monte-Carlo simulation against the GUM approach are outlined and discussed and the principle of propagation of distributions is explained. The procedure of Monte-Carlo analysis is illustrated by two case studies. A first simple example quoted from the EURACHEM Guide and dealing with the preparation of a calibration standard is used to present the technique with detail in a step-by-step way. In this case the results obtained by both approaches are very similar. A second example deals with the calibration of mass according to a strong non-linear model. In this case, the Monte-Carlo analysis leads to better results.     

Modelling the calibration of the industrial platinum-resistance thermometers according to GUM

According to the Guide to the Expression of Uncertainty in Measurement (GUM, JCGM 100: 2008), the calibration process and its uncertainty evaluation should be expressed in terms of mathematical function(s) of input quantities. However, in practice, expressing measurement or calibration in a way that is fully compliant with GUM might be unrealistic and require a clear definition of the calibration process itself. Depending on the applied calibration process, different modelling equations with various complexities can be written. In this paper, four different approaches are given to model the calibration process of industrial platinum-resistance thermometers.     

为“探究式-小班化”教学培训助教的实践

Sichuan University establishes teaching assistants of master candidates (AMC) for reform of "inquiry-small class" teaching.The tutor arranges the good teaching assistants to take part in the pre-service training of AMC,and guides all the graduate assistant students to participate in the training of "fine example mini lesson" and "interactive seminar mini lesson".As a result,the students' participation and training quality are improved.     

Estimation of the standard uncertainty of a calibration curve: application to sulfur mass concentration determination in fuels

The construction of a calibration curve using least square linear regression is common in many analytical measurements, and it comprises an important uncertainty component of the whole analytical procedure uncertainty. In the present work, various methodologies are applied concerning the estimation of the standard uncertainty of a calibration curve used for the determination of sulfur mass concentration in fuels. The methodologies applied include the GUM uncertainty framework, the Kragten numerical method, the Monte Carlo method (MCM) as well as the approximate equation calculating the standard error of prediction. The standard uncertainty results obtained by all methodologies agree well (0.172?C0.175?ng???L^?1). Aspects of inappropriate use of the approximate equation of the standard error of prediction, which leads to overestimation or underestimation of calculated uncertainty, are discussed. Moreover, the importance of the correlation between calibration curve parameters (slope and intercept) within GUM, MCM and Kragten approaches is examined.     

Implementation in MATLAB of the adaptive Monte Carlo method for the evaluation of measurement uncertainties

The ISO 98:1995 Guide to the expression of uncertainty in measurement (GUM) presents important application limitations. For its improvement, different supplements are being developed that will progressively enter into effect. The first of these supplements describes an alternative method for calculating uncertainties, the Monte Carlo method (MCM), which is not restricted to the conditions of the method described in the GUM: the linearity of the model and the application of the central limit theorem. MCM requires computer calculation systems for generating pseudo-random numbers and for evaluating the model a large number of times. There are software applications that have been specifically developed for calculating uncertainties, some of which include MCM; but they do not allow the user to control all factors in the process, particularly the result stabilization criteria. On the contrary, its implementation in a mathematical program for general purposes such as MATLAB, enables total control over the process, is simple and benefits from its calculation speed. This article details programming in MATLAB for the implementation of the adaptive MCM method.     

Uncertainty estimation in measurement of pKa values in nonaqueous media: A case study on basicity scale in acetonitrile medium

The difficulties in estimating uncertainty of pK_a values determined in nonaqueous media are reviewed and two different uncertainty estimation approaches are presented and applied to the pK_a values of the compounds on a previously established self-consistent spectrophotometric basicity scale in acetonitrile. One approach is based on the ISO GUM methodology (the “ISO GUM” approach) and involves careful analysis of the uncertainty sources and quantifying the respective uncertainty components. The second approach is based on the standard-deviation-like statistical parameter that has been used for characterization of the consistency of the scale (the “statistical” approach). It is demonstrated that the ISO GUM approach somewhat overestimates the uncertainty. The statistical approach is based on long-term within-laboratory statistical data and it is demonstrated that it underestimates the uncertainty. In particular it neglects the laboratory bias effects that are taken into account at least to some extent by the ISO GUM approach. Thus, together these two approaches allow to “bracket” the uncertainties of the pK_a values on the scale. The uncertainties of the pK_a values are defined in two different ways. Definition (a) includes the uncertainty of the pK_a of the reference base (anchor base of the scale) pyridine. Definition (b) excludes it. It is demonstrated that both definitions have their virtues. Definition (a) leads to the uncertainty ranges of 0.12-0.22 and 0.12-0.14 pK_a units at standard uncertainty level for different bases using the ISO GUM and statistical approach, respectively. Definition (b) leads to the uncertainty ranges of 0.04-0.19 and 0.02-0.08 pK_a units, respectively. The uncertainty of the pK_a of a given base is dependent on the quality of the measurements involved and on the distance from the reference base on the scale. The importance of the correlation between the pK_a values of bases belonging to the same scale is stressed.     

A practitioner's approach to the assessment of the quality of sampling, sample preparation, and subsampling

 The methodology of evaluating the performance of sampling, sample preparation, and subsampling is reviewed. The requirements to be set for a successful experiment are revisited. The central role of the reference method is explained, and so is the choice of the parameters and the measurement methods. Based on the principles of the "Guide to the expression of uncertainty in measurement" (GUM), a statistical model is developed that demonstrates the influence of the experimental design on the outcome of the assessment experiment. This relationship is often overlooked in practice, as it is hardly mentioned in written standards dealing with this kind of quality assessments. The statistical framework thus developed covers the statistical procedures commonly appearing in written standards. Finally, the issue of testing the significance of the bias obtained from the experiment is discussed. Received: 14 June 1997 · Accepted: 2 September 1997     

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。