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     

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.     

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 .     

Introduction of measurement uncertainty estimation into analytical instrument software: mission impossible?

In this paper we argue that introduction of ISO GUM based uncertainty estimation into analytical equipment software is a “mission possible” and is wholly realistic at this stage of development of the art. A possible general scheme of implementation of uncertainty estimation into analytical instrument software is presented based on the example of high-performance liquid chromatography (HPLC) but is also applicable to most other analytical instruments. This implementation would be very beneficial for the analysts/practitioners as the uncertainty would be handled within their everyday software environment.

     

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.     

Introduction of measurement uncertainty estimation into analytical instrument software: mission impossible?

In this paper we argue that introduction of ISO GUM based uncertainty estimation into analytical equipment software is a “mission possible” and is wholly realistic at this stage of development of the art. A possible general scheme of implementation of uncertainty estimation into analytical instrument software is presented based on the example of high-performance liquid chromatography (HPLC) but is also applicable to most other analytical instruments. This implementation would be very beneficial for the analysts/practitioners as the uncertainty would be handled within their everyday software environment.     

Evaluation of uncertainty of reference materials

 Certification of reference materials is far more than just characterisation of a selected homogeneous batch of material. From the perspective of the ISO Guide on the Expression of Uncertainty in Measurement (GUM) all uncertainty sources relevant to the user of an individual certified reference material (CRM) sample at a moment in time should be part of the CRM uncertainty. This not only includes the full uncertainty of the batch characterisation (rather than the statistical variation), but also all uncertainties related to possible between-bottle variation, instability upon long-term storage and instability during transport to the customer. Received: 21 April 1999 · Accepted: 24 September 1999     

Estimating the uncertainty of stability for matrix CRMs.

The new version of ISO Guide 34 requires producers of certified reference materials (CRMs) to include contributions of possible instability to the overall CRM uncertainty, to obtain a value for the uncertainty in compliance with the Guide to the Expression of the Uncertainty in Measurement (GUM). A pragmatic approach to estimating the uncertainty of stability is presented. It relies on regression analysis of stability data with subsequent testing of the slope of the regression line for significance. If the slope is found to be statistically insignificant, a shelf life is chosen and the uncertainty connected with this time is estimated via the standard deviation of the slope. This uncertainty is included in the overall uncertainty of the CRM. This approach is explained with examples showing its applicability to matrix CRMs.     

Uncertainty in liquid chromatographic analysis of pharmaceutical product: influence of various uncertainty sources

An ISO GUM measurement uncertainty estimation procedure was developed for a liquid-chromatographic drug quality control method-assay of simvastatin in drug formulation. In quantification of uncertainty components several practical approaches for including difficult-to-estimate uncertainty sources (such as uncertainty due to peak integration, uncertainty due to nonlinearity of the calibration curve, etc.) have been presented. Detailed analysis of contributions of the various uncertainty sources was carried out. The results were calculated based on different definitions of the measurand and it was demonstrated that unequivocal definition of the measurand is essential in order to get rigorous uncertainty estimate. Two different calibration methods - single-point (1P) and five-point (5P) - were used and the obtained uncertainties and uncertainty budgets were compared. Results calculated using 1P and 5P calibrations agree very well. The uncertainty estimate for 1P is only slightly larger than with 5P calibration.     

Estimating the uncertainty of stability for matrix CRMs

The new version of ISO Guide 34 requires producers of certified reference materials (CRMs) to include contributions of possible instability to the overall CRM uncertainty, to obtain a value for the uncertainty in compliance with the Guide to the Expression of the Uncertainty in Measurement (GUM). A pragmatic approach to estimating the uncertainty of stability is presented. It relies on regression analysis of stability data with subsequent testing of the slope of the regression line for significance. If the slope is found to be statistically insignificant, a shelf life is chosen and the uncertainty connected with this time is estimated via the standard deviation of the slope. This uncertainty is included in the overall uncertainty of the CRM. This approach is explained with examples showing its applicability to matrix CRMs. Received: 12 October 2000 / Revised: 2 January 2001 / Accepted: 3 January 2001     

Estimation of uncertainty in p<Emphasis Type="Italic">K</Emphasis><Subscript>a</Subscript> values determined by potentiometric titration

A procedure is presented for estimation of uncertainty in measurement of the pK(a) of a weak acid by potentiometric titration. The procedure is based on the ISO GUM. The core of the procedure is a mathematical model that involves 40 input parameters. A novel approach is used for taking into account the purity of the acid, the impurities are not treated as inert compounds only, their possible acidic dissociation is also taken into account. Application to an example of practical pK(a) determination is presented. Altogether 67 different sources of uncertainty are identified and quantified within the example. The relative importance of different uncertainty sources is discussed. The most important source of uncertainty (with the experimental set-up of the example) is the uncertainty of pH measurement followed by the accuracy of the burette and the uncertainty of weighing. The procedure gives uncertainty separately for each point of the titration curve. The uncertainty depends on the amount of titrant added, being lowest in the central part of the titration curve. The possibilities of reducing the uncertainty and interpreting the drift of the pK(a) values obtained from the same curve are discussed.     

Uncertainty budget for final assay of a pharmaceutical product based on RP–HPLC

Compliance with specified limits for the content of active substance in a pharmaceutical drug requires knowledge of the uncertainty of the final assay. The uncertainty of measurement is based on the ISO recommendation as expressed in the Guide to the Expression of Uncertainty in Measurement (GUM). The reported example illustrates the estimation of uncertainty for the final determination of a protein concentration by HPLC using UV detection, using the approach described by EURACHEM/CITAC. The combined standard uncertainty for a protein concentration of 2400 µmol/L was estimated to be 14 µmol/L.. All known and potential uncertainty components are presented in Ishikawa diagrams and were carefully evaluated using Type A or Type B estimates. Special efforts were made to avoid duplication or omission of significant contributions to the combined uncertainty. Hence, before accepting the uncertainty budget, the estimated combined standard uncertainty was verified using the variation observed in a number of quality control samples.     

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 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 .

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.

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”.     

The GUM and its planned supplemental guides

The work of the Joint Committee for Guides in Metrology on the expression of uncertainty in measurement is considered. Statements are made about the current edition of the Guide to the Expression of Uncertainty in Measurement (the "GUM") and the nature of the process of "GUM revision". In particular, the supplemental guides being prepared to give added value to the GUM are outlined. The guides will cover (a) numerical methods for the propagation of distributions, (b) models with more than one measurand, (c) conformity assessment and (d) modelling.     

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.     

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.     

Uncertainty estimation of anions and cations measured by ion chromatography in fine urban ambient particles (PM2.5)

The present work presents a measurement uncertainty evaluation according to Guide to the Expression of Uncertainty in Measurement (GUM) of the concentration of the cations K⁺ and Li⁺ and anions NO₃⁻² and SO₄⁻² in fine airborne particulate matter, refers to particles less than 2.5 μm in diameter (PM_2.5), as measured by ion chromatography (US-EPA 300 method). The GUM method is not typically used to report uncertainty. In general, the analytical results only report the measurement’s standard deviation under repetition as an uncertainty; thus, not all sources of uncertainty are considered. In this work, the major sources of uncertainty regarding the measurements were identified as contributions to linear least square regression lines, repeatability, precision, and trueness. The expanded uncertainty was approximately 20% for anions and cations. The largest contribution to uncertainty was found to be repeatability.