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     

Consideration of the uncertainty in the CRM value with the analysis of solid materials using atomic spectrometry

 The principles of the ISO "Guide to the expression of uncertainty in measurement" are applied to the analysis of solid materials by graphite furnace atomic absorption spectrometry. Assessment of trueness is achieved by the analysis of a certified reference material (CRM) under fixed instrumental conditions. For the evaluation of the method's uncertainty (as part of the validation) a model equation is derived, considering all significant contributions, including the uncertainty in the CRM value and the uncertainty in the CRM analysis. A concrete example is presented and discussed (soya flour as an unknown sample and CRM BCR rye grass). For routine analysis a pooled estimate from the validation experiment can be used, leading to an acceptable small uncertainty range even in the case of "duplicate determination". The test for trueness (acceptance) of the result of the CRM analysis is applied and the correction for detected bias is discussed. Received: 28 June 1998 · Accepted: 13 July 1998     

A computer program for a general case evaluation of the expanded uncertainty

The ISO Guide to the Expression of Uncertainty in Measurement provides a uniform method for the evaluation of combined standard uncertainty of a measurand whose expectation and standard deviation are stable over the measurement period. However, the method provided for the evaluation of the expanded uncertainty is not complete. Particularly, it does not include the case where the contributing components are correlated. Also, the probability distribution of the combined uncertainty must be close to a Normal distribution otherwise other methods must be used. The method presented here, which is implemented in a computer program, is based on a combination of the ISO guide method and Monte-Carlo simulation.The Monte-Carlo Simulation can obtain the data needed for the evaluation of the expanded and standard uncertainties directly from the measurement equation (that defines the measurand in terms of the contributing components) or from a spreadsheet-like format. Some sample results obtained by the computer program using both methods are compared and discussed.     

Reply to comments on EURACHEM/CITAC guide “Measurement uncertainty arising from sampling”

The Eurachem/CITAC Guide on ‘Measurement uncertainty arising from sampling’ describes a number of methods and approaches that can be used for the estimation of this uncertainty. A recent comment upon this Guide by Wilrich questions the expression of the measurement uncertainty in a form that is relative to the concentration, rather than just as an absolute number (i.e. as relative expanded uncertainty rather than expanded uncertainty), in one of the worked examples. This reply argues that the measurement results from the ‘duplicate’ method cannot reliably distinguish between constant standard deviation and constant relative standard deviation over the range observed in the example and that the most appropriate model must accordingly rely on prior knowledge. Since extensive prior knowledge indicates that the precision of sampling and of chemical analysis both tend to increase as a function of concentration, the body of the Guide recommends expression as a relative standard deviation. It is acknowledged that this assumption should be restated with the results of the worked examples as well as in its current position in the main body of the text, in a future edition of the Guide.     

Measurement uncertainty of food carotenoid determination

For consistent interpretation of an analytical method result it is necessary to evaluate the confidence that can be placed in it, in the form of a measurement uncertainty estimate. The Guide to the expression of Uncertainty in Measurement issued by ISO establishes rules for evaluating and expressing uncertainty. Carotenoid determination in food is a complex analytical process involving several mass transfer steps (extraction, evaporation, saponification, etc.), making difficult the application of these guidelines. The ISO guide was interpreted for analytical chemistry by EURACHEM, which includes the possibility of using intra- and interlaboratory information. Measurement uncertainty was estimated based on laboratory validation data, including precision and method performance studies, and also, based on laboratory participation in proficiency tests. These methods of uncertainty estimation were applied to analytical results of different food matrices of fruits and vegetables. Measurement uncertainty of food carotenoid determination was 10–30% of the composition value in the great majority of cases. Higher values were found for measurements near instrumental quantification limits (e.g. 75% for β-cryptoxanthin, and 99% for lutein, in pear) or when sample chromatograms presented interferences with the analyte peak (e.g. 44% for α-carotene in orange). Lower relative expanded measurement uncertainty values (3–13%) were obtained for food matrices/analytes not requiring the saponification step. Based on these results, the saponification step should be avoided if food carotenoids are not present in the ester form. Food carotenoid content should be expressed taking into account the measurement uncertainty; therefore the maximum number of significant figures of a result should be 2.     

Evaluating uncertainty in analytical measurements: the pursuit of correctness

 Simple in principle, the evaluation of uncertainty, especially in chemical analysis, is not a routine task and needs great care to be correct. This can be seen, particularly, from an examination of the EURACHEM Guide, Quantifying Uncertainty in Analytical Measurement (1995), which is the most important document on the subject. The examination reveals, in the author's opinion, a shortage of correctness in some principal details of the uncertainty estimation process as presented in worked examples in the Guide, and the author has therefore formulated some "in pursuit of correctness" rules for estimating uncertainty. The rules and respective comments are concerned with the following items: (1) choosing an appropriate distribution function in type B evaluation of uncertainty, (2) the necessity for consideration of separate contributions to the combined uncertainty, and (3) taking account of actual influence factors in the uncertainty estimation process. Furthermore, the problem of estimation of conditional versus overall uncertainty is touched upon in connection with comparative trials where only internal consistency of results is required. Received: 29 January 1998 · Accepted: 10 February 1998     

The Japanese traceability system and the role of uncertainty evaluation in measurement

 The new traceability system of measurement standards based on the Japanese Measurement Law has been established since November 1993. Some reference materials such as metal standard solutions, pH standard solutions and standard gas mixtures are included in the system together with relevant physical quantities. In this system, primary measurement standard instruments or primary reference materials are designated by the regulation for each quantity. For the practical dissemination of each quantity, accreditation of calibration bodies is recognized by the steering committee under the supervision of the government. In the course of assessment of a candidate calibration body, the concepts of ISO/IEC Guide 25 and ISO/IEC Guide 58 are effectively introduced. For the estimation of reliability, the concept of how to introduce the statistical approach is effectively considered. The method of uncertainty evaluation described in the ISO document entitled "Guide to the expression of uncertainty in measurement" is adopted.     

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.     

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. Received: 12 October 2000 / Revised: 2 January 2001 / Accepted: 3 January 2001     

Use of ISO Guides 25, 30, 31, 34, 35, and 9001 in re-engineering Bethlehem Steel Corporation's analytical chemistry reference materials program

 Many certified reference materials are needed to calibrate and control analytical measurement processes in integrated steel works. It is beyond the scope and capacity of most national laboratories to supply all of these needs. Yet, the demand for these materials is steadily increasing as more steel producers update their quality systems in preparation for ISO 9000 registration and/or ISO Guide 25 laboratory accreditation assessments. This paper describes how the Bethlehem Steel Corporation updated its reference materials program to meet its internal needs and offers a model for use by others in improving their programs. Received: 22 April 1998 · Accepted: 12 May 1998     

Contribution to the certification of cadmium and lead amount content in the BCR CRM-278R mussel tissue by isotope dilution mass spectrometry

 Metrological certification through a primary method of measurement and how it can be achieved is demonstrated in this paper, using the example of re-certification of cadmium and lead content in a biological material, the Bureau Communataire de Reference, reference material CRM-278R mussel tissue. The measurement method used was isotope dilution in combination with inductively coupled plasma mass spectrometry. Microwave digestion was applied to the samples prior to the measurements. A detailed uncertainty budget was evaluated according to the International Organisation of Standardisation, Guide to the Expression of Uncertainty and EURACHEM Guide, resulting in an expanded uncertainty. Received: 20 August 1999 / Accepted: 3 January 2000     

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.     

Reference materials – a view from a small country

ISO/IEC 17025 has an increased emphasis on traceability and estimation of uncertainty of measurement compared with ISO Guide 25. Demonstration of traceability is a new concept in analytical chemistry and depends on access to relevant reference materials or use of reference methods. Until now most reference materials used in New Zealand have been imported, because they offered international comparability. New Zealand is currently starting to develop the required infrastructure so that it will be able to produce unique reference materials that will contribute to the total international effort in improving the reliability of analytical chemistry. Received: 12 October 2000 / Revised: 18 January 2001 / Accepted: 23 January 2001     

Uncertainty in analytical results from solid materials with electrothermal atomic absorption spectrometry: a comparison of methods

The combined uncertainty in the analytical results of solid materials for two methods (ET-AAS, analysis after prior sample digestion and direct solid sampling) are derived by applying the Guide to the Expression of Uncertainty in Measurement from the International Standards Organization. For the analysis of solid materials, generally, three uncertainty components must be considered: (i) those in the calibration, (ii) those in the unknown sample measurement and (iii) those in the analytical quality control (AQC) process. The expanded uncertainty limits for the content of cadmium and lead from analytical data of biological samples are calculated with the derived statistical estimates. For both methods the expanded uncertainty intervals are generally of similar width, if all sources of uncertainty are included. The relative uncertainty limits for the determination of cadmium range from 6% to 10%, and for the determination of lead they range from 8% to 16%. However, the different uncertainty components contribute to different degrees. Though with the calibration based on reference solutions (digestion method) the respective contribution may be negligible (precision < 3%), the uncertainty from a calibration based directly on a certified reference material (CRM) (solid sampling) may contribute significantly (precision about 10%). In contrast to that, the required AQC measurement (if the calibration is based on reference solutions) contributes an additional uncertainty component, though for the CRM calibration the AQC is “built-in”. For both methods, the uncertainty in the certified content of the CRM, which is used for AQC, must be considered. The estimation of the uncertainty components is shown to be a suitable tool for the experimental design in order to obtain a small uncertainty in the analytical result.     

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.     

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.     

Comments to EURACHEM/CITAC guide “Measurement uncertainty arising from sampling”

The EURACHEM/CITAC Guide “Measurement uncertainty arising from sampling” deals with the design and analysis of experiments for the evaluation of the sampling and analytical standard deviation when a defined sampling and analytical method is used for the determination of the concentration, expressed as mass fraction (mg/kg), of an analyte in a specified material. The Guide recommends reporting the relative expanded uncertainty and using it directly, i.e. it implicitly assumes that the standard deviation is proportional to the mass fraction even in case the experimental data do not support this assumption. Example A1 (and some of the other examples of the Guide) demonstrates that this can result in extreme levels of underestimation or overestimation of the uncertainty of measurement results. Hence, such recommendations should be avoided!     

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.