Estimation of measurement uncertainty by the budget approach for heavy metal content in soils under different land use

A reference database was used for the estimation of the standard uncertainties resulting from sampling, sample preparation, and analysis of soil samples from a target area in Switzerland. This evaluation was based on an extended reference sampling of the Comparative Evaluation of European Methods for Sampling and Sample Preparation of Soils Project. Samples were taken according to the national sampling protocols of 15 European countries and were analyzed for zinc, cadmium, copper, and lead. The combined uncertainty for all laboratories was estimated according to the ISO Guide to the Expression of Uncertainty in Measurement. It was found that the sampling uncertainty was not larger than the analytical uncertainty if more than ten sample increments were taken. The uncertainty due to variation in sampling depth and sample size reduction was only significant under unfavorable conditions. On the basis of an uncertainty budget the sampling protocols can be optimized and a ranking is possible, aimed at conditions that are fit for the specific purpose.Electronic Supplementary Material Supplementary Material is available in the online version of this article at     

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     

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     

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.     

Reference measurement procedure for Δ9-tetrahydrocannabinol in serum

An isotope dilution gas chromatography/mass spectrometry (ID-GC/MS) reference measurement procedure for Δ9-tetrahydrocannabinol (THC) in serum was developed and validated. The method complies with the concept of a ratio primary reference measurement procedure. The uncertainty was determined for two concentrations of THC in serum (1 ng/mL and 2.4 ng/mL). The calculation procedure is based on the Guide to the Expression of Uncertainty in Measurement (GUM). The relative expanded uncertainty was found to be less than 2% for both concentration levels, corresponding to a 95% confidence interval. For the reference method, it was shown that the measurement of THC within the concentration range covered by the current threshold values is very accurate. The method has the potential to provide traceability for the methods used in practical forensics.     

Overall measurement uncertainty of k0-based neutron activation analysis

Summary Special aspects of the uncertainty quantification in k₀-NAA are discussed and applied in accordance with the Guide to the Expression of Uncertainty in Measurement (GUM), on a model case. The uncertainty budget is calculated highlighting the contribution and the importance of the different parameters to be taken into account. The importance of the nuclide-specific and neutron fluence-specific approach in estimating individual uncertainty contributions is emphasized and demonstrated by examples of Au, Cr, Rb, and Sb determinations.     

Homogeneity and stability of reference materials

 Homogeneity and stability are two crucial characteristics of any certified reference material (CRM). Utmost care must be taken during preparation to create materials as homogeneous and stable as possible. Degradation can generally be minimised by reducing the water activity of the material to a level between 0.15 and 0.35. However, careful preparation by itself is not enough. Positive demonstration of homogeneity and stability is required from the perspective of implementing uncertainty calculus according to the Guide to the Expression of Uncertainty in Measurement (GUM). In many cases, homogeneity and stability studies fail to give sufficient quantitative information on homogeneity and stability, mainly because of a lack of measurement repeatability and insufficient number of replicates. In this work, some solutions to these problems and their implications are presented. Received: 25 April 2000 / Accepted: 12 September 2000     

From a single analyzer to multiple instruments—The GUM approach

Assessment and expression of analytical quality have become novel spotlights in medical laboratories since accreditation began in the early 1990s, in Europe. Evaluation of uncertainty of measurement by definition was launched in Finland when the Finnish Accreditation Service (FINAS) accredited the first medical laboratories in the mid 1990s. In spite of all the analytical and statistical knowledge which has been available in medical laboratories for years, evaluation of total uncertainty of measurement has not yet caught on. The concept is still unfamiliar to experts and, indeed, little guidance has been available. National and international activities, with good results, can be shown when the educational aspect is considered. The Guide to the Expression of Uncertainty in Measurement (GUM) remains the main document for uncertainty evaluation. Uncertainty of measurement together with target value of uncertainty can be used as a good measure for analytical quality in large or smaller laboratories over time, because it is a quantitative indication and the evaluation is easy to repeat as running practical tools are available.Presented at the 8th Conference on Quality in the Spotlight, 17–18 March 2003, Antwerp, Belgium     

Validation of the HS-GC-FID method for the determination of ethanol residue in tablets

This paper describes the validation of a HS-GC-FID method (based on the Pharmacopeia’s method) for the determination of ethanol content in tablets. A general view of the procedure development/optimization process is presented. The main point of this study is the calculation of validation parameters. Selectivity of the method was determined. Linearity (r > 0.997) was observed in the range from 9.0 to 3,040 μg of ethanol per sample (because the mass of the tablets used was around 200 mg, this corresponds to 45–15,200 μg g⁻¹). The method showed good recoveries (average 99.0%), and a relative standard deviation for repeatability and intermediate precision of 4.5% and 5.5% respectively. The limit of detection was calculated to be 3.0 μg of ethanol per sample (15 μg g⁻¹). The uncertainty budget was done according to the "Guide to the Expression of Uncertainty in Measurement" (GUM)[1], and a relative expanded uncertainty was estimated as 4.8%.     

Ménage À Trois: Activation, Analysis and Uncertainty, 10 Projections into the Impending Millenium

For more than half a century we have been using activation of stable isotopes to determine chemical elements, and significant contributions have been made to a variety of scientific subjects. Nevertheless, activation analysis has not yet become integrated in the field of chemical analysis, and therefore the special features characteristic of activation analysis have not been fully realised in analytical chemistry. At the same time basic chemical knowledge has only to a limited extent been utilised in the development of analytical methods based on activation. This situation has only now become painfully clear, when a world-wide requirement is being made to express the uncertainty of analytical results in accordance with the BIPM philosophy. The identification and estimation of all uncertainty components needed to produce a reliable uncertainty budget requires the combined efforts of all parties. An attempt is here made to extrapolate current trends for the expression of uncertainty in activation and analysis into the future and to show, how the implementation of the BIPM Guidelines with respect to correction for all known or suspected biases, achievement of statistical control, and full traceability, can help bringing analytical chemistry into its rightful position as a scientific discipline in the field of metrology.     

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.     

Uncertainty of nitrogen determination by the Kjeldahl method

 The uncertainty of the Kjeldahl method for determination of nitrogen in insulin was evaluated according the procedure described in the Guide to the Expression of Uncertainty in Measurement. The relative standard uncertainty of the method was found to be 0.19%, compared to the relative intermediate precision experimentally found to be 0.085%. The uncertainty components were organized in Tables, which allowed an easy overview and evaluation. The largest contribution to the uncertainty came from volumetric equipment. Systematic uncertainty budgets such as the design presented here facilitate the uncertainty evaluation process and makes it easier to compare uncertainty evaluations performed by different analysts. Received: 5 April 1999 / Accepted: 31 August 1999     

Novel concept for the mass spectrometric determination of absolute isotopic abundances with improved measurement uncertainty: Part 1 – theoretical derivation and feasibility study

The development of a new method for the experimental determination of absolute isotopic abundances using a modified isotope dilution mass spectrometry (IDMS) technique is described. The intention and thus main application will be the quantification of molar masses M of highly enriched materials with improved measurement uncertainty (U_rel(M) ≈ 10^?8 with k = 2). In part 1 of the current work, the theoretical foundation of the new method and its mathematical derivation is shown in detail, while part 2 will cover the experiments based on the new method described. Its core idea is the introduction of a virtual element (VE) consisting of all isotopes but the one having the largest or smallest abundance. IDMS is used to determine the mass fraction of this VE in its matrix, namely the element itself. A new set of equations serve to calculate all isotopic abundances (even the large one omitted with the introduction of the VE) merely from the mass fraction of the VE. A comprehensive uncertainty budget according to the Guide to the Expression of Uncertainty in Measurement (GUM) was set up in order to discuss and validate the novel concept. The hypothetical input data of the uncertainty budget were estimated to resemble a silicon material highly enriched with respect to ²⁸Si used in the context of the international Avogadro Project. Considering the calculated results, the experimental determination of the molar mass of the above mentioned silicon seems very promising. As far as the authors know, this will be the first time IDMS was applied to determine a molar mass.     

Uncertainty analysis of the microtiter plate method for determining trypsin inhibitor activity

Protease inhibitor activity is frequently measured in legume seeds as protease inhibitors are thought to have anti-nutritional as well as anti-carcinogenic properties. Trypsin inhibitor activity (TIA) can be measured using different methods. The microtiter plate method is very convenient and routinely used; therefore, in this study, we analyzed the measurement uncertainty of the microtiter plate method to understand what affects the measurement results, as well as to compare TIA values obtained by similar and different methods. For uncertainty analysis of TIA measurement, we used the soybean variety ‘Vojvodjanka,’ which is known to have TIA greater than 80 trypsin units inhibited (TUI) per mg of seed. We followed the Guide to the Expression of Uncertainty in Measurement (GUM) for our uncertainty analysis of the microtiter plate method for TIA testing, which we present in the form of an uncertainty budget. Absorbance measurement and preparation of sample reaction mixture took the largest percent (71 %) of overall uncertainty of TIA value. The TIA of soybean variety ‘Vojvodjanka’ was (94.1 ± 8.4) TUI/mg, and this result is consistent with those obtained by other authors. The microtiter plate method is a reliable method for TIA measurement, making seed quality testing more efficient.     

矿石金分析结果不确定度评定的几点思考

详细论述了不能按照JJF 1059-1999《测量不确定度评定与表示》和《化学分析中不确定度的评估指南》对矿石金分析结果进行不确定度评定的几个原因,并对现在使用的不确定度评定方法提出了建议。     

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     

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.     

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.     

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.     

Estimation of the uncertainty of mass measurements from in-house calibrated analytical balances

The uncertainty evaluation of mass measurements when using “in-house” calibrated analytical balances is revisited according to the Guide to the expression of Uncertainty Measurement (GUM). The calibration of analytical balances is discussed according to the guidelines of several bodies such as ASTM, UKAS and DKD/PTB. The remainder components of uncertainty can be estimated from the balance data sheet specifications.