Evaluation of the uncertainty of environmental measurements of radioactivity

Results obtained by measurement of radioactivity have traditionally been associated with an expression of their uncertainty, based on the so-called counting statistics. This is calculated together with the actual result on the assumption that the number of counts observed has a Poisson distribution with equal mean and variance. Most of the nuclear scientific community has, therefore, assumed that it already complied with the latest ISO 17025 requirements. Counting statistics, however, express only the variability observed among repeated measurements of the same sample under the same counting conditions, which is equivalent to the term repeatability used in quantitative analysis. Many other sources of uncertainty need to be taken into account before a statement of the uncertainty of the actual result can be made. As the first link in the traceability chain calibration is always an important uncertainty component in any kind of measurement. For radioactivity measurements in particular we find that counting geometry assumes the greatest importance, because it is often not possible to measure a standard and a control sample under exactly the same conditions. In the case of large samples we have additional uncertainty components associated with sample heterogeneity and its influence on self-absorption and counting efficiency. In this paper we prepared an uncertainty budget for existing data for ¹³⁷Cs in Danish soil, which is shown to account adequately for all sources of uncertainty. This revised version was published online in July 2006 with corrections to the Cover Date.     

An alternative to the effective number of degrees of freedom

 In order to calculate the expanded uncertainty when one or more of the components of the standard uncertainty is based on a small number of degrees of freedom, the ISO Guide recommends utilising the 'effective number of degrees of freedom'. Calculating and utilising the 'effective number of degrees of freedom' to obtain a confidence interval both depend upon approximations, which, however, are adequate for determining an expanded uncertainty. This paper puts forward an alternative and simpler approximation which is also adequate but which is much easier to apply than the multi-step process given in the ISO Guide. Received: 2 July 1998 · Accepted: 12 August 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.     

Estimation of the uncertainty components associated with the measurement of radionuclides in air filters using γ-ray spectrometry

This paper discusses and assesses the major sources of uncertainty arising in measurement of radionuclide activity concentrations in air. Besides counting statistics, the main contributors to the overall uncertainty of the activity concentration of long-lived radionuclides are the heterogeneities of the calibration source and the test samples (approximately 4%). In addition, in the case of radionuclides with half-lives of the order of days or shorter, a significant uncertainty results from the variability of the source term because the peak concentration of the radionuclide might occur either at the beginning or at the end of the sampling period. For¹³¹I (T_1/28 days), for instance, the relative standard uncertainty was estimated as 17% owing to this effect. In addition, the uncertainty introduced by the software used for evaluation of the -ray spectra is discussed. Details of the uncertainty components, including their assessed probability distributions and degrees of freedom, and the conversion into standard uncertainties are reported in this paper, following the ISO Guide to the expression of uncertainty in measurement. A standard form for documenting and reporting the uncertainty budged is proposed and illustrated with an example.     

Metrology for chemical engineers

 The first full-semester course on Quality Assurance in Chemical Measurement was held at the Technical University of Denmark from September to December 1999. The course required sufficient knowledge of basic statistics to understand and apply the methods recommended in ISO 5725–1/6 Accuracy of Measurement Methods and Results. The main purpose of the course was, however, to familiarize PhD students with the BIPM philosophy, using the International Organization for Standardization (ISO) Guide to Expression of Uncertainty in Measurement, which was accepted by IUPAC and other international scientific organizations in 1993. Chemists are notoriously reluctant to accept the BIPM philosophy, but the appearance of a new Draft Guide Quantifying Uncertainty in Analytical Measurement at the EURACHEM Workshop in Helsinki in June 1999 stimulated us to make an attempt to overcome such chemical prejudice. After thorough reading of the examples presented in the Draft Guide, each of the participating students had to prepare an uncertainty budget for their own particular project and present it to the other participants for discussion. Eventually the students learned how to verify their uncertainty budgets by means of experimental results; this invariably entailed a re-evaluation of the uncertainty components in the original budget. The revised budget was again verified, and this iteration was continued until the budget correctly predicted the uncertainty of individual results covering the whole range of applicability of the analytical method. The paper presents the detailed structure of this first course, as well as improvements in the next course scheduled for the year 2000.     

Measurement uncertainty of microbiological viable counts

Estimation of the uncertainty of microbiological viable counts by the statistical analysis of series of observations is impractical because the observed value, the number of colonies, usually determines a large share of the uncertainty. Every test result, therefore, has a unique uncertainty and no general method-specific values exist. The most practical ways to estimate the uncertainty are based on mathematical models and assumed statistical distributions where the observed value is a significant parameter. The article describes the traditional solution based on the Poisson distribution and more advanced models based on the negative binomial distribution. The latter model is capable of combining technical and procedural components of uncertainty with the inevitable random scatter of microbial suspensions. The additional uncertainty due to subsampling in the confirmation of presumptive positives is estimated with the help of a binomial model. Traceability issues are discussed.Presented at the Metro Trade Workshop on Traceability and Measurement Uncertainty in Testing, 30–31 January 2003, Berlin, Germany     

Limited variations in 15N CSA magnitudes and orientations in ubiquitin are revealed by joint analysis of longitudinal and transverse NMR relaxation

The site-specific magnitudes and orientations of the chemical shift tensors have been estimated for 70 backbone (15)N-nuclei in human ubiquitin from the field dependence of dynamic independent ratios between relaxation rates, both longitudinal and transverse, measured at 9.4, 11.7, 14.1, and 18.8 T. The results were jointly analyzed with previously published relaxation data [Fushman; Tjandra; Cowburn. J.Am. Chem. Soc. 1998, 120, 10947-10952] [Kover; Batta. J. Mag. Reson. 2001, 150, 137-146]. The effective magnitudes of the anisotropies distribute around 169 ppm with a variability of 5 ppm. The orientation factors, reflecting the orientation of the CSA relative to the NH bond, distribute around -0.80 with a variability of 0.04, which corresponds to an angle between the symmetry axis of an assumed axially symmetric shielding tensor and the NH bond of 21.4 degrees, and a variability of 2.3 degrees. Correlations with the isotropic (15)N-chemical shifts are observed. Variations in the shielding anisotropies add uncertainty to the obtained order parameters proportional to the square of the magnetic field, when data are analyzed using an assumed invariant CSA tensor for all sites. Around 3% additional uncertainty in the order parameters for 800 MHz data is expected. The optimal TROSY field for amide nitrogen TROSY is estimated, with only marginal variations due to site-to-site variations. Variations in the shielding tensors add uncertainty to the exchange terms calculated from cross-correlation rates. An approach for estimating the exchange terms is suggested, where the uncertainty due to CSA-variations is minimized.     

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.     

Indirect determination of soluble trace elements in certified reference materials by neutron activation analysis

Since 1983 we have analyzedaqua regia extracts from environmental reference materials of 5 different soils and 4 different sludges by neutron activation analysis. Aqua regia as such is not accepted for irradiation in a nuclear reactor, and therefore the solution has to be evaporated to dryness, mixed and dried to constant weight before an aliquot can be taken and subjected to instrumental neutron activation analysis (INAA). Results for leachable Cr and Zn were found to display greater variability than results for total contents of these elements, and the reasons for this will be discussed.For the 1994 certification campaign for one soil and two sludges we have chosen to determine the total content of trace elements in these reference materials by INAA before and afteraqua regia leaching. The leachable contents are then found indirectly as a difference between the two results; in this way we eliminate the sources of uncertainty associated with the drying and handling of theaqua regia extracts, and we reduce the contributions from counting statistics.     

Uncertainty budget for multi-elemental analysis of plant nutrients in conifer foliar material using inductively coupled plasma atomic emission spectrometry (ICP-AES)

Measurement uncertainties evaluated according to GUM were given in an uncertainty budget for the measurement of mass fractions of 12 elements in conifer tree needle materials. The measurement was performed using ICP-AES, with prior microwave digestion of the dried sample material. The uncertainty budget for Ca as an example showed that correction for a systematic error was the main source of measurement uncertainty. The key to reduced measurement uncertainty therefore lies in identifying the main sources of systematic errors, and reducing the uncertainty associated with their correction. The usefulness of the uncertainty budget was demonstrated in its application to method validation, to the design of a quality control program, and finally for guiding method optimization.     

Determination of zinc in plant samples by isotope dilution inductively coupled plasma mass spectrometry

Determination of zinc involved spiking with (68)Zn enriched solution, digestion by HNO(3)+H(2)O(2) in microwave decomposition unit, off-line separation of zinc on Chelex-100 column and measurement of ((64)Zn+(66)Zn)/(68)Zn isotope ratio on ICP-MS spectrometer with a quadrupole mass filter. After optimization of standard operation procedure (details are given) the method was validated. LOD was found to be 0.3 mug g(-1) for the procedure without zinc separation and 3.6 mug g(-1) for the procedure involving zinc separation, respectively. The accuracy of results was proved by analyses of several CRM and a primary solution of zinc, the concentration of which was verified by gravimetry and complexometric titration. Barium is the only element causing serious interferences and it must be removed from samples. The uncertainty budget is given together with the scheme of combined uncertainty calculation. The main uncertainty components are contamination during zinc separation and uncertainty of isotopic composition of natural zinc.     

Uncertainty in quantitative thin-layer chromatography

Globalization forces analysts to demand extended control of variability in analytical measurements. A calculation procedure named the "error budget model" following recommendations proposed more than 20 years ago by the Bureau International des Poids et Mesures is established as a rule for evaluating and expressing the measurement uncertainty across a broad spectrum of measurements. This metrological approach common in physical measurement is not applicable in separation techniques and cannot quantitate measurement uncertainty. Our experiments show that it can be used as a planning tool in the validation of thin-layer chromatographic (TLC) methods. A computer program that quantitates uncertainty components associated with potential sources of uncertainty in quantitative TLC is prepared and tested with experimental data. TLC plates with different qualities of stationary phases (TLC and high-performance TLC) spotted with different types of samples are measured. Application is performed manually and automatically. Plates are scanned with UV-vis scanners and a video documentation system in remission and transmission mode and fluorescence. Although the calculated values are close to the values obtained with validation procedures, the error budget approach cannot substitute validation. Calculated results can predict critical points in real quantitative TLC, but they cannot confirm the validity of a selected chromatographic procedure.     

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.     

The determination of the uncertainty of reference materials certified by laboratory intercomparison

A pragmatic method is proposed for the implementation of the Guide to the expression of uncertainty in measurement in the certification of reference materials by laboratory intercomparison. It is based on the establishment of a full uncertainty budget for each laboratory result and the estimation of the impact of various laboratory standard uncertainties and of between-units variability on the certified reference material (CRM) uncertainty.     

Application of significant structures theory to amorphous polyethylene

The thermodynamic properties of amorphous polyethylene are calculated from a model based on the method of significant structures. The motion of a molecule as a whole is described by the motion of segments, each segment moving independently of all others. It is assumed that on melting, holes appear in the solid lattice and the segments can move into these vacancies, obtaining some gaslike degrees of freedom. The complete frequency distribution for polyethylene is used for the solidlike degrees of freedom, while a corrected classical partition function is used for the gaslike degrees of freedom. The calculated thermodynamic properties are in reasonable agreement with experimentally determined values, assuming each gaslike segment to consist of 20 CH₂ groups.     

Crystallographic Basis for the Stability of Abundant (Popular) Structure Types

In compliance with the hypothesis that the crystal structure stability increases with a decrease in the degrees of freedom of the constituent atoms, we propose quantitative criteria for structures: the ratio between the amount of the degrees of freedom of atoms to their number in a primitive cell (S) and the fundamental volume (V*)–the quotient of the cell volume (asymmetric unit) and the order of the symmetry group (M) that is the general position multiplicity. The crystallographic analysis of diamond and spinel structure types and their comparative analysis with stability and packing criteria are performed. The study uses the findings from the analysis of abundant less symmetrical tourmaline and apatite structure types which confirm the existence of standard frameworks–symmetrical spatial configurations of atomic sites that can be taken by atoms of various types.     

Evaluation of sample processing and sub-sampling performance

A methodology for the estimation of sample processing and sub-sampling performance based on the comparison of the global method experimental dispersion of results with the uncertainty estimated from developed models for the subsequent analytical steps is presented. This approach is a valuable alternative to the evaluation of adequate experimental information using a classical ANOVA, since the significance of the sample processing and sub-sampling is evaluated with a higher number of degrees of freedom for the same number of experimental assays, due to the high number of degrees of freedom associated with the uncertainty estimated for the subsequent analytical steps from the combination of the involved sources of uncertainty.Considering the construction of a model to describe the performance of the analytical steps following sample processing and sub-sampling over a broad concentration range, the experimental assays involved at the evaluation of the sample processing and sub-sampling can be performed at any concentration meeting the previously validated range and several months after the development of that model once its adequacy has been proven over time.This approach, which also allows the construction of a detailed performance model for the global analytical method over a broad concentration range, was applied to the determination of pesticide residues in apples by gas-chromatography with electron capture detector.Considering that no information was available regarding the samples heterogeneity, sub-sampling performance was evaluated considering a sample representing the worst expectable homogeneity. This was accomplished by spiking just one out of the 10 halves of apples processed in each sample.The developed model for the performance of the analytical method was successfully and easily applied to routine analysis through an automated link between the information generated by the chromatograph software with a file containing the model.     

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.     

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.