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In this study we demonstrate that the method of standard additions can provide unreliable results in chemical analysis when the linear calibration model is forced to fit the data. A well designed standard addition experiment can still yield results biased by 10% when the analyst relies only on the linear model. Recently, the Joint Committee for Guides in Metrology (GUM-6) has emphasized the need to address the uncertainty inherent to the choice of measurement models and here we show how model averaging can provide a practical way to account for model uncertainty in the method of standard additions.

A model for errors-in-variables regression is described that can be used to overcome the challenge posed by mutually inconsistent calibration data. The model and its implementation are illustrated in applications to the measurement of the amount fraction of oxygen in nitrogen from key comparison CCQM-K53, and of carbon isotope delta values in steroids from human urine. These two examples clearly demonstrate that inconsistencies in measurement results can be addressed similarly to how laboratory effects are often invoked to deal with mutually inconsistent results from interlaboratory studies involving scalar measurands. Bayesian versions of errors-in-variables regression, fitted via Markov Chain Monte Carlo sampling, are employed, which yield estimates of the key comparison reference function in one example, and of the analysis function in the other. The fitting procedures also characterize the uncertainty associated with these functions, while quantifying and propagating the ‘excess’ dispersion that was unrecognized in the uncertainty budgets for the individual measurements, and that therefore is missing from the reported uncertainties. We regard this ‘excess’ dispersion as an expression of dark uncertainty, which we take into account in the context of calibrations that involve regression models. In one variant of the model the estimate of dark uncertainty is the same for all the participants in the comparison, while in another variant different amounts of dark uncertainty are assigned to different participants. We compare these models with the conventional errors-in-variables model underlying the procedure that ISO 6143 recommends for building analysis functions. Applications of this procedure are often preceded by the selection of a subset of the measurement results deemed to be mutually consistent, while the more discrepant ones are set aside. This new model is more inclusive than the conventional model, in that it easily accommodates measurement results that are mutually inconsistent. It produces results that take into account contributions from all apparent sources of uncertainty, regardless of whether these sources are already understood and their contributions have been included in the reported uncertainties, or still require investigation after they will have been detected and quantified.

Main text The CCQM-K148.a comparison was coordinated by the BIPM on behalf of the CCQM Organic Analysis Working Group for NMIs and DIs which provide measurement services in organic analysis under the CIPM MRA. It was undertaken as a "Track A" comparison within the OAWG strategic plan. CCQM-K148.a demonstrates capabilities for assigning the mass fraction content of a solid organic compound having moderate molecular complexity, where the compound has a molar mass in the range (75 - 500) g/mol and is non-polar (pKow < −2), when present as the primary organic component in a neat organic solid and where the mass fraction content of the primary component in the material is in excess of 950 mg/g. Participants were required to report the mass fraction of Bisphenol A present in one supplied unit of the comparison material. Participants using a mass balance method for the assignment were also required to report their assignments of the impurity components present in the material. Methods used by the seventeen participating NMIs or DIs were predominantly based on either stand-alone mass balance (summation of impurities) or qNMR approaches, or the combination of data obtained using both methods. The results obtained using thermal methods based on freezing-point depression methods were also reported by a limited number of participants. There was excellent agreement between assignments obtained using all three approaches to assign the BPA content. The assignment of the values for the mass fraction content of BPA consistent with the KCRV was achieved by most of the comparison participants with an associated relative standard uncertainty in the assigned value in the range (0.1 - 0.5)%. To reach the main text of this paper, click on Final Report. Note that this text is that which appears in Appendix B of the BIPM key comparison database https://www.bipm.org/kcdb/. The final report has been peer-reviewed and approved for publication by the CCQM, according to the provisions of the CIPM Mutual Recognition Arrangement (CIPM MRA).

The concept of the relative sensitivity factors required for the correction of the measured ion beam ratios in pin-cell glow discharge mass spectrometry is examined in detail. We propose a data-driven model for predicting the relative response factors, which relies on a non-linear least squares adjustment and analyte/matrix interchangeability phenomena. The model provides a self-consistent set of response factors for any analyte/matrix combination of any element that appears as either an analyte or matrix in at least one known response factor.

Isotope dilution is among the most accurate quantitation approaches in chemical analysis. This calibration method is often employed using a plurality of mathematical formulations. While most analysts find the calibration curve approach most appealing, there is a lack of rigorous general procedures involving calibration curves in isotope dilution and analysts resort to empirical polynomial calibration functions. In this contribution we discuss the adoption of regression analysis, commonly known as least squares methods, to solve isotope dilution equations of varied complexity. This manuscript introduces general regression-based methods to isotope dilution applicable to all known variants of classical isotope dilution known to date, including the fusion of the isotope dilution and standard additions methods.

We outline a general framework to compute consensus reference values of standard atomic weights, isotope ratios, and isotopic abundances, and to evaluate associated uncertainties using modern statistical methods for consensus building that can handle mutually inconsistent measurement results. The multivariate meta-regression approach presented here is directly relevant to the work of the IUPAC Commission on Isotopic Abundances and atomic weights (CIAAW), and we illustrate the proposed method in meta-analyses of the isotopic abundances and atomic weights of zinc, platinum, antimony, and iridium.

The combination of isotope dilution and mass spectrometry has become an ubiquitous tool of chemical analysis. Often perceived as one of the most accurate methods of chemical analysis, it is not without shortcomings. Current isotope dilution equations are not capable of fully addressing one of the key problems encountered in chemical analysis: the possible effect of sample matrix on measured isotope ratios. The method of standard addition does compensate for the effect of sample matrix by making sure that all measured solutions have identical composition. While it is impossible to attain such condition in traditional isotope dilution, we present equations which allow for matrix-matching between all measured solutions by fusion of isotope dilution and standard addition methods.

ICP-MS has played a key role in inorganic chemical metrology for 25 years, from the 1993 CIPM feasibility study which led to establishment of the CCQM. Since that time, the Inorganic Analysis Working Group of the CCQM has organised 56 international comparisons involving measurements by ICP-MS and, in a recent comparison, 16 different national institutes submitted their results using the technique. Metrological applications of ICP-MS currently address an enormous range of measurements using a wide variety of instrumentation, calibration strategies and methodologies. This review provides an overview of the ICP-MS field with an emphasis on developments which are of particular relevance to chemical metrology. Examples from CCQM comparisons and the services available from the participants are used to illustrate how the capability and scope of ICP-MS methods have expanded far beyond the expectations of 1993. This is due in part to the research and development Programmes of the national institutes which participate in the CCQM. They have played a key role in advancing new instrumentation and applications for elemental analysis, isotope dilution mass spectrometry, determination of isotopic ratio or composition, and speciation of organometallic compounds. These developments are continuing today, as demonstrated by work in new fields such as heteroatom quantitation of proteins, characterisation and counting of nanoparticles using spICP-MS, and LA-ICP-MS analysis of solid materials.

Within the Organic Analysis Working Group (OAWG) of the Comité Consultatif pour la Quantitè de Matiére (CCQM), key comparison CCQM-K141 and associated pilot study CCQM-P178 were coordinated by the National Research Council Canada (NRC). This comparison was a Track A key comparison that formed part of the OAWG 10-year strategic plan. The comparison demonstrated capabilities for measuring high-polarity analytes in a high-fat and high-protein matrix. The measurand chosen as the model system was enrofloxacin and sulfadiazine in bovine tissue. Thirteen National Metrology Institutes or Designated Institutes participated in the CCQM-K141, while two National Metrology Institutes participated in CCQM-P178. The bovine muscle tissue study material was derived from a single live animal that was administered with chemical based pharmaceutical agents prior to processing. Therefore, the study material was naturally incurred, providing a true test of extraction procedures relative to more commonly encountered spiked materials. NRC confirmed excellent homogeneity and stability of the material prior to shipping. Three 10 g bottles of freeze dried powdered muscle tissue were supplied. NRC also provided isotopically labelled solutions of the two measurands, 13C6-sulfadiazine and enrofloxacin-d5 (HI Salt), to those interested in using isotope dilution mass spectrometry (IDMS) methodologies. Procurement and purity assignment with appropriate metrological traceability of native calibrants were the responsibility of individual participants. The study required extraction, clean-up, analytical separation, and selective detection of the analytes. The level of agreement was reasonable given the measurands and matrix were new for most laboratories. The KCRV values and their uncertainties at the 95% confidence level of 57.81 ± 2.57 μg/kg for enrofloxacin and 2285 ± 68 μg/kg for sulfadiazine were calculated using the DSL means. While one participant's value was voluntarily excluded from the KCRV calculations for enrofloxacin, all other participants demonstrated equivalence for both measurands. Significant effort was undertaken post-study to identify the major sources of variability between results. In particular, the various extraction conditions used by participants were investigated thoroughly. While there appeared to be a correlation between highly acidic conditions and higher recovery, this was not definitive and could not be confirmed. The form of standards employed (i.e. free base vs salts) and potential differential solubility between forms was also a suspected source of variability. Biases could also have been introduced with the choice of solvents used for standard preparation, with some solvents better able to minimize adsorption of the analytes to glass surfaces. KEY WORDS FOR SEARCH enrofloxacin, sulfadiazine, bovine tissue, incurred, key comparison Main text To reach the main text of this paper, click on Final Report. Note that this text is that which appears in Appendix B of the BIPM key comparison database kcdb.bipm.org/. The final report has been peer-reviewed and approved for publication by the CCQM, according to the provisions of the CIPM Mutual Recognition Arrangement (CIPM MRA).