Correlation between repeated measurements: bane and boon of the GUM approach to the uncertainty of measurement

With measurement uncertainty estimation accounting for all relevant uncertainty contributions, the results of measurements using the same procedure on different objects or samples may no longer be considered as being independent, and correlations have to be taken into account. For this purpose, a simple approximation for the estimation of covariances is derived and applied to the estimation of uncertainty for some basic combinations of two measurement results. This covariance estimate is also applied to the estimation of uncertainty for the mean value of the results of replicate measurements on the same object or sample.

Exhaust gas analysers and optimised sampling, uncertainties and costs

Decision-making in the conformity assessment of exhaust gas analysers with due account of measurement uncertainty and limited sampling is considered. Risks of incorrect decisions where test results lie in the vicinity of a specification limit are assessed in terms of percentage probability and the costs of measurement and environmental consequences, with examples based on the metrological requirements on these analysers stipulated in the new EU Measurement Instrument Directive. An optimised uncertainty methodology is proposed for the first time in legal metrology based on quantitative testing of new instruments for type approval and initial verification, and gives valuable insight into traditional rules limiting uncertainty in conformity assessment in general. Further, an analysis of subsequent verification of exhaust gas analysers in use in society, leads to a new optimised uncertainty methodology based on attribute sampling.

Metrological traceability: I make it 42; you make it 42; but is it the same 42?

The paper reproduces a talk given at a 2-day symposium on quality assurance in chemistry held in Brisbane, Australia in 2005. Intended for an audience of analysts in the field, the theme of the symposium drew inspiration from the series of books by Douglas Adams “The Hitchhiker's Guide to the Galaxy”. An introduction to basic concepts of metrological traceability is followed by a discussion of practical steps to ensure metrological traceability of field measurement results. The relationship between metrological traceability and comparability of measurement results is discussed. To achieve metrological traceability in the field, the use of appropriate certified reference materials for calibration is recommended. Examples of atmospheric carbon dioxide and roadside breathalyzer measurements are given.

Model-based measurement uncertainty evaluation,with applications in testing

Basic concepts and implementations of the model-based approach to uncertainty evaluation are discussed. One implementation is that of the law of propagation of uncertainty with the use of the central limit theorem as recommended in the Guide to the expression of uncertainty in measurement (GUM). Another is the propagation of distributions, the subject of a supplemental guide to the GUM, which is at an advanced stage of development. It falls in the category of other analytical and numerical methods indicated in the GUM. Two testing applications are used to illustrate the principles: tennis-ball rebound and tensile strength.

Accounting for bias in measurement uncertainty estimation

Generic issues and current approaches in the evaluation of bias studies with respect to estimation of measurement uncertainty are discussed, focusing on two main scenarios. In the first, for a within-laboratory assessment of a fully developed uncertainty budget, bias studies are carried out to verify the pre-established performance of a measurement procedure, and design corrective actions if necessary. In the second scenario, for an estimation of measurement uncertainty from within-laboratory validation data, bias studies are carried out to calibrate the whole measurement procedure and evaluate its performance, more specifically to estimate the uncertainty of measurement by combination of bias and precision estimates.

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Uncertainty from sampling,in the context of fitness for purpose

Sampling is an integral part of nearly all chemical measurement and often makes a substantial or even a dominant contribution to the uncertainty of the measurement result. In contrast with analysis, however, the uncertainty contribution from sampling has usually been ignored. Indeed, far less is known about sampling uncertainty, although in some application sectors it is known to exceed the analytical uncertainty, especially when raw materials (natural or industrial) are under test. In 1995 the authors of this paper proposed a framework of concepts and procedures for studying, quantifying, and controlling the uncertainty arising from the sampling that normally precedes analysis. Many of the ideas were based on analogy with well-established procedures and considerations relating to quality of analytical measurement, ideas such as validation of the sampling protocol, sampling quality control and fitness for purpose. Since that time many of these ideas have been explored experimentally and found to be effective. This paper is a summary of progress to date. Presented at the AOAC Europe Workshop, November 2006, Limassol, Cyprus.

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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 .

The increasing demands of quality assurance in chemical testing

The chemical and microbiological testing community is going through a rather difficult period of change. Publication of ISO/IEC 17025 (General requirements for the competence of Calibration and Testing Laboratories, 1999) [1] is placing additional demands on testing laboratories to ensure traceability and estimate uncertainty in their measurements. At the same time, laboratories must remain mindful of the need to provide relevant, timely and economic services to their clients. International Accreditation New Zealand (IANZ) and its accredited laboratories are currently focussing on establishing realistic methods for ensuring traceability to national and international standards and estimating measurement uncertainty. To this end, IANZ recognizes that it has an important role in providing as much advice and assistance as possible, not only to its accredited chemical laboratories but also to all those contemplating accreditation in New Zealand.

In defence of the correlation coefficient

The relationship between calibrated range, residual standard deviation and correlation coefficient r is discussed. It is shown that in typical chemical calibration applications with appropriately distributed calibration points (particularly, with range comparable to mean and with approximately even or with ‘successive dilution’ spacing), the linear correlation coefficient has valid application as a routine criterion for acceptable fit if used with due care.

The OIML and the purpose of international recommendations

This article was presented to the CITAC workshop in Wellington, New Zealand on 3 May 2004. It explains the role of the Organisation Internationale de Métrologie Legalé (OIML) and work carried out to promote harmonisation in the field of legal metrology—the part of metrology relating to activities which result from statutory requirements and concern measurement, units of measurement, measuring instruments and methods of measurement and which are performed by competent bodies. It also discusses the publications issued to achieve harmonisation. The article also discusses New Zealands recent elevation to full membership of the OIML and the commitment to make the membership work to the benefit of the whole New Zealand measurement industry.

The Australian perspective

This presentation deals with issues of comparability and traceability in food analysis in Australia from several perspectives. This includes the current national (Australian) and increasingly international (Codex) performance-based approach to food analysis. The Australian food regulatory process will be described, particularly those aspects that impact on the analysis of food in a regulatory sense. This section will also describe two areas where specific methods have been mandated in legislation and discuss two case studies where the analytical method has impacted on the elaboration of standards. Other areas to be covered include regulation/requirements relating to supply/availability of reference materials, the use of proficiency testing as a means of ensuring comparability, and, finally, some thoughts on what role BIPM/CCQM may play in the analysis of food.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.

Core-shell structured electrode materials for lithium ion batteries

Recent progress in studies of several types of core-shell structured electrode materials, including TiO₂/C, Si/C, Si/SiO _x , LiCoO₂/C, and LiFePO₄/C nanocomposites, including details of their preparation and their electrochemical performance is briefly reviewed. Results clearly show that the coating shell can effectively prevent the aggregation of the nanosized cores, which are the electrochemically active materials. In addition, the diffusion coefficients of lithium ions can be increased, and the reversibility of lithium intercalation and deintercalation is improved. As a result, the cycling behavior is greatly improved. The reviewed results suggest that core-shell nanocomposites are a good starting point for further development of new promising electrode materials.

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Operating ‘cost’ characteristics in sampling by variable and attribute

A discussion in economic terms of common rules in conformity assessment based on measurement is given. The present work extends tools of sampling when using inspection by variable and attribute, such as the setting of acceptance quality limits (AQL) and limiting quality limits (LQL), by including an economic decision theory approach, leading, amongst other things, to a new ‘cost’ curve as a complement to the traditional operating characteristic curves of statistical significance testing. The methodology is of general applicability but is illustrated in the present work in the simple case of homogeneously pre-packaged goods priced linearly with the amount of content. The relation to the optimised uncertainty methodology is explained. Optimum strategies for the supplier are illustrated in terms of minimising production and testing costs, while at the same time maintaining satisfactory levels of customer satisfaction.

Chemistry,commentary and community: Discussion of “The NaDyBr<Subscript>4</Subscript> complex: its molecular structure and thermodynamic properties” by Varga and Hargittai

The molecular geometries, relative stabilities, binding energies, and dissociation energies of NaDyBr₄ and its molecular ion are discussed. Both the bidentate and tridentate isomers are stable for the neutral species, while only the bidentate form is stable for NaDyBr₄ ⁺.

The use of LCMS as an analytical tool for hydrolysis/polycondensation monitoring of a chiral ORMOSIL precursor

The kinetic of the sol–gel hydrolysis and polycondensation reactions of a chiral ORMOSIL precursor was investigated by LCMS technique as a function of water excess and pH. While the amount of water does not significantly change the kinetics, the reactions strongly depend on the [H]⁺ concentration. At pH ≤ 3, the hydrolysis is very fast and the conversion of the precursor is completed within less than 1 h whereas at 80% of the precursor is still present after 50 h at pH = 3.5. This kinetic study allows to define a set of initial conditions and time ranges required to provide good optical quality dip coated films .

Single-molecule spectroscopy of fluorescent proteins

The discovery and use of fluorescent proteins has revolutionized cellular biology. Despite the widespread use of visible fluorescent proteins as reporters and sensors in cellular environments the versatile photophysics of fluorescent proteins is still subject to intense research. Understanding the details of the photophysics of these reporters is essential for accurate interpretation of the biological and biochemical processes illuminated by fluorescent proteins. Some aspects of the complex photophysics of fluorescent proteins can only be observed and understood at the single-molecule level, which removes averaging inherent to ensemble studies. In this paper we review how single-molecule emission detection has helped understanding of the complex photophysics of fluorescent proteins.

X-ray structural analyses and DFT study of 7-thianorbornenes: 4-aza-4-phenyl-10-thiatricyclo[5.2.1.0.<Superscript>2,6</Superscript>]deca-8-ene-3,5-dione and 4-aza-l,4,7-trimethyl-10-thiatricyclo[5.2.1.0.<Superscript>2,6</Superscript>]deca-8-ene-3,5-dione

X-ray structures of Diels–Alder adducts of thiophene with N-methylmaleimide and 2,5-dimethylthiophene with N-phenylmaleimide were determined and compared to literature data. In addition, quantum chemical calculations at various levels of theory were used to study their molecular and electronic structure. A comparison with experimental results showed that MP2/6-31G^*, HF/6-311+G^** and PBE1PBE/6-31G^* methods give the most accurate structures.

Branched trichain sulfosuccinates as novel water in CO2 dispersants

A series of highly branched trichain sulfosuccinate surfactants have been synthesized and studied in condensed CO₂ and aqueous environments. Aqueous critical micelle concentrations (CMCs) showed a general trend of increasing CMC with decreasing chain length, whereas increased branching appeared to increase solubility in CO₂ and aid the dispersion of water. Near infrared spectra confirmed observed cloud with a large increase in solubility above the cloud pressures in this solvent.