Maurice Cox

National Physical Laboratory | NPL · Mathematics and Modelling

A statistical testing method is developed to analyse a Regional Metrology Organisation (RMO) key comparison (KC) with linking to the corresponding KC conducted by the International Committee of Weights and Measures (CIPM). We establish a statistical model to which a generalized least-squares method is applied to estimate a linking invariant, ensuri...

The result of a measurement, including the expression of uncertainty in the measurement, should represent a carefully considered opinion based on the metrologist's experience and expertise, as well as on the data and other information sources. This is the position of the Guide to the expression of uncertainty in measurement (GUM), where the require...

Uncertainty assessment is a fundamental step in quantitative magnetic resonance imaging because it makes comparable, in a strict metrological sense, the results of different scans, for example during a longitudinal study. Magnetic resonance-based electric properties tomography (EPT) is a quantitative imaging technique that retrieves, non-invasively...

The medical use of radionuclides depends on the accurate measurement of activity (Bq) for regulatory compliance, patient safety, and effective treatment or image quality. In turn, these measurements rely on the realization of primary standards of activity by national metrology institutes (NMIs), with uncertainties that are fit for purpose. This art...

The GUM suite of documents (Guide to the expression of uncertainty in measurement and related documents) has been expanded with the addition of a new guidance document describing the development and use of measurement models for obtaining a value for the measurand and an associated measurement uncertainty. The methods for estimating the measurand a...

The Guide to the expression of uncertainty in measurement (GUM) has been the enduring guide on measurement uncertainty for metrologists since its first publication in 1993. According to the GUM, a measurement should always be accompanied by a reasoned and defensible expression of uncertainty, and the primary such expression is the standard uncertai...

Following the Guide to the expression of uncertainty in measurement (GUM), the slope and intercept in straight-line regression tasks can be estimated and their uncertainty evaluated by defining a measurement model. Minimizing the weighted total least-squares functional appropriately defines such a model when both regression input quantities (X and...

Comparison of methods for flow measurement in closed conduits based on measurement uncertainty

In this document, the examples illustrate various aspects of uncertainty evaluation and the use of uncertainty statements in conformity assessment. These aspects include, but are not limited to – choice of the mechanism for propagating measurement uncertainty, – reporting measurement results and measurement uncertainty, – conformity assessment, and...

Precipitation measurement has diverse applications in contexts such as hydrology, meteorology and climatology, and is of increasing importance for the assessment of climate change, both as an indicator and as a parameter applied in modelling aiming at the interpretation of climatological phenomena and forecasting. To obtain the quantities of concer...

The main motivation for this research is the growing awareness of the impact of climate change and the increasing relevance of the United Nations Sustainable Development Goals, aiming to contribute to the measurement of quantities like precipitation and rate of rainfall. This knowledge is widely used in hydrology, climatology and meteorology, provi...

Purpose Patient-specific dosimetry is required to ensure the safety of molecular radiotherapy and to predict response. Dosimetry involves several steps, the first of which is the determination of the activity of the radiopharmaceutical taken up by an organ/lesion over time. As uncertainties propagate along each of the subsequent steps (integration...

This set of examples addresses measurements relating to industrial and societal requirements. The examples show improved and alternative treatments of the evaluation of measurement uncertainty, building on current practice in these areas. There is a need in the aerospace industry for calculations relating to quantities that are not directly measura...

This set of examples addresses measurement in healthcare in the following topic areas. The examples show improved and alternative treatments of the evaluation of measurement uncertainty, building on current practice in these areas. A diversity of topics is addressed, such as uncertainty arising in image reconstruction, determination of nanoparticle...

This set of examples pf measurement uncertainty valuation is related to environmental issues in the selected topic areas. The examples show improved and alternative treatments of the evaluation of measurement uncertainty, building on current practice in these areas. A diversity of topics is addressed, ranging from allocation of water resources, rep...

This set of examples addresses the evaluation of measurement uncertainty in relation to assessing conformity to regulation or specification, for example, EU Regulation No 1169/2011 on the provision of food information to consumers or ISO/IEC 17025, General requirements for the competence of testing and calibration laboratories, taking into account...

This set of examples addresses the calculations required in the energy sector in the following topic areas. The examples show improved and alternative treatments of the evaluation of measurement uncertainty, building on current practice in these areas. A diversity of topics is addressed, such as totalisation of fluids (water, natural gas) and energ...

The evaluation of measurement uncertainty is often perceived by laboratory staff as complex and quite distant from daily practice. Nevertheless, standards such as ISO/IEC 17025, ISO 15189 and ISO 17034 that specify requirements for laboratories to enable them to demonstrate they operate competently, and are able to generate valid results, require t...

Calibration examples in this collection relate to pH, mass spectrometry, mass measurement and unstable (drifting) reference materials. A testing example concerns the reaction of a test item to adverse fire conditions. Comparison examples relate to (i) gauge blocks and the underpinning of calibration and measurement capabilities, and (ii) linking of...

Assessment of Specific Absorption Rate (SAR) by using vector-measurement-based systems that measure complex E-field inside a phantom at multiple locations.

The authors of this reply published an article in International Journal of Environmental Research and Public Health and received comments from Douglas and Kuster. Responses are made to these comments with complementary explanations and numerical results.

On the 27th of November 2015, at 10:43:45.526 UTC, a fireball was observed across South Australia by ten Desert Fireball Network observatories lasting 6.1 s. A $\sim37$ kg meteoroid entered the atmosphere with a speed of 13.68$\pm0.09\,\mbox{km s}^{-1}$ and was observed ablating from a height of 85 km down to 18 km, having slowed to 3.28$\pm0.21 \,...

Human exposure to mobile devices is traditionally measured by a system in which the human body (or head) is modelled by a phantom and the energy absorbed from the device is estimated based on the electric fields measured with a single probe. Such a system suffers from low efficiency due to repeated volumetric scanning within the phantom needed to c...

Human exposure to mobile devices is traditionally measured by a system in which the human body (or head) is modelled by a phantom and the energy absorbed from the device is estimated based on the electric fields measured with a single probe. Such a system suffers from low efficiency due to repeated volumetric scanning within the phantom needed to c...

According to the CIPM mutual recognition arrangement, a calibration and measurement capability (CMC) uncertainty for a laboratory offering a particular calibration or measurement service is normally expressed at a 95 % level of confidence. When laboratories’ CMC claims are unsupported by the relevant key comparison (KC), after publishing the final...

The Earth is impacted by 35–40 metre-scale objects every year. These meteoroids are the low-mass end of impactors that can do damage on the ground. Despite this they are very poorly surveyed and characterized, too infrequent for ground-based fireball observation efforts, and too small to be efficiently detected by NEO telescopic surveys whilst stil...

A framework is proposed for modelling the uncertainty in the measurement processes constituting the dosimetry chain that are involved in internal absorbed dose calculations. The starting point is the basic model for absorbed dose in a site of interest as the product of the cumulated activity and a dose factor. In turn, the cumulated activity is giv...

Data analysis of a regional metrology organization (RMO) when linked to an International Committee of Weights and Measures key comparison (KCs) is discussed. One of the purposes of an RMO KC is to check the appropriateness of participants' results from a statistical point of view. For this purpose, a statistical test is useful. In this study, we di...

It is generally acknowledged that calibration of the imaging system (be it a SPECT or a PET scanner) is one of the critical components associated with in vivo activity quantification in nuclear medicine. The system calibration is generally performed through the acquisition of a source with a known amount of radioactivity. The decay-corrected calibr...

Fundamental and thematic climate data records derived from satellite observations provide unique information for climate monitoring and research. Since any satellite operates over a limited period of time only, creating a climate data record requires the combination of space-born measurements from a series of several (often similar) satellites. Sim...

A criticism levelled at the Guide to the Expression of Uncertainty in Measurement (GUM) is that it is based on a mixture of frequentist and Bayesian thinking. In particular, the GUM's Type A (statistical) uncertainty evaluations are frequentist, whereas the Type B evaluations, using state-of-knowledge distributions, are Bayesian. In contrast, makin...

The eutectic alloys rhenium-carbon, platinum-carbon and cobalt-carbon have been proposed as reference standards for thermometry, with temperature and uncertainty values specified within the mise en pratique of the definition of the kelvin. These alloys have been investigated in a collaboration of eleven national measurement institutes and laborator...

The contents of the current edition, JCGM 100:2008, of the Guide to the Expression of Uncertainty in Measurement (GUM) and its Supplements are reviewed and remarks made concerning a proposed revision of the GUM. A committee draft of the revision was circulated to member organizations of the Joint Committee for Guides in Metrology (JCGM) and all nat...

Introduction: Murrili (pronounced moo-RRil-y) is the 3 rd meteorite recovered by the Desert Fireball Network (for details of the fall and orbit see [1]). It fell as a single, heart-shaped, 1.68 kg stone, measuring ~13 × 7 × 6 cm, and was entirely fusion crusted. Two small wedges and a thin slab were cut from the main mass for examination and analys...

Introduction: Beginning in 1959, a dozen projects – professional and amateur – have pursued the goal of recovering meteorites with known orbits (e.g. [1]). This combined effort yielded 10 meteorites. Although the numbers are small, even this handful generated fundamental insights: the early work provided the proof that meteorites come from the aste...

Introduction: The Murrili meteorite fell in the Kati Thanda – Lake Eyre South region of South Australia (29.26089 o S, 137.53765 o E) on 27 Nov. 2015, after being imaged and located by the Desert Fireball Network. This meteorite fell as a single stone of mass 1.68 kg. Petrography and a description of the fall and recovery are detailed elsewhere [1,...

The thermodynamic temperature of the point of inflection of the melting transition of Re-C, Pt-C and Co-C eutectics has been determined to be 2747.84 ± 0.35 K, 2011.43 ± 0.18 K and 1597.39 ± 0.13 K, respectively, and the thermodynamic temperature of the freezing transition of Cu has been determined to be 1357.80 ± 0.08 K, where the ± symbol represe...

Over the last years 177Lu has received considerable attention from the clinical nuclear medicine community thanks to its wide range of applications in molecular radiotherapy, especially in peptide-receptor radionuclide therapy (PRRT). In addition to short-range beta particles, 177Lu emits low energy gamma radiation of 113 keV and 208 keV that allow...

A computer model of a patient-specific clinical (177)Lu-DOTATATE therapy dosimetry system is constructed and used for investigating the variability of renal absorbed dose and biologically effective dose (BED) estimates. As patient models, three anthropomorphic computer phantoms coupled to a pharmacokinetic model of (177)Lu-DOTATATE are used. Aspect...

International Standard ISO 7730:2005 defines thermal comfort as that condition of mind that expresses the degree of satisfaction with the thermal environment. Although this definition is inevitably subjective, the Standard gives formulae for two thermal comfort indices, predicted mean vote (PMV) and predicted percentage dissatisfied (PPD). The PMV...

The therapeutic effect from molecular radiation therapy (MRT), on both tumour and normal tissue, is determined by the radiation absorbed dose. Recent research indicates that as a consequence of biological variation across patients the absorbed dose can vary, for the same administered activity, by as much as two orders of magnitude. The internationa...

The ‘Guide to the Expression of Uncertainty in Measurement’ (GUM) provides a framework and procedure for evaluating and expressing measurement uncertainty. The procedure has two main limitations. Firstly, the way a coverage interval is constructed to contain values of the measurand with a stipulated coverage probability is approximate. Secondly, in...

This paper is directed at practitioners seeking a degree of assurance in the quality of the results of an uncertainty evaluation when using the procedure in the Guide to the Expression of Uncertainty in Measurement (GUM) (JCGM 100 : 2008). Such assurance is required in adhering to general standards such as International Standard ISO/IEC 17025 or ot...

As a result of the complex nature of operating multi-station national air quality networks it is rare that complete data sets are produced from these networks. The reliance of most air quality legislation on the assessment of measured annual average concentrations against target or limit concentrations necessitates the use of methods to calculate a...

The 'Guide to the Expression of Uncertainty in Measurement' (GUM) requires that the way a measurement uncertainty is expressed should be transferable. It should be possible to use directly the uncertainty evaluated for one measurement as a component in evaluating the uncertainty for another measurement that depends on the first. Although the method...

Circular dichroism (CD) spectroscopy of proteins is widely used to measure protein secondary structure, and to detect changes in secondary and higher orders of structure, for applications in research and in the quality control of protein products such as biopharmaceuticals. However, objective comparison of spectra is challenging because of a limite...

The European Metrology Research Programme (EMRP) is currently funding project EMRP- NEW04 on novel mathematical and statistical approaches to uncertainty evaluation. One focus of the project is uncertainty evaluation in the context of regression and parametric inverse problems. The development of methods for such problems will be carried out in clo...

The consequences of missing data during air quality monitoring activities and the calculation of the annual average mass concentration of ambient pollutants are discussed. Possible strategies for mitigating totally and partially missing data during given measurement periods are presented and evaluated. A mathematical description of a preferred meth...

Antonio Possolo shares his views on the assessment and expression of measurement uncertainty. He treats a diverse selection of example problems, including a simple measurement function, an inter-laboratory comparison, a regression problem, and an unconventional measurement in the form of a map and the pooling of expert knowledge. These examples giv...

The Joint Committee for Guides in Metrology, Working Group 1, JCGM-WG1, is currently revising the 'Guide to the Expression of Uncertainty in Measurement'. In this communication, the motivation for undertaking such a revision is given and the main changes with respect to the current, 2008 edition are outlined.

The concern is with key comparisons for which the participating laboratories provide measured data at each of a number of prescribed values of an auxiliary parameter, such as wavelength or frequency. Key comparison reference curves provide a continuous counterpart of the key comparison reference values (KCRVs) currently determined independently fro...

The number of Monte Carlo trials in the application of Supplement 1 to the GUM (GUM S1) can be determined automatically with the help of adaptive Monte Carlo schemes. Such schemes aim at achieving for a chosen confidence level a prescribed numerical accuracy in the results obtained. Recently we proposed a two-stage adaptive scheme and demonstrated...

Supplement 2 to the GUM is concerned with multivariate measurement models, i.e., models having any number of output quantities. The Supplement describes two approaches – a generalisation of the GUM uncertainty framework and the use of a Monte Carlo method – as implementations of the propagation of distributions, and extends the concept of coverage...

Numerical quantification of the results from a measurement uncertainty computation is considered in terms of the inputs to that computation. The primary output is often an approximation to the PDF (probability density function) for the univariate or multivariate measurand (the quantity intended to be measured). All results of interest can be derive...

October 1999A discussion of approaches for determining a reference value in the analysis of key-comparison data*

Radiology for human health diagnosis is an important field for metrological research in ionizing radiation since it combines metrological analysis with improvement in health care quality. Diagnostic radiology methods require radiation detectors for quality control of X-ray radiation qualities, with the measurement procedure and the parameters to be...

The bandpass of spectrometers can cause appreciable errors when making radiometric measurements. This paper describes a practical method for correcting a set of equispaced measured values provided by a spectrometer with a finite bandwidth, an arbitrary bandpass function and at an arbitrary wavelength step. The paper reviews the limits of the approa...

Monitoring of a cancer patient, following initial administration of a drug, provides a time sequence of measured response values constituting the level in serum of the relevant enzyme activity. The ability to model such clinical data in a rigorous way leads to (a) an improved understanding of the biological processes involved in drug uptake, (b) a...

Quantitative evidence that global temperature is rising is provided by three data sets, produced independently, of monthly global average temperature at a resolution of several hundred kilometres. Less well known is how climate is changing on a relatively short time scale in different regions on the surface of the globe, a vital concern because of...

The evaluation of measurement uncertainty, in certain fields of science, faces the problem of scarcity of data. This is certainly the case in the testing of geological soils in civil engineering, where tests can take several days or weeks and where the same sample is not available for further testing, being destroyed during the experiment. In this...

A method for the evaluation of international comparison results is demonstrated by consideration of the CCL-K2 key comparison of long gauge block calibration. CCL-K2 is selected for this illustrative example because the comparison measurand is a geometrically simple case of the gauge block central length, and challenging measurement issues often en...

Adaptive Monte Carlo schemes can be used to determine the number of Monte Carlo trials (the number of evaluations of the measurement model) necessary for the evaluation of uncertainty according to Supplement 1 to the GUM (GUM S1). The goal is to reach a prescribed numerical accuracy of the Monte Carlo results (the estimate, associated standard unce...