The Comité international des poids et mesures (CIPM) has projected a major revision of the International System of Units (SI) in which all of the base units will be defined by fixing the values of fundamental constants of nature. In preparation for this we have carried out a new, low-uncertainty determination of the Boltzmann constant, k B , in terms of which the SI unit of temperature, the kelvin, can be re-defined. We have evaluated k B from exceptionally accurate measurements of the speed of sound in argon gas which can be related directly to the mean molecular kinetic energy, 3 2 k B T . Our new estimate is k B = 1.380 651 56 (98) × 10 −23 J K −1 with a relative standard uncertainty u R = 0.71 × 10 −6 .

A number of Joint Committees of the Bureau International des Poids et Mesures and other international organizations carry out particular tasks of common interest. The Joint Committee for Guides in Metrology (JCGM) has amongst its tasks the promotion of the 'Guide to the Expression of Uncertainty in Measurement' (GUM), the preparation of further documents for its broad application, and revision and promotion of the use of the 'International Vocabulary of Basic and General Terms in Metrology'. This paper summarizes the documents relating to the GUM planned by JCGM.

The CCPR K1-a key comparison of spectral irradiance (from 250 nm to 2500 nm) was carried out to meet the requirements of the Mutual Recognition Arrangement by 13 participating national metrology institutes (NMIs). Because of the fragile nature of the tungsten halogen lamps used as comparison artefacts, the comparison was arranged as a star comparison with three lamps per participant. NPL (United Kingdom) piloted the comparison and, by measuring all lamps, provided a link between participants' measurements. The other participants were BNM–INM (France), CENAM (Mexico), CSIRO (Australia), HUT (Finland), IFA–CSIC (Spain), MSL–IRL (New Zealand), NIM (China), NIST (United States of America), NMIJ (Japan), NRC (Canada), PTB (Germany) and VNIIOFI (Russian Federation).Before the analysis was completed and the results known, the pilot discussed with each participant which lamp measurements should be included as representative of their comparison. As a consequence of this check, at least one measurement was excluded from one third of the lamps because of changes due to transportations. The comparison thus highlighted the difficulty regarding the availability of suitable transfer standards for the dissemination of spectral irradiance. The use of multiple lamps and multiple measurements ensured sufficient redundancy that all participants were adequately represented. In addition, during this pre-draft A phase all participants had the opportunity to review the uncertainty budgets and methods of all other participants. This new process helped to ensure that all submitted results and their associated uncertainties were evaluated in a consistent manner.The comparison was analysed using a model-based method which regarded each lamp as having a stable spectral irradiance and the measurements made by an NMI as systematically influenced by a factor that applies to all that NMI's measurements. The aim of the analysis was to estimate the systematic factor for each NMI.Across the spectral region (250 nm to 2500 nm) there were 44 wavelengths at which a comparison was made. These were treated entirely independently and thus the report describes 44 comparisons. For wavelengths from 250 nm to 800 nm (apart from 300 nm) all participants had unilateral degrees of equivalence (DoEs) with values consistent with their uncertainties for a coverage level k = 2. At all other wavelengths (apart from 1400 nm) all participants achieved consistency at the k = 4 level for the unilateral DoEs and the vast majority within k = 3.The results are a significant improvement over those of the previous comparison in 1990, especially considering that the declared uncertainties of most participants have been substantially improved over the intervening decade. These results are evidence of the value of the effort devoted to the development of improved spectral scales (and of the evaluation of their uncertainty) by many NMIs in recent years.Main text. To reach the main text of this paper, click on Final Report. Note that this text is that which appears in Append...

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The determination of a best-fit calibration curve that describes the response of a measuring system to the value of a standard is one of the most widely used procedures in metrology. The mathematical basis for a generalized least-squares solution to this problem is reviewed. Examples of the application of a software implementation of the method are presented to illustrate the treatment of calibration problems with different uncertainty structures for the calibration data, including correlated data. The examples concern the calibration of analysers to measure the composition of natural gas and the calibration of a gas flow dilutor.

Using exceptionally accurate measurements of the speed of sound in argon, we have made estimates of the difference between thermodynamic temperature, T, and the temperature estimated using the International Temperature Scale of 1990, T90, in the range 118 K to 303 K. Thermodynamic temperature was estimated using the technique of relative primary acoustic thermometry in the NPL-Cranfield combined microwave and acoustic resonator. Our values of (T-T90) agree well with most recent estimates, but because we have taken data at closely spaced temperature intervals, the data reveal previously unseen detail. Most strikingly, we see undulations in (T-T90) below 273.16 K, and the discontinuity in the slope of (T-T90) at 273.16 K appears to have the opposite sign to that previously reported.

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, insufficient guidance is given for the multivariate case in which there is more than one measurand. In order to address these limitations, two specific guidance documents (or ‘Supplements to the GUM’) on, respectively, a Monte Carlo method for uncertainty evaluation (Supplement 1) and extensions to any number of measurands (Supplement 2) have been published. A further document on developing and using measurement models in the context of uncertainty evaluation (Supplement 3) is also planned, but not considered in this paper. An overview is given of these guidance documents. In particular, a Monte Carlo method, which is the focus of Supplements 1 and 2, is described as a numerical approach to implement the ‘propagation of distributions’ formulated using the ‘change of variables formula’. Although applying a Monte Carlo method is conceptually straightforward, some of the practical aspects of using the method are considered, such as the choice of the number of trials and ensuring an implementation is memory-efficient. General comments about the implications of using the method in measurement and calibration services, such as the need to achieve transferability of measurement results, are made.

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 uncertainty and coverage interval endpoints) for a chosen confidence level. It is shown that simple sequential adaptive Monte Carlo schemes may not perform well in this regard and an alternative method based on a two-stage procedure due to Stein is proposed. The implementation of this two-stage scheme for GUM S1 is described, and its performance and robustness are demonstrated in terms of simulation results.