Table of contents

Classically the non-parametric coverage interval is estimated by empirical quantiles. We introduce an alternative way for estimating the coverage interval by symmetric quantiles given by Chen and Chiang (1996 J. Nonparametric Stat.7 171–85). We further show that this alternative has a better precision in the sense that its asymptotic variances are smaller than the classical one.

A procedure is presented to evaluate the uncertainty of integrals computed from an approximate function that interpolates a set of measured data. The procedure, a Monte Carlo-based uncertainty propagation technique, yields the integral uncertainty taking into account the uncertainties associated with the involved experimental data. As expected, we found that the uncertainty of the integral strongly depends on the error sources affecting the ordinates. As an example, we assessed the uncertainty of the so-called UV index, evaluated by integrating in the range 250 nm to 400 nm the biologically weighted spectral ultraviolet irradiance. The presented procedure agrees with international recommendations and is valid independently of the experimental technique from which data are obtained.

Methods for reducing reflectance losses at multiple wavelengths with a silicon photodiode detector are described. Using thick oxide layer and Brewster-angle operation it is shown that specular reflectance losses can be theoretically decreased below 1 ppm (part per million) in a simple measurement arrangement. Additionally, a detector structure is presented which can be used to reduce the measurement uncertainties due to diffuse reflectance below 1 ppm, even if the total diffuse reflectance losses from a plain photodiode would be two orders of magnitude larger.

High purity tin samples were doped with Fe, Sb, Pb, In and Al. These impurities shifted the run-off point of the melting curve of tin by −0.75 mK (ppm wt)⁻¹, +0.23 mK (ppm wt)⁻¹, −0.16 mK (ppm wt)⁻¹, −0.21 mK (ppm wt)⁻¹ and −2.3 mK (ppm wt)⁻¹, respectively (ppm wt denoted the mass fraction in parts million). However, 1654 ppm wt of Fe and 12.2 ppm wt of Al concentrations appear to supersaturate tin. The extra amount of these impurities then gradually precipitated as the doped samples were subjected to repeat melting.

In the 10 ppm wt Fe to about 970 ppm wt Fe concentration range tin has a solid–liquid phase transformation of very narrow melting range, 6.9 mK below the tin-point.

A simple method of evaluating the measurement capability of a practical Fizeau-type flatness measurement machine is proposed. In this method, by measuring only the peak-to-valley (PV) value of a calibrated test flat, the measurement capability of the flatness measurement machine for the PV value is evaluated while maintaining the traceability of the measurement. A simple approximate equation for estimating the measurement capability of the flatness measurement machine is presented.

By applying the Algos timescale algorithm to a worldwide ensemble of clocks, the BIPM calculates the offset of UTC from the UTC realization of each participating laboratory. Given the uncertainties and correlations of the time-transfer links between the laboratories, one can evaluate the resultant uncertainties and correlations of the offsets. This paper gives an improved and simplified method for carrying out these evaluations.

Since the 1980s, GPS time links have been essential to the TAI computation and, until 2006, the Common View (CV) technique has been used for this purpose. Recent advances in obtaining precise satellite orbits and clock parameters now permit us to obtain better results using another technique, which we name All in View (AV). By comparing the GPS CV and AV with the independent and more accurate TW and PPP time transfer techniques, we quantify the gain that can be obtained on a given time link. The AV technique also allows us to choose a more efficient network of GPS links between the tens of laboratories participating in TAI, which further improves the uncertainty in the access to UTC. The BIPM TAI software has been updated and the AV technique has been effectively used since the computation for the month of September 2006.

A constant pressure gas flowmeter using a directly driven diaphragm bellows as a volume displacer was studied. This flowmeter is perfectly vacuum-sealed, does not contain elastomers and liquids that would prevent outgassing at elevated temperatures and can achieve a smaller ratio of the final volume to the displaced volume than when bellows are used, so that the uncertainty in generating small flow rates can be small. As, when a bellows is used in the volume displacer, the displaced volume cannot be calculated from the geometric dimensions and its dependence on the displacement is non-linear, a sensitive method had to be developed for measuring this dependence. The uncertainty in measuring the displaced volume by this method and the achieved uncertainty of the flowmeter were determined.

General theory for uncertainty propagations of atomic weight measurement results is presented and the impact of correlation of input variables (isotope ratios and correction factors) on the overall atomic weight uncertainty is discussed. Currently all uncertainty propagations use equations that are fitted for uncorrelated isotope ratios and uncorrelated mass bias correction factors. It is shown here that the correlation of isotope ratios is significant in TIMS and multi-collector ICPMS measurements and ignoring these correlations can lead to significant underestimation of the uncertainty of atomic weight measurement results. Atomic weight uncertainties are inconsistent with reported isotope ratio uncertainties in numerous recent reports as a result of improper uncertainty propagation.

An internally consistent procedure of uncertainty analysis will give the same results no matter how the calculations are legitimately rearranged. This paper identifies an apparent internal inconsistency arising with the full procedure described in the Guide to the Expression of Uncertainty in Measurement. The phenomenon occurs when the measurand is expressible as a function of quantities with common sources, and is related to the calculation of an effective number of degrees of freedom. One common situation in which this inconsistency arises is where a point on a line is measured using estimates of the intercept and slope derived from the same dataset; the numbers of degrees of freedom obtained differ according to whether this point is measured directly from the dataset or from the estimates of the intercept and slope. An example is given where the widths of the corresponding expanded uncertainty intervals differ by a factor of approximately 2. Statistical principles explaining this issue are discussed, and a principle for the calculation of an effective number of degrees of freedom is proposed.

A cryogenic dual compensated calorimeter was constructed for energy loss measurements in superconducting materials. The losses induced by slowly varying periodic magnetic fields (amplitudes <50 mT) in field-generating coils fabricated from different niobium wires were at the level of 500 nJ/cycle. Measurable losses are caused by incomplete Meissner effect in tested superconducting materials. The results of the study show the difficulties and limitations in the implementation of the kilogram standard using the 'superconducting magnetic levitation mass' method.

Melting/freezing curves are studied for the single-component Ga and bimetallic eutectic alloys Ga–In, Ga–Sn, Ga–Zn and Ga–Al in small-size cells. These phase-transition studies were conducted at VNIIOFI and SDL in order to design small-size fixed-point devices for metrological monitoring of temperature sensors on autonomous platforms. Our prime objective is to develop technology to improve the long-term performance of in-flight blackbody calibration sources of space-borne radiometers. The repeatability of the melting temperature of Ga and the eutectic melting temperatures of Ga–In, Ga–Sn and Ga–Zn fixed points were studied. Our results show that small cells containing Ga and some Ga-based eutectic alloys can be used as melting fixed-point standards.

The optical low-coherence reflectometer (OLCR) is a very powerful tool to characterize optical fibres and integrated optical components. However, this is a very complex set-up and in addition to that it performs Fourier transforms. Evaluating uncertainty in these conditions becomes very complicated. To overcome this difficulty, we chose to use an alternative statistical method as partly described in the ISO5725 standard. The most significant quantities which can be extracted from the OLCR measurements are length and chromatic dispersion (CD) of the optical component. An uncertainty of 0.036 mm (k = 2) for the length and of 0.12 ps nm⁻¹ km⁻¹ (k = 2) for the CD can be achieved for a 1 m long G652 type fibre.

Conventional Johnson noise thermometers based on switching correlators have conflicting matching requirements for the sensing resistance. To mitigate distortion effects in the correlator, the RT products of the two sensors must be the same, and to mitigate frequency-response errors in nominally identical input circuits, the two sensing resistances should be the same. A noise thermometer using synthetic noise for the primary reference signal overcomes this conflict because the output voltage and output resistance are independent. This paper presents the rationale and design constraints for a noise thermometer using a synthetic-noise source based on Josephson junctions. The quantized voltage noise source developed at NIST produces tunable waveforms with a spectral density composed of a comb of frequencies of equal amplitude and random phase. In addition to the conventional noise-power and impedance constraints, it has additional constraints relating to the number of tones and the tone spacing.

The quantum metrology triangle is a test of the consistency of three quantum electrical standards: the single-electron tunnelling current standard, the Josephson voltage standard and the quantum Hall resistance standard. This paper considers what is known about each of these effects separately in terms of (1) theory, (2) empirical tests of universality and (3) 'direct' tests involving fundamental constants. The current status of each of the three 'legs' of the triangle is quite different, with the single-electron leg being the weakest by far. This leads to the conclusion that a recent experimental result for the triangle should be interpreted primarily in terms of corrections to the quantum of charge transferred by single-electron devices.

We have examined the influence of surface stress in the measurement of the (2 2 0) lattice plane spacing of a Si crystal by combined x-ray and optical interferometry. By means of a finite element simulation we have obtained first a quantitative description of various non-linear displacement fields of the diffracting planes; the simulation indicates that surface stress does not cause a significant difference between bulk and surface lattice spacing. Subsequently, to quantify the effect of the above fields on the period of the interference fringes, we have solved numerically the perturbed Takagi–Taupin equations; these results indicate that the fringe period is determined by the atom spacing on the crystal entrance surface, whereas, intuitively, we might have expected this period to be a kind of average of the (2 2 0) lattice plane spacing. To corroborate our numerical calculations, we have found analytical expressions which allow us to isolate the contribution of the non-linear superficial terms on the measurement of the plane spacing.

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Equation (10) in this paper contains two errors. Incorrect summation boundaries and referenced constants were quoted, and the first constant had the negative sign omitted. The corrected equation is . where t is the temperature (°C) and the constants are given below: .