Relative Combined Uncertainty Research Articles

Viscosity and Dew Point Measurements of {xCH4 + (1 – x)C4H10} for x = 0.9484 with a Vibrating-Wire Viscometer

The viscosity of {xCH4 + (1 – x)C4H10} with x = 0.9484 has been measured at temperatures and pressures in the range (200 to 423) K and (2 to 30) MPa, respectively, corresponding to densities between (20 and 371) kg·m–3. The measurements were made using a vibrating-wire-viscometer with the wire clamped at both ends and operated in steady-state mode with a combined relative uncertainty of 1 %. The viscometer was also used to investigate the ability of a vibrating-wire instrument to determine the upper and lower dew pressures of the mixture in the retrograde region at (263 and 273) K. The dew pressures were determined by identifying the point along an isothermal pathway at which the slope of the wire’s resonance half-width with pressure exhibited a discontinuity. At the upper dew pressures near 10 MPa the results were consistent to within 0.2 MPa of predictions made using the GERG-2008 equation of state (EOS), while at the lower dew pressures near 3 MPa the agreement was within 0.3 MPa. To facilitate future ...

Direct measurement of electron beam quality conversion factors using water calorimetry.

In this work, the authors describe an electron sealed water calorimeter (ESWcal) designed to directly measure absorbed dose to water in clinical electron beams and its use to derive electron beam quality conversion factors for two ionization chamber types. A functioning calorimeter prototype was constructed in-house and used to obtain reproducible measurements in clinical accelerator-based 6, 9, 12, 16, and 20 MeV electron beams. Corrections for the radiation field perturbation due to the presence of the glass calorimeter vessel were calculated using Monte Carlo (MC) simulations. The conductive heat transfer due to dose gradients and nonwater materials was also accounted for using a commercial finite element method software package. The relative combined standard uncertainty on the ESWcal dose was estimated to be 0.50% for the 9-20 MeV beams and 1.00% for the 6 MeV beam, demonstrating that the development of a water calorimeter-based standard for electron beams over such a wide range of clinically relevant energies is feasible. The largest contributor to the uncertainty was the positioning (Type A, 0.10%-0.40%) and its influence on the perturbation correction (Type B, 0.10%-0.60%). As a preliminary validation, measurements performed with the ESWcal in a 6 MV photon beam were directly compared to results derived from the National Research Council of Canada (NRC) photon beam standard water calorimeter. These two independent devices were shown to agree well within the 0.43% combined relative uncertainty of the ESWcal for this beam type and quality. Absorbed dose electron beam quality conversion factors were measured using the ESWcal for the Exradin A12 and PTW Roos ionization chambers. The photon-electron conversion factor, kecal, for the A12 was also experimentally determined. Nonstatistically significant differences of up to 0.7% were found when compared to the calculation-based factors listed in the AAPM's TG-51 protocol. General agreement between the relative electron energy dependence of the PTW Roos data measured in this work and a recent MC-based study are also shown. This is the first time that water calorimetry has been successfully used to measure electron beam quality conversion factors for energies as low as 6 MeV (R50=2.25 cm).

Measurement of phthalates diesters in food using gas chromatography–tandem mass spectrometry

An analytical strategy dedicated to 4 major phthalate diesters (DiBP, DnBP, BBzP and DEHP) monitoring in food items has been developed and validated according to normalized guidelines. The method has been applied to a wide range of foodstuffs (n=54) to generate first-ever occurrence data at the French level. This method involves separation and detection using gas chromatography coupled to tandem mass spectrometry, in electron ionisation with highly specific selected reaction monitoring, quantification being performed according to the isotope dilution principle. A particular attention has been paid to background contamination management at any stage of the analytical process, from the sampling to the expression of the results. Limits of reporting, defined as statistically different from background contamination, were found to be 2.7, 0.53, 0.18 and 3.4μgkg−1, and relative combined uncertainties were finally found to be 7.6%, 12.2%, 12.0% and 14.1%, for DiBP, DnBP, BBzP and DEHP, respectively.

Accuracy of dose planning for prostate radiotherapy in the presence of metallic implants evaluated by electron spin resonance dosimetry.

Radiotherapy is one of the main approaches to cure prostate cancer, and its success depends on the accuracy of dose planning. A complicating factor is the presence of a metallic prosthesis in the femur and pelvis, which is becoming more common in elderly populations. The goal of this work was to perform dose measurements to check the accuracy of radiotherapy treatment planning under these complicated conditions. To accomplish this, a scale phantom of an adult pelvic region was used with alanine dosimeters inserted in the prostate region. This phantom was irradiated according to the planned treatment under the following three conditions: with two metallic prostheses in the region of the femur head, with only one prosthesis, and without any prostheses. The combined relative standard uncertainty of dose measurement by electron spin resonance (ESR)/alanine was 5.05%, whereas the combined relative standard uncertainty of the applied dose was 3.35%, resulting in a combined relative standard uncertainty of the whole process of 6.06%. The ESR dosimetry indicated that there was no difference (P>0.05, ANOVA) in dosage between the planned dose and treatments. The results are in the range of the planned dose, within the combined relative uncertainty, demonstrating that the treatment-planning system compensates for the effects caused by the presence of femur and hip metal prostheses.

Absolute distance measurement by dual-comb interferometry with multi-channel digital lock-in phase detection

We present a dual-comb-based heterodyne multi-wavelength absolute interferometer capable of long distance measurements. The phase information of the various comb modes is extracted in parallel by a multi-channel digital lock-in phase detection scheme. Several synthetic wavelengths of the same order are constructed and the corresponding phases are averaged to deduce the absolute lengths with significantly reduced uncertainty. Comparison experiments with an incremental HeNe reference interferometer show a combined relative measurement uncertainty of 5.3 × 10−7 at a measurement distance of 20 m. Combining the advantage of synthetic wavelength interferometry and dual-comb interferometry, our compact and simple approach provides sufficient precision for many industrial applications.

The multi-position calibration of the stiffness for atomic-force microscope cantilevers based on vibration

Calibration of the stiffness of atomic force microscope (AFM) cantilevers is critical for industry and academic research. The multi-position calibration method for AFM cantilevers based on vibration is investigated. The position providing minimum uncertainty is deduced. The validity of the multi-position approach is shown via theoretical and experimental means. We applied it to the recently developed vibration method using an AFM cantilever with a normal stiffness of 0.1 N m−1. The standard deviation of the measured stiffness is 0.002 N m−1 with a mean value of 0.189 N m−1 and the relative combined uncertainty is approximately 7%, which is better than the approach using the single position at the tip of the cantilever.

Theoretical constraints on the precision and age range of rehydroxylation dating.

Accurate and precise dating methods are of central importance to archaeology, palaeontology and earth science. This paper investigates the expected precision and age range of rehydroxylation dating, a recently proposed technique for fired clays. An expression for combined measurement uncertainty is presented, which takes into account all significant sources of experimental uncertainty. Numerical simulations are performed for comparison. Combined measurement uncertainties of approximately 5% with respect to the age of the ceramic should be possible given well-designed experiments. In this case, the most significant contribution to combined measurement uncertainty is from effective lifetime temperature. In addition, it is shown that precision should be acceptable for recently fired material (less than 1 year). Mismatch of balance resolution to sample mass results in large variation in combined relative uncertainties, which vary by four orders of magnitude (approx. 1–1160%) across recent experimental studies, rendering some recently reported dates meaningless. It is recommended that this ratio be less than 10−6 for a combined relative uncertainty of less than 1%. The age limits of the technique are set by the value of the rate constant and individual sample mineralogy. This theoretical framework should help future interlaboratory comparison as well as optimizing instrument design.

Uncertainty evaluation of the diffusive gradients in thin films technique.

Although the analytical performance of the diffusive gradients in thin films (DGT) technique is well investigated, there is no systematic analysis of the DGT measurement uncertainty and its sources. In this study we determine the uncertainties of bulk DGT measurements (not considering labile complexes) and of DGT-based chemical imaging using laser ablation - inductively coupled plasma mass spectrometry. We show that under well-controlled experimental conditions the relative combined uncertainties of bulk DGT measurements are ∼10% at a confidence interval of 95%. While several factors considerably contribute to the uncertainty of bulk DGT, the uncertainty of DGT LA-ICP-MS mainly depends on the signal variability of the ablation analysis. The combined uncertainties determined in this study support the use of DGT as a monitoring instrument. It is expected that the analytical requirements of legal frameworks, for example, the EU Drinking Water Directive, are met by DGT sampling.

Validation and Uncertainty of the method for multiresidue analysis of 35 pesticides in melon using Gas Chromatography Coupled to Quadrupole Mass Spectrometry (GC-QP/MS)

QuEChERS method and detection in GC/SQ-MS were validated for the analysis of 35 pesticides in melon. Validation parameters (selectivity, linearity, LOD, LOQ, accuracy and precision) were determined according ABNT NBR 14029:2005. The recoveries rates for all the pesticides studied were from 63% to 117% with relative standard deviation (RSD) lower than 15% in the concentration range of 0.05 – 0.20 mg/kg. The limit of quantification (LOQ) for most compounds were below the MRLs established in Brazil. The combined relative uncertainty (Uc) and expanded uncertainty (Ue) was determined using repetitivity, recovery and calibration curves data for each pesticide.

Multi-channel absolute distance measurement system with sub ppm-accuracy and 20 m range using frequency scanning interferometry and gas absorption cells.

We present an implementation of an absolute distance measurement system which uses frequency scanning interferometry (FSI). The technique, referred to as dynamic FSI, uses two frequency scanning lasers, a gas absorption cell and a reference interferometer to determine the unknown optical path length difference (OPD) of one or many measurement interferometers. The gas absorption cell is the length reference for the measurement system and is traceable to international standards through knowledge of the frequencies of its absorption features. The OPD of the measurement interferometers can vary during the measurement and the variation is measured at the sampling rate of the system (2.77 MHz in the system described here). The system is shown to measure distances from 0.2 m to 20 m with a combined relative uncertainty of 0.41 × 10⁻⁶ at the two sigma level (k = 2). It will be shown that within a scan the change in OPD of the measurement interferometer can be determined to a resolution of 40 nm.

Line strength and collisional broadening coefficients of H2O at 2.7 μm for natural gas quality assurance applications

We employed tunable diode laser absorption spectroscopy to measure the line strength, the methane (CH4), ethane (C2H6) and the propane (C3H8) broadening coefficients for the 523–422 H2O transition at 3619.61 cm−1. Water amount fractions generated by a stable and accurate humidity transfer standard, traceable to the SI units via the German national humidity standard, were used to calibrate the spectroscopic line strength measurements. We focus on the traceability of the measured line data to the SI and on uncertainty assessments following the guidelines of the Guide to the Expression of Uncertainty in Measurement. We determined the line strength to be (8.42 ± 0.07)×10−20 cm−1/(cm−2 molecule) corresponding to a relative uncertainty of ±0.8%. To the best of our knowledge, we report the first methane, ethane and propane broadening coefficients of (8.037 ± 0.056)×10−5 cm−1/hPa, (9.077 ± 0.064)×10−5 cm−1/hPa and (10.469 ± 0.073)×10−5 cm−1/hPa for the 523–422 H2O transition at 3619.61 cm−1, respectively. The relative combined uncertainties of the stated CH4, C2H6 and C3H8 broadening coefficients are in the ±0.7% range.

Analysis of 11-nor-9-carboxy-Δ9-tetrahydrocannabinol in urine samples by hollow fiber-liquid phase microextraction and gas chromatography–mass spectrometry in consideration of measurement uncertainty

Marijuana abuse can be detected by means of toxicological analysis of the most important metabolite 11-nor-9-carboxy-Δ9-tetrahydrocannabinol (THC-COOH) in urine samples. The aim of this study is the establishment of the detailed procedure for analysis of THC-COOH in urine by combination of hollow fiber-liquid phase microextraction (HF-LPME) and gas chromatography–mass spectrometry (GC–MS). The conditions of hydrolysis and extraction were optimized. The method was shown to be very simple and rapid, and a low amount of organic solvent was necessary for extraction. The limit of detection was 1.5 ng/ml. The calibration curves were linear over the specified range (2.0–170 ng/ml; r 2 > 0.99). The main sources of uncertainty were found to be analyte concentration, accuracy, method precision and sample volume. The effect of the analyte concentration on the overall combined uncertainty was most significant. The developed method was successfully applied to a human urine standard reference material at two levels of concentration. The obtained relative combined uncertainty was 8 %, which can be considered acceptable according to international guidelines. The present method seems very useful in clinical and forensic toxicology, because of its simplicity, rapidness and inexpensiveness.

Optical Path Length Calibration: A Standard Approach for Use in Absorption Cell-Based IR-Spectrometric Gas Analysis

We employed a comparison method to determine the optical path length of gas cells which can be used in spectroscopic setup based on laser absorption spectroscopy or FTIR. The method is based on absorption spectroscopy itself. A reference gas cell, whose length is a priori known and desirably traceable to the international system of units (SI), and a gas mixture are used to calibrate the path length of a cell under test. By comparing spectra derived from pressure-dependent measurements on the two cells, the path length of the gas cell under test is determined. The method relies neither on the knowledge of the gas concentration nor on the line strength parameter of the probed transition which is very rarely traceable to the SI and of which the uncertainty is often relatively large. The method is flexible such that any infrared light source and infrared active molecule with isolated lines can be used. We elaborate on the method, substantiate the method by reporting results of this calibration procedure applied to multipass and single pass gas cells of lengths from 0.38 m to 21 m, and compare this to other methods. The relative combined uncertainty of the path length results determined using the comparison method was found to be in the ±0.4% range.

Assessment of AERONET-OC LWN uncertainties

This study presents a detailed analysis of the uncertainties affecting the normalized water-leaving radiance (LWN) from above-water measurements performed within the context of the Ocean Colour component of the Aerosol Robotic Network (AERONET-OC). The analysis, conducted in agreement with the ‘Guide to the Expression of Uncertainty in Measurement’ (GUM), indicates uncertainties of LWN markedly dependent on the optical properties of seawater for a number of AERONET-OC sites located in different marine regions. Results obtained for the Adriatic Sea site, characterized by a large variety of measurement conditions, confirm previous uncertainties from an independent study indicating median values of relative combined uncertainties of 5% in the blue–green part of the spectrum and of approximately 7% in the red. Additional investigations show that the former uncertainties can be reduced by ∼1% when restricting the determination of AERONET-OC LWN to measurements performed at low sun zenith angle and low aerosol optical thickness.

Determination of Metals in Olive Oil by Electrothermal Atomic Absorption Spectrometry: Validation and Uncertainty Measurements

The determination of trace metals in organic matrices is still highly demanding despite improvements in analytical instrumentation. The present study was undertaken in order to evaluate electrothermal atomic absorption spectrometry for the determination of cadmium, copper, iron, lead, and nickel in olive oil. A variety of approaches were used. The most suitable digestion procedure was heating the samples at 300°C for 24 hours and ashing in a muffle furnace at 450°C for 16 hours. The validation data were detection limits of 0.2–153 ng g−1; mean trueness on certified reference materials of 81–94%; mean recovery on spikes of 90–120%; and repeatability of 12–53%. The combined relative uncertainty was 0.298–0.766. Oils processed by pressing had higher copper, iron, and lead concentrations than oils processed by centrifugation. The reported method provides an efficient way for monitoring trace metal content during olive oil production.

Estimation of uncertainty in the determination of nitrogen and oxygen in U(Al, Si)3

U(Al, Si)3, an inter-metallic compound, is a proposed fuel in advanced nuclear reactors. Determination of trace amounts of nitrogen and oxygen in this material is an essential requirement for quality assurance. Mass fraction of nitrogen and oxygen were determined in this compound employing inert gas fusion in conjunction with thermal conductivity and infrared detection techniques, respectively. Uncertainty in the measured data has been estimated employing bottom-up approach as per ISO guidelines. Uncertainty in the calibration of the measurement procedure employing standards with own uncertainty of the measurement was estimated following linear regression equation and uncertainty propagation laws. The relative combined uncertainty of measurement has been calculated employing law of uncertainty propagation. Finally, the expanded uncertainty of measurement (coverage factor k = 2) for the determination of nitrogen and oxygen was estimated, and they were found to be 10 and 12 %, respectively.

Direct comparison of two NIST PJVS systems at 10 V

Two NIST programmable Josephson voltage standard (PJVS) systems are directly compared at 10 V using different nanovoltmeters. These PJVS systems use arrays of triple-stacked superconducting niobium Josephson junctions with barriers made of niobium silicide. Compared with the voltages produced by Josephson voltage standards based on hysteretic junctions, PJVS systems using damped junctions produce predictable voltage levels. However, in order to guarantee the quantization of the voltages and to minimize the errors at the room-temperature voltage output, additional precautions are required. We report several experimental results of voltage measurements that contain significant systematic errors. The generated voltages appear reproducible but they are, in fact, inaccurate. When proper measurement procedures are followed, the results of a direct comparison using an analogue detector show that the two independent PJVS systems agree within 2.6 parts in 1011 at 10 V with a relative total combined uncertainty of 3.4 parts in 1011 (k = 1). Investigations show that the largest systematic error and most significant contribution to the uncertainty budget is caused by the leakage resistance of each PJVS to ground. This paper describes a measurement procedure to characterize this leakage resistance and one approach to including the resulting voltage error in the uncertainty budget.

Evaluation of measurement uncertainty in EA–IRMS: for determination of δ 13C value and C-4 plant sugar content in adulterated honey

In this study, the method for determining the stable carbon isotope ratio value was validated. Measurement uncertainty of stable carbon isotope ratio value of whole honey and its extracted protein derived from repeatability, reference gas, reference standards and calibration curve was calculated by applying the “bottom-up” approach according to Eurachem/CITAC guide. The expanded uncertainties for all results ranged from 0.14 to 0.19 ‰, with most of them between 0.15 and 0.16 ‰ (the coverage factor k = 2, the level of confidence p is approximately 95 %). The percentage contribution of each source to the relative combined uncertainty was calculated. The data indicated that calibration curves have more contribution to the relative combined uncertainty than repeatability and reference standards. On the other hand, the measurement uncertainty of C-4 sugar content in honey was estimated. Based on these results, 58 honey samples, such as acacia, chaste, Northeast China black bee, flowers and jujube honey, have been gathered to determine the C-4 plant sugar content adulteration in honey by elemental analyzer with an isotope ratio mass spectrometer. It can be found that all honey samples were not adulterated by C-4 plant sugar.

Flat Frequency Response in the Electronic Measurement of Boltzmann's Constant

A new quantum-voltage-calibrated Johnson noise thermometer was developed at the National Institute of Metrology to demonstrate the electrical approach that determines Boltzmann's constant <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> , by comparing electrical and thermal noise power. A measurement with an integration period of 19 h and a bandwidth of 638 kHz results in a relative offset of 1 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-6</sup> , from the current Committee on Data for Science and Technology value of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> , and a type A relative standard uncertainty of 17 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-6</sup> . Closely matched noise powers and transmission-line impedances were achieved, and consequently, the quadratic fitting parameters of the ratio spectrum show flat frequency responses with respect to the measurement bandwidth. This flat response produces a dramatically reduced systematic error compared to that of the National Institute of Standards and Technology measurement of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> , in which the relative combined uncertainty was dominated by this error.

Evaluation of an analytical methodology using QuEChERS and GC-SQ/MS for the investigation of the level of pesticide residues in Brazilian melons

A multiresidue method based on the sample preparation by modified QuEChERS and detection by gas chromatography coupled to single quadruple mass spectrometers (GC-SQ/MS) was used for the analysis of 35 multiclass pesticides in melons (Cucumis melo inodorus) produced in Ceara-Brazil. The rates of recovery for pesticides studied were satisfactory (except for the etridiazole), ranging from 85% to 117% with a relative standard deviation (RSD) of less than 15%, at concentrations between 0.05 and 0.20mgkg−1. The limit of quantification (LOQ) for most compounds was below the MRLs established in Brazil. The combined relative uncertainty (Uc) and expanded uncertainty (Ue) was determined using repeatability, recovery and calibration curves data for each pesticide. Analysis of commercial melons samples revealed the presence of pesticides bifenthrin and imazalil at levels below the MRLs established by ANVISA, EU and USEPA.