Statistical Measurement Uncertainty Research Articles

A-092 Siemens Healthineers Commitment to Quality - A Focus on Continuous Improvement and Customer Experience

Abstract Background It is necessary that each step of in vitro diagnostic assay development and manufacturing processes be documented and executed in alignment with established quality management systems. Here, we describe how Siemens Healthineers (SHS) maintains assay traceability and focus on continuous improvement using the Atellica® CH A-LYTE® Integrated Multisensor Technology (IMT) assays measuring electrolytes sodium (Na), potassium (K), and chloride (Cl) as a prime example. Methods Establishing an unbroken chain of comparison from the National Institute of Standards and Technology (NIST) higher standard references to the product calibrators ensures accurate value assignment within stated measurement uncertainties. Traceability and standardization are achieved by creating a panel of 10 serum anchor pools spanning the analytical measuring interval for each electrolyte: Na, K, and Cl. The concentrations of the anchor pools are determined at a reference laboratory using methods calibrated with standard solutions derived from NIST reference material. These serum anchor pools are used by SHS, assigning values to product calibrator material which maintains the chain of traceability to the primary reference methods. In addition to traceability, onboard stability for the A-LYTE® IMT multisensor is continuously monitored and evaluated against allowable drift limits for each electrolyte. Although observed drift was within allowable limits, a design change was implemented to improve recovery drift over the use life of the sensor. Results To ensure consistent, robust, and accurate performance of the A-LYTE IMT, a strict set of testing procedures are used to verify the accuracy of value assignments for each manufactured lot of master standards. The recovery of the NIST standard reference material must fall within manufacturer established acceptable bias limits. Consistency over nine master lots is shown with bias ranging from -0.9% to +1.9%, -2.4% to +1.8% and -1.8 to +0.5%, for Na, K and Cl, respectively. By further optimizing the amount of Na ionophore and the polymer matrix of the Na sensor, drift over the use life was minimized and onboard stability improved. Prior to making the sensor change, customer Na QC data at 116 mmol/L showed an SD of 1.1 mmol/L (n=585), whereas the precision improved to an SD of 0.6 mmol/L (n=470) post-optimization. As Manufacturers optimize assay performance, it may become necessary for laboratories to re-evaluate reference intervals for their patient populations. For example, one large integrated delivery network established a new reference interval for patient anion gap (AG). A re-evaluation of the historical AG reference interval which was 5-15 mmol/L identified the need for an update. AG values were calculated from 16,948 healthy patients and used to establish a new reference interval of 2-10 mmol/L. Conclusions Accurate clinical laboratory measurements are critical for diagnosing, monitoring, and treating diseases. A-LYTE assays have an unbroken chain of traceability to NIST reference material and minimal drift over the life of the multisensor. Continuous monitoring to identify improvement projects and rigorous control systems ensure sensor performance over time. This provides confidence that the patient results produced by the laboratory are accurate and consistent over time and across different laboratory locations.

Traceable frequency measurements with counters

Received signals from Global Navigation Satellite Systems (GNSS) are nowadays widely used by industry laboratories for ensuring metrological traceability for their respective range of calibration services in the field of time and frequency. Usually, a local frequency standard is steered by continuous GNSS signal reception providing at its output stable and accurate reference signals for the laboratory measurement equipment, in general for synthesizers and counters. Reception of GNSS signals is surely an adequate and practical tool for the purpose, however further steps are needed to establish traceability in a strict metrological sense. Based on already available guidelines and publications, this paper is a contribution to the discussion how metrological traceability to internationally accepted standards can be established in a calibration laboratory. We restrict the discussion to equipment in common use which may not necessarily be of the highest sophistication. In this spirit, we develop a detailed scheme for an uncertainty budget comprising all links of the traceability chain from the device under test to the SI second, the scale-unit of Coordinated Universal Time. Then we go through and apply this scheme step by step to a demonstration setup for frequency measurements with a counter with varying operational parameters. In this framework, a novel approach to distinguish between components of statistical measurement uncertainty is introduced. Furthermore, the limiting uncertainty contributions are discussed and based on a suitable set of parameters an expression for the best measurement capability is given. With this scheme at hand a user may develop an uncertainty budget adapted to his own setup, especially if acceptance from a national accreditation body is sought.

Concurrent estimation of noise and compact-binary signal parameters in gravitational-wave data

Gravitational-wave parameter estimation for compact binary signals typically relies on sequential estimation of the properties of the detector Gaussian noise and of the binary parameters. This procedure assumes that the noise variance, expressed through its power spectral density, is perfectly known in advance. We assess the impact of this approximation on the estimated parameters by means of an analysis that simultaneously estimates the noise and compact binary parameters, thus allowing us to marginalize over uncertainty in the noise properties. We compare the traditional sequential estimation method and the new full marginalization method using events from the GWTC-3 catalog. We find that the recovered signals and inferred parameters agree to within their statistical measurement uncertainty. At current detector sensitivities, uncertainty about the noise power spectral density is a subdominant effect compared to other sources of uncertainty.

Interlaboratory comparison of voltage sweep methods used for the electrical characterization of encapsulated high‐efficiency c‐Si solar cells

AbstractThis work presents the comparison of measurement results for four types of encapsulated high‐efficiency c‐Si solar cells measured by 10 laboratories based in Asia, Europe and North America utilizing a wide range of voltage sweeping methods, which include well‐established procedures that represent good industry practice, as well as recently introduced ones that have not been verified yet. The aim of the round‐robin interlaboratory comparison was to examine the measurement comparability of different laboratories with respect to their measurement methods of high‐efficiency solar cells. A proficiency test was employed to examine the consistency of results and their corresponding uncertainties. The short‐circuit current (ISC) under STC measured by four accredited laboratories was firstly compared. In order to investigate the consistency related to the high device capacitance, the value of the ISC was fixed for all 10 participants. The results of all participant laboratories—compared via En number analysis—generally remained well within [−1; 1], thus indicating consistency between the measured values and the reference values within stated measurement uncertainties. The differences remained within ±1.15% in PMAX and within ±0.35% in VOC for all participants and methods applied. Correlations were observed among the PMAX, VOC, and FF differences from their weighted mean. An analysis of the effects of transient current (dQ/dt) at maximum power point caused by hysteresis effect on the measurement error of PMAX showed a significant linear correlation between error of maximum power and junction voltage sweep rate for heterojunction (HJT) solar cells. This work forms the basis to validate all applied methods and their stated measurement uncertainties.

Impact of a course transformation on students’ reasoning about measurement uncertainty

Physics lab courses are integral parts of an undergraduate physics education, and offer a variety of opportunities for learning. Many of these opportunities center around a common learning goal in introductory physics lab courses: measurement uncertainty. Accordingly, when the stand-alone introductory lab course at the University of Colorado Boulder (CU) was recently transformed, measurement uncertainty was the focus of a learning goal of that transformation. The Physics Measurement Questionnaire (PMQ), a research-based assessment of student understanding around statistical measurement uncertainty, was used to measure the effectiveness of that transformation. Here, we analyze student responses to the PMQ at the beginning and end of the CU course. We also compare such responses from two semesters: one before and one after the transformation. We present evidence that students in both semesters shifted their reasoning in ways aligned with the measurement uncertainty learning goal. Furthermore, we show that more students in the transformed semester shifted in ways aligned with the learning goal, and that those students tended to communicate their reasoning with greater sophistication than students in the original course. These findings provide evidence that even a traditional lab course can support valuable learning, and that transforming such a course to align with well-defined learning goals can result in even more effective learning experiences.4 MoreReceived 14 August 2020Accepted 19 October 2020DOI:https://doi.org/10.1103/PhysRevPhysEducRes.16.020160Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasAssessmentInstructional strategiesScientific reasoning & problem solvingProfessional TopicsLower undergraduate studentsPhysics Education Research

Toward Comprehensive Industrial Computed Tomography Image Quality Assessment: I. Phantom Design

Abstract When comparing the performance of different industrial X-ray computed tomography (CT) systems, reconstruction algorithms, or scan protocols, it is important to assess how well the required inspection and measurement tasks can be performed. Furthermore, it can be very informative to quantify image quality (IQ) metrics that can provide insight into the IQ characteristics that lead to the resulting inspection or measurement task performance. Inspection and measurement task performance is determined by basic characteristics such as spatial resolution; feature contrast, size, and shape; random noise (noise due to statistical uncertainty in measurements); and image artifacts. In this report, we describe a modular phantom set that enables robustly quantifying these characteristics and also enables assessing the performance of the inspection or measurement tasks themselves. The phantom set includes two phantom bodies and several insert types that can be optionally installed in the bodies. Phantom body extensions can be optionally included to increase scatter. The phantom bodies combined with the available insert types can comprehensively evaluate all important IQ metrics and inspection or measurement tasks. The precisely-known phantom body geometry and insert location, geometry, and orientation supports automatic analysis of large, complex experiments of multiple variables. This phantom set, with the associated image analysis software, could potentially serve as a general evaluation method for non-destructive testing (NDT) CT.

Towards mapping turbulence in the intra-cluster medium

X-ray observations of the hot gas filling the intra-cluster medium (ICM) provide a wealth of information on the dynamics of clusters of galaxies. The global equilibrium of the ICM is believed to be ensured by non-thermal and thermal pressure support sources, among which gas movements and the dissipation of energy through turbulent motions. Accurate mapping of turbulence using X-ray emission lines is challenging due to the lack of spatially resolved spectroscopy. Only future instruments such as the X-ray Integral Field Unit (X-IFU) on Athena will have the spatial and spectral resolution to quantitatively investigate the ICM turbulence over a broad range of spatial scales. Powerful diagnostics for these studies are line shift and the line broadening maps, and the second-order structure function. When estimating these quantities, instruments will be limited by uncertainties of their measurements, and by the sampling variance (also known as cosmic variance) of the observation. Here, we extend the formalism started in our companion Paper I to include the effect of statistical uncertainties of measurements in the estimation of these line diagnostics, in particular for structure functions. We demonstrate that statistics contribute to the total variance through different terms, which depend on the geometry of the detector, the spatial binning and the nature of the turbulent field. These terms are particularly important when probing the small scales of the turbulence. An application of these equations is performed for the X-IFU, using synthetic turbulent velocity maps of a Coma-like cluster. Results are in excellent agreement with the formulas both for the structure function estimation (≤3%) and its variance (≤10%). The expressions derived here and in Paper I are generic, and ensure an estimation of the total errors in any X-ray measurement of turbulent structure functions. They also open the way for optimisations in the upcoming instrumentation and in observational strategies.

Measurement of serum progesterone by isotope dilution liquid chromatography tandem mass spectrometry: a candidate reference method and its application to evaluating immunoassays.

Measurement of serum progesterone is important in determining ovarian function. Most progesterone measurements are performed with immunoassays and results are often variable. Standardization of the measurements requires a reliable reference method. An isotope dilution liquid chromatography tandem mass spectrometry (ID-LC/MS/MS) method for the measurement of serum progesterone was developed. Serum samples were spiked with 13C3-progesterone, extracted with a three-step liquid-liquid extraction, and analyzed by LC/MS/MS. A bracketing calibration was used for the analysis and samples were prepared gravimetrically. The developed method showed intra-run and total relative standard deviations (RSDs) of 0.50~0.58% and 0.71~1.33%, respectively. The analytical recoveries were 99.08~101.50%. Measurement results on certified reference materials obtained with this method agreed with the certified values within the stated measurement uncertainties. The method was applied to evaluate immunoassays through split-sample comparisons. A panel of 48 fresh frozen individual samples were measured with the ID-LC/MS/MS method, and six immunoassays and results were compared. Significant calibration biases and sample-specific deviations were observed on some of the immunoassays.

3D-printing and vibration (including resonance)

The material contained in this paper focuses on using 3D printing of relatively simple, flexible structural components and plane frames. The relatively high resolution of modern 3D printers facilitates the production of slender structures, and thus provides an opportunity to exploit geometric parameter variations to enhance a practical understanding of stiffness and vibration. This approach has proved successful in initial inclusion in both the classroom via demonstration models, as well as in the lab in which elementary facilities can be utilized to acquire data. An especially useful facet of this approach is the assessment and justification for modeling simplifications, e.g., judging the circumstances under which the familiar sway assumption is valid in portal frames. Furthermore, minor parametric variations can be easily incorporated into sensitivity studies, and the production of multiple copies of essentially the same geometry promotes an effective use of statistical measurement uncertainty. We then extend this approach to forced vibration, with examples including the vibrating reed tachometer and sympathetic resonance.The material contained in this paper focuses on using 3D printing of relatively simple, flexible structural components and plane frames. The relatively high resolution of modern 3D printers facilitates the production of slender structures, and thus provides an opportunity to exploit geometric parameter variations to enhance a practical understanding of stiffness and vibration. This approach has proved successful in initial inclusion in both the classroom via demonstration models, as well as in the lab in which elementary facilities can be utilized to acquire data. An especially useful facet of this approach is the assessment and justification for modeling simplifications, e.g., judging the circumstances under which the familiar sway assumption is valid in portal frames. Furthermore, minor parametric variations can be easily incorporated into sensitivity studies, and the production of multiple copies of essentially the same geometry promotes an effective use of statistical measurement uncertainty. We then ...

Methods of statistical analysis in collider experiments by incorporating different types of systematic and statistical uncertainties

A number of statistical analysis techniques are described which meet demands arising in collider experiments in problems of processing the sampled data distributions by including systematic and statistical uncertainties of measurements.

The elephant in the room – A comparative study of uncertainties in carbon offsets

The clean development mechanism (CDM) is a flexible mechanism under the Kyoto Protocol, which makes it possible for developed countries to offset their emissions of greenhouse gases through investing in climate change mitigation projects in developing countries. When the mitigation benefit of a CDM project is quantified, measurable uncertainties arise that can be minimised using established statistical methods. In addition, some unmeasurable uncertainties arise, such as the rebound effect of demand-side energy efficiency projects. Many project types related to land use, land-use change and forestry (LULUCF) have been excluded from the CDM in part because of the high degree of statistical uncertainty in measurements of the carbon sink and risk of non-permanence. However, recent discussions within the United Nations Framework Convention on Climate Change (UNFCCC) have opened up for the possibility of including more LULUCF activities in the future. In the light of this discussion, we highlight different aspects of uncertainties in LULUCF projects (e.g. the risk of non-permanence and the size of the carbon sink) in relation to other CDM project categories such as renewables and demand-side energy efficiency. We quantify the uncertainties, compare the magnitudes of the uncertainties in different project categories and conclude that uncertainties could be just as significant in CDM project categories such as renewables as in LULUCF projects. The CDM is a useful way of including and engaging developing countries in climate change mitigation and could be a good source of financial support for LULUCF mitigation activities. Given their enormous mitigation potential, we argue that additional LULUCF activities should be included in the CDM and other future climate policy instruments. Furthermore, we note that Nationally Appropriate Mitigation Actions (NAMAs) are currently being submitted to the UNFCCC by developing countries. Unfortunately, the under-representation of LULUCF in comparison to its potential is evident in the NAMAs submitted so far, just as it has been in the CDM. Capacity building under the CDM may influence NAMAs and there is a risk of transferring the view on uncertainties to NAMAs.

Interlaboratory comparison in the pressure range from 0 to 2 MPa for accredited calibration laboratories

This paper describes procedure and results of the interlaboratory comparison that was organised by Croatian national pressure laboratory (HMI/FSB-LPM) between eight accredited pressure calibration laboratories. Comparison was performed in the gauge pressure range from 0 to 2 MPa with pressure transducer as transfer standard and using gas as transmitting medium. Basic aim of this comparison was to improve measurement methods and the measurement uncertainties of each participating laboratory. Analysis of the measurement results are given by calculating the deviation, E n , normalized with respect to the stated measurement uncertainties.

Estimate for the doppler shift of a non-Gaussian signal upon coherent detection of scattered optical radiation in a turbulent atmosphere

A non-Gaussian model for estimating the radial velocity of turbulent flows in the atmosphere for coherent detection of scattered optical radiation is proposed. The model was obtained based on a theoretical approach that includes results of the statistical analysis of a pulse Doppler lidar signal in a turbulent medium, as well as on the perturbation-theory methods that have been developed in the theory of probability and mathematical statistics. It is shown that the estimate of the Doppler shift in the first-order perturbation theory is a sum of a regular component and two conditional fluctuation components—Gaussian and non-Gaussian ones. In the case of a homogeneous and isotropic turbulence, the estimate of the radial wind velocity is approximately equal to its true average value. The statistical uncertainty in measurements of the average radial wind velocity is determined by the behavior of conditional Gaussian and non-Gaussian components and significantly depends on the state of atmospheric turbulence. It is shown that basic equations of the non-Gaussian model in the limit case coincide with formulas of the local and nonlocal models, as well as with those of the Gaussian model.

Final charged-lepton angular distribution and possible anomalous top-quark couplings in [formula omitted

Possible anomalous (or nonstandard) top-quark interactions with the gluon and those with the W boson induced by SU(3)×SU(2)×U(1) gauge-invariant dimension-6 effective operators are studied in pp→tt¯X→ℓ+X′ (ℓ=e or μ) at the Large Hadron Collider (LHC). The final charged-lepton (ℓ+) angular distribution is first computed for nonvanishing nonstandard top-gluon and top-W couplings with a cut on its transverse momentum. The optimal-observable procedure is then applied to this distribution in order to estimate the expected statistical uncertainties in measurements of those couplings that contribute to this process in the leading order.

Laser-welded Interconnection of Screen-printed Si Solar Cells

We demonstrate the laser welding of Al interconnects to the BSF rear-side of screen-printed two-side-contacted solar cells. The Al paste on the rear side of solar cell is laser-welded to an Al foil. This reduces the silver consumption of the solar cells by making silver pads on the rear side obsolete. Our proof-of-concept modules are free of laser damage. A 3-cell-module from 6” solar cells shows no change in fill factor within the statistical measurement uncertainty after artificial aging in 500 humidity-freeze cycles.

Investigation of CO, C<sub>2</sub>H<sub>6</sub> and aerosols in a boreal fire plume over eastern Canada during BORTAS 2011 using ground- and satellite-based observations and model simulations

Abstract. We present the results of total column measurements of CO, C2H6 and fine-mode aerosol optical depth (AOD) during the "Quantifying the impact of BOReal forest fires on Tropospheric oxidants over the Atlantic using Aircraft and Satellites" (BORTAS-B) campaign over eastern Canada. Ground-based observations, using Fourier transform spectrometers (FTSs) and sun photometers, were carried out in July and August 2011. These measurements were taken in Halifax, Nova Scotia, which is an ideal location to monitor the outflow of boreal fires from North America, and also in Toronto, Ontario. Measurements of fine-mode AOD enhancements were highly correlated with enhancements in coincident trace gas (CO and C2H6) observations between 19 and 21 July 2011, which is typical for a smoke plume event. In this paper, we focus on the identification of the origin and the transport of this smoke plume. We use back trajectories calculated by the Canadian Meteorological Centre as well as FLEXPART forward trajectories to demonstrate that the enhanced CO, C2H6 and fine-mode AOD seen near Halifax and Toronto originated from forest fires in northwestern Ontario that occurred between 17 and 19 July 2011. In addition, total column measurements of CO from the satellite-borne Infrared Atmospheric Sounding Interferometer (IASI) have been used to trace the smoke plume and to confirm the origin of the CO enhancement. Furthermore, the enhancement ratio – that is, in this case equivalent to the emission ratio (ERC2H6/CO) – was estimated from these ground-based observations. These C2H6 emission results from boreal fires in northwestern Ontario agree well with C2H6 emission measurements from other boreal regions, and are relatively high compared to fires from other geographical regions. The ground-based CO and C2H6 observations were compared with outputs from the 3-D global chemical transport model GEOS-Chem, using the Fire Locating And Modeling of Burning Emissions (FLAMBE) inventory. Agreement within the stated measurement uncertainty (~3% for CO and ~8% for C2H6) was found for the magnitude of the enhancement of the CO and C2H6 total columns between the measured and modelled results. However, there is a small shift in time (of approximately 6 h) of arrival of the plume over Halifax between the results.

Short-range optical air data measurements for aircraft control using rotational Raman backscatter

A first laboratory prototype of a novel concept for a short-range optical air data system for aircraft control and safety was built. The measurement methodology was introduced in [Appl. Opt. 51, 148 (2012)] and is based on techniques known from lidar detecting elastic and Raman backscatter from air. A wide range of flight-critical parameters, such as air temperature, molecular number density and pressure can be measured as well as data on atmospheric particles and humidity can be collected. In this paper, the experimental measurement performance achieved with the first laboratory prototype using 532 nm laser radiation of a pulse energy of 118 mJ is presented. Systematic measurement errors and statistical measurement uncertainties are quantified separately. The typical systematic temperature, density and pressure measurement errors obtained from the mean of 1000 averaged signal pulses are small amounting to < 0.22 K, < 0.36% and < 0.31%, respectively, for measurements at air pressures varying from 200 hPa to 950 hPa but constant air temperature of 298.95 K. The systematic measurement errors at air temperatures varying from 238 K to 308 K but constant air pressure of 946 hPa are even smaller and < 0.05 K, < 0.07% and < 0.06%, respectively. A focus is put on the system performance at different virtual flight altitudes as a function of the laser pulse energy. The virtual flight altitudes are precisely generated with a custom-made atmospheric simulation chamber system. In this context, minimum laser pulse energies and pulse numbers are experimentally determined, which are required using the measurement system, in order to meet measurement error demands for temperature and pressure specified in aviation standards. The aviation error margins limit the allowable temperature errors to 1.5 K for all measurement altitudes and the pressure errors to 0.1% for 0 m and 0.5% for 13000 m. With regard to 100-pulse-averaged temperature measurements, the pulse energy using 532 nm laser radiation has to be larger than 11 mJ (35 mJ), regarding 1-σ (3-σ) uncertainties at all measurement altitudes. For 100-pulse-averaged pressure measurements, the laser pulse energy has to be larger than 95 mJ (355 mJ), respectively. Based on these experimental results, the laser pulse energy requirements are extrapolated to the ultraviolet wavelength region as well, resulting in significantly lower pulse energy demand of 1.5 - 3 mJ (4-10 mJ) and 12-27 mJ (45-110 mJ) for 1-σ (3-σ) 100-pulse-averaged temperature and pressure measurements, respectively.

Probing non-standard top-quark couplings via optimal-observable analyses at LHC

Focusing attention on top-quark pair production and its decay processes at the LHC, non-standard top-quark couplings are studied based on the effective Lagrangian constructed with SU(3)X SU(2)X U(1) invariant dimension-6 operators. The optimal-observable analysis is carried out for the charged-lepton distributions in pp -> t t-bar X -> l^+ X' (l=e or mu) in order to estimate the expected statistical uncertainties in measurements of those non-standard t t-bar g and tbW couplings that contribute to this process in the leading order.

Manufacture and Performance of a 60GHz-Band High-Efficiency Antenna with a Thick Resin Layer and the Feed through a Hole in a Silicon Chip

As a first step towards the realization of high-efficiency on-chip antennas for 60 GHz-band wireless personal area networks, this paper proposes the fabrication of a patch antenna placed on a 200 mu m thick dielectric resin and fed through a hole in a silicon chip. Despite the large tan 5 of the adopted material (0.015 at 50 GHz), the thick resin reduces the conductor loss at the radiating element and a radiation efficiency of 78%, which includes the connecting loss from the bottom is predicted by simulation. This calculated value is verified in the millimeter-wave band by experiments in a reverberation chamber. Six stirrers are installed, one on each wall in the chamber, to create a statistical Rayleigh environment. The manufactured prototype antenna with a test jig demonstrates the radiation efficiency of 75% in the reverberation chamber. This agrees well with the simulated value of 76%, while the statistical measurement uncertainty of our handmade reverberation chamber is calculated as +/- 0.14 dB.

Is “consensus value” a correct term for the product of pooling measurement results?

We often pool measurement results (entry 2.9 in [1]) and expect somehow a more adequate value from such an operation, especially in two cases. In the process leading to a certified reference material, CRM (entry 5.14 in [1]), we frequently pool various measurement results obtained by various measurement procedures (sometimes in various laboratories) expecting to come closer to a more adequate value for embodiment in the CRM than just the one value obtained by one measurement laboratory only. By a more adequate value, we mean a value that makes the CRM into a more reliable tool to assist in calibration or in the search of compensation for systematic effects (entry 2.17 in [1]) in a measurement. In a Proficiency Testing Scheme (one of the various types of Interlaboratory Programme—see description of ILC types in Table 7.2–1 in [2]), we frequently pool various measurement results obtained by possibly various measurement procedures, expecting to establish a more adequate ‘‘reference value’’ (entry 5.18 in [1]) for the Scheme than just the one value obtained by one measurement laboratory only. Again, by more adequate, we mean a value that makes a reference value in a PTS into a more reliable tool to assist in the evaluation of the performance of the PTS participants, that is, of their ‘‘measurement capability’’ (concept 7.3–1 in [2]). Thus, in both cases, we expect that pooling measurement results enables us to come closer to a more adequate value for its intended use. But what is the thinking underlying the pooling of multiple measurement results? There is this overwhelming belief that the greater the number of measurement results we pool, the better the resulting mean value. But, in an ILC with the purpose of arriving at a reliable value for certification, the goal is different from that in a PTS: detecting unknown systematic effects. Let us analyse the application of that thinking a little deeper. First, one would think that the individual measurement results of a set of results obtained by different analysts by definition includes a measurement uncertainty (entry 2.26 in [1]). All of them are intended to assist somehow in the certification of a CRM and therefore ought to be reliable, in principle, within their respective stated measurement uncertainty. One would expect such results to be metrologically compatible (entry 2.47 in [1]) even if obtained through possibly different measurement procedures, reference measurement procedures, or even primary reference measurement procedures (entries 2.6–2.7–2.8 in [1]). One would even expect that these results are metrologically equivalent, that is, that they are ‘‘acceptable for the same specified intended use’’ (concept 5–4 in [2]). The question then arises whether we indeed need multiple results for the same measurand (entry 2.3 in [1]). As they should all be equivalent in the sense of the definition, we could logically conclude that one of these results—with its measurement uncertainty—is sufficient to attribute a trustworthy value to the measurand, thus making the other values superfluous. So, what could be the point of having multiple results? The answer seems to be that these additional—if superfluous— values do offer confirmation of each other, thus making all Disclaimer: The author is a member of the Joint Committee on Guides for Metrology (JCGM), Working Group 2 (VIM). The opinions expressed in this Column do not necessarily represent the view of the Working Group or of ACQUAL.