Beyond the GUM: variance-based sensitivity analysis in metrology

This paper focuses on the application of the variance-based global sensitivity analysis for a topological derivative method in order to solve a stochastic nonlinear time-dependent magnetoquasi-static interface problem. To illustrate the approach a permanent magnet (PM) synchronous machine has been considered. Our key objective is to provide a robust design of the rotor poles and of the tooth base in a stator for the reduction of the torque ripple and electromagnetic losses, while taking material uncertainties into account. Input variations of material parameters are modeled using the polynomial chaos expansion technique, which is incorporated into the stochastic collocation method in order to provide a response surface model. Additionally, we can benefit from the variance-based sensitivity analysis. This allows us to reduce the dimensionality of the stochastic optimization problems, described by the random-dependent cost functional. Finally, to validate our approach, we provide the 2-D simulations and analysis, which confirm the usefulness of the proposed method and yield a novel topology of a PM synchronous machine.

Modeling green recycled aggregate concrete using machine learning and variance-based sensitivity analysis

A fuzzy approach for the expression of uncertainty in measurement

The debate comparing the benefits of measurement uncertainty (uncertainty in measurement, MU) with total error (TE) for the assessment of laboratory performance continues. The summary recently provided in this journal by members of the Task and Finish Group on Total Error (TFG-TE) of the EFLM put the arguments into clear perspective. Even though there is generally strong support for TE in many laboratories, some of the arguments proposed for its on-going support require further comment. In a recent opinion which focused directly on the TFG-TE summary, several potentially confusing statements regarding ISO15189 and the Evaluation of measurement data - Guide to the expression of uncertainty in measurement (GUM) were again promulgated to promote TE methods for assessing uncertainty in laboratory measurement. In this opinion, we present an alternative view of the key issues and outline our views with regard to the relationship between ISO15189, uncertainty in measurement and the GUM.

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 uncertainty. In this article, we distinguish between the use of an expression of uncertainty as information for the recipient of a measurement result and its use when propagating uncertainty about inputs to a measurement model in order to derive the uncertainty in a measurand. We propose a new measure of uncertainty, the characteristic uncertainty, and argue that it is more fit for these purposes than standard uncertainty. For the purpose of reporting a measurement result, we demonstrate that standard uncertainty does not have a meaningful interpretation for the recipient of a measurement result and can be infinite. These deficiencies are resolved by the characteristic uncertainty, which we therefore recommend for use in reporting. For similar reasons, we advocate the use of the median estimate as the measured value. For the purpose of propagating uncertainty in a measurement model, we propose simple propagation of the median and characteristic uncertainty and show through some examples that this characteristic uncertainty framework is simpler and at least as reliable and accurate as the propagation of estimate, standard uncertainty and effective degrees of freedom according to the GUM uncertainty framework.

Modeling a production scale milk drying process: parameter estimation, uncertainty and sensitivity analysis

This paper discusses a fiducial approach for constructing uncertainty intervals for the distance between k normal means and the origin. When k = 2 this distance is equivalent to the magnitude of a complex-valued quantity. A simulation study was conducted to assess the frequentist performance of the proposed fiducial intervals and to compare their performance with the methods from the Guide to the Expression of Uncertainty in Measurement and from Supplement 1 to the ‘Guide to the Expression of Uncertainty in Measurement’—Propagation of Distributions using a Monte Carlo Method. Our results indicate that the fiducial intervals generally outperform the GUM and GUM Supplement 1 methods with respect to frequentist coverage probabilities. Computer programs for calculating the fiducial intervals, written using open-source software, are listed.

Identifying key sources of uncertainty in the modelling of greenhouse gas emissions from wastewater treatment

The determination of the uncertainty of the result of a measurement is presently attained by means of a statistical inference, as suggested by the IEC-ISO Guide to the Expression of Uncertainty in Measurements. This approach has been proved to be not totally viable when the result of the measurement comes from a complex elaboration of the input signals. The paper proposes the application of the fuzzy variables and mathematics to the determination of the uncertainty, since they appear to be able to describe the possible distribution of the results of a measurement in a more effective way than the statistical approach. The fundamentals of the employed mathematics are recalled, and applied to the determination of the uncertainty in power measurements. The results obtained by the proposed method are compared with those obtained experimentally.

Traditional error analysis to estimate the uncertainties in experimental measurements and predictions has given way during the last two decades to uncertainty analysis. The current methodology is described in the GUM (Guide to the Expression of Uncertainty in Measurement) issued by ISO. The reasoning behind the change was the recognition that one could never know the true value of a measurement and thus the error could not be determined. As promulgated, the uncertainties are represented in statistical terms based upon sampling (classical statistics) and upon subjective reasoning (Bayesian). The approach combines these uncertainties in the usual error analysis approach of summing the variances (now labeled the ‘Law of Propagation of Uncertainties’) and then using the student-t distribution to attach some meaning to the result. The correct procedure is to apply the Bayesian approach throughout, but many investigators have heard only that Bayesian inference is computationally expensive and question the idea of subjective probability and resort to using the Law of Propagation of Uncertainties. This short note treats the common problem of the uncertainty of a measurement using a calibrated device. It compares the two methods, reminding the reader of what the GUM calls for and assumes, and showing that with our current computing power there is no good reason to avoid Bayesian inference to provide more exact and informative understandings of measurement uncertainties.

The aim of the Guide to Expression of Uncertainty in Measurement (GUM) is to harmonize the different practices for estimating and reporting uncertainty of measurement. Although there are clear advantages in having a common approach for evaluating uncertainty, application of the GUM approach to chemistry measurements is not straightforward. In the above commentary, Krouwer suggests that the GUM approach should not be applied to diagnostic assays, because (a) the quality of diagnostic assays is to low, and (b) the GUM uncertainty intervals are too narrow to predict the outliers that occasionally trouble these methods. Some of the examples presented by Krouwer are reviewed. Sodium measurements are modeled mathematically to illustrate the GUM approach to uncertainty. A standardized uncertainty evaluation process is presented. Modeling of sodium measurements demonstrates how the GUM uncertainty interval reflects the treatment of a bias: The width of the uncertainty interval varied depending on whether a correction for a calibrator lot bias was applied, but in both cases it was consistent with the distribution of measurement results. Expanding the uncertainty interval to include outliers runs counter to the definition of uncertainty. Used appropriately, the GUM uncertainty can be helpful in detecting outliers. In standardizing the uncertainty evaluation, the importance of the analytical imprecision and traceability was emphasized. It is problematic that manufacturers of commercial assays rarely inform about the uncertainty of the values assigned to the calibrators. As demonstrated by an example, external quality-assurance data may be used to estimate this uncertainty. The GUM uncertainty should be applied to measurements in laboratory medicine because it may actually support the forces that drive the work on improving the quality of measurement procedures. However, it is important that the GUM approach is made more manageable by standardizing the uncertainty evaluation procedure as much as possible. It is essential to focus on the traceability and uncertainty of calibrators and reagents supplied by manufacturers of assays. Information about uncertainty is necessary in the evaluation of the uncertainty associated with manufacturers' measurement procedures, and in general it may force manufacturers to increase their efforts in improving the metrologic and analytical quality of their products.

As an independent scientific discipline, metrology needs its own terminological dictionary. Beginning from 1984, ISO has published three editions of the International Vocabulary of Metrology (VIM). The first such dictionary – “International Vocabulary of Basic and General Terms in Metrology” appeared in 1984. In 1993 came out the second edition of this document, and in 2007 the third (and current) edition. All three editions were prepared under the auspices of BIPM. The third edition has a new name – “International Vocabulary of Metrology – Basic and General Concepts and Associated Terms (VIM)” [1] – in order to stress the fundamental differences from the prior editions. The new VIM indeed differs significantly from the previous ones. Instead of the traditional philosophical foundations of metrology the new VIM adopts the philosophy of the “Guide to the Expression of Uncertainty in Measurement (GUM)” – the document prepared under the auspices of BIPM and published by ISO in 1995 [2]. This philosophy was named in VIM the “uncertainty approach”.

Principles of the expression of uncertainty in measurements are briefly reviewed and special aspects of the uncertainty quantification in NAA are discussed in detail regarding the relative and k0-standardization in both modes of the technique, i.e., INAA and RNAA. A survey of uncertainty sources is presented and calculation of the combined uncertainty is demonstrated by an example of manganese determination in biological material by RNAA.

The Guide to the Expression of Uncertainty in Measurement (GUM) provides instructions for constructing uncertainty intervals for a measurement. This method is usually reserved for reference materials, but GUM has been recently proposed as a way to express uncertainty for commercial diagnostic assays. Using the official GUM standard and published applications of GUM to commercial diagnostic assays, I undertook an analysis to evaluate whether applying GUM to commercial diagnostic assays is warranted. Certain important assays, such as troponin I, would not be candidates for GUM because troponin I is not a well-defined physical quantity. Unlike definitive methods, in which efforts are taken to detect and eliminate all systematic error sources, commercial assays often trade off features such as ease of use and cost with accuracy and allow systematic errors to be present as long as the overall accuracy meets the medical need goal. Laboratories are hindered in preparing GUM models because the knowledge required to specify some systematic errors is often available only to manufacturers. Some non-GUM methods to estimate uncertainty rely on observed data, which include both known and unknown sources of error. The occurrence of large, unknown errors for assays in routine use (e.g., outliers) is not unusual because diagnostic assays must be chemically specific in the presence of thousands of potentially interfering substances. There is no provision in GUM to deal with unexplained outliers, which may lead to uncertainty intervals that are not wide enough. Some clinicians assume that diagnostic assay results have little uncertainty. This situation may be made worse by including an uncertainty interval, which implies certification. Evaluations for accuracy (total analytical error) based on describing the distribution of result differences between commercial assays and reference methods indicate that some assays have a few results with large differences (e.g., outliers). This leads to a wide accuracy interval (total analytical error limits). It is unlikely that GUM would be able to predict these wide intervals, especially because there is little or no provision for outlier treatment in GUM. Presenting too narrow GUM uncertainty intervals to clinicians would be misleading. The modeling used by practitioners of the GUM method is potentially useful in improving quality, but commercial diagnostic assays are not ready for GUM uncertainty statements.

The “Guide to the expression of uncertainty in measurement” (GUM) is an extremely important document. It unifies methods for calculating measurement uncertainty and enables the consistent interpretation and comparison of measurement results, regardless of who obtained these measurements and where they were obtained. Since the document was published in 1995, it has been realised that its recommendations do not properly address an important class of measurements, namely, non-linear indirect measurements. This drawback prompted the initiation of the revision of the GUM in the Working Group 1 of the Joint Committee for Guides in Metrology, which commenced in October 2006. The upcoming revision of the GUM provides the metrological community with an opportunity to improve this important document, in particular, to reflect developments in metrology that have occurred since the first GUM publication in 1995. Thus, a discussion of the directions for this revision is important and timely. By identifying several shortcomings of the GUM and proposing directions for its improvement, we hope this article will contribute to this discussion.