Interpretation and use of standard atomic weights (IUPAC Technical Report)

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Adriaan M. H. van der Veen ◽  
Juris Meija ◽  
Antonio Possolo ◽  
David Brynn Hibbert
Keyword(s):  
Monte Carlo ◽  
Atomic Weight ◽  
Standard Uncertainty ◽  
Uncertainty In Measurement ◽  
Propagation Of Uncertainty ◽  
A Value ◽  
The Monte Carlo Method ◽  
Technical Report ◽  
Molecular Masses ◽  
Expression Of Uncertainty

Abstract Many calculations for science or trade require the evaluation and propagation of measurement uncertainty. Although relative atomic masses (standard atomic weights) of elements in normal terrestrial materials and chemicals are widely used in science, the uncertainties associated with these values are not well understood. In this technical report, guidelines for the use of standard atomic weights are given. This use involves the derivation of a value and a standard uncertainty from a standard atomic weight, which is explained in accordance with the requirements of the Guide to the Expression of Uncertainty in Measurement. Both the use of standard atomic weights with the law of propagation of uncertainty and the Monte Carlo method are described. Furthermore, methods are provided for calculating uncertainties of relative molecular masses of substances and their mixtures. Methods are also outlined to compute material-specific atomic weights whose associated uncertainty may be smaller than the uncertainty associated with the standard atomic weights.

scholarly journals Getting started with uncertainty evaluation using the Monte Carlo method in R

2021 ◽  
Author(s):  
Adriaan M. H. van der Veen ◽  
Maurice G. Cox
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Measurement Uncertainty ◽  
Daily Practice ◽  
International Standards ◽  
Iso 15189 ◽  
Laboratory Staff ◽  
Uncertainty In Measurement ◽  
Propagation Of Uncertainty ◽  
The Monte Carlo Method

AbstractThe evaluation of measurement uncertainty is often perceived by laboratory staff as complex and quite distant from daily practice. Nevertheless, standards such as ISO/IEC 17025, ISO 15189 and ISO 17034 that specify requirements for laboratories to enable them to demonstrate they operate competently, and are able to generate valid results, require that measurement uncertainty is evaluated and reported. In response to this need, a European project entitled “Advancing measurement uncertainty—comprehensive examples for key international standards” started in July 2018 that aims at developing examples that contribute to a better understanding of what is required and aid in implementing such evaluations in calibration, testing and research. The principle applied in the project is “learning by example”. Past experience with guidance documents such as EA 4/02 and the Eurachem/CITAC guide on measurement uncertainty has shown that for practitioners it is often easier to rework and adapt an existing example than to try to develop something from scratch. This introductory paper describes how the Monte Carlo method of GUM (Guide to the expression of Uncertainty in Measurement) Supplement 1 can be implemented in R, an environment for mathematical and statistical computing. An implementation of the law of propagation of uncertainty is also presented in the same environment, taking advantage of the possibility of evaluating the partial derivatives numerically, so that these do not need to be derived by analytic differentiation. The implementations are shown for the computation of the molar mass of phenol from standard atomic masses and the well-known mass calibration example from EA 4/02.

scholarly journals Coverage Intervals

2021 ◽  
Vol 126 ◽  
Author(s):  
Sara Stoudt ◽  
Adam Pintar ◽  
Antonio Possolo
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Applied Statistics ◽  
Tolerance Intervals ◽  
Uncertainty In Measurement ◽  
The Monte Carlo Method ◽  
Measurement Science ◽  
Credible Intervals ◽  
Expression Of Uncertainty ◽  
Common Misunderstanding

Since coverage intervals are widely used expressions of measurement uncertainty, this contribution reviews coverage intervals as defned in the Guide to the Expression of Uncertainty in Measurement (GUM), and compares them against the principal types of probabilistic intervals that are commonly used in applied statistics and in measurement science. Although formally identical to conventional confdence intervals for means, the GUM interprets coverage intervals more as if they were Bayesian credible intervals, or tolerance intervals. We focus, in particular, on a common misunderstanding about the intervals derived from the results of the Monte Carlo method of the GUM Supplement 1 (GUM-S1), and offer a novel interpretation for these intervals that we believe will foster realistic expectations about what they can deliver, and how and when they can be useful in practice

scholarly journals Análise dos Riscos em Projetos: Uma Aplicação do Método de Monte Carlo em uma Empresa do Setor Moveleiro

2018 ◽  
Vol 10 (2) ◽  
pp. 332-357
Author(s):  
Fernando Rodrigues de Amorim ◽  
Pedro Henrique Camargo de Abreu ◽  
Marco Tulio Ospina Patino ◽  
Leonardo Augusto Amaral Terra
Keyword(s):  
Monte Carlo ◽  
Investment Project ◽  
Modern Society ◽  
Exploratory Research ◽  
Investment Projects ◽  
A Value ◽  
The Monte Carlo Method ◽  
Monte Carlo Em ◽  
A Company

Globalization is a phenomenon that is present in modern society and, with its expansion, it is essential that companies can meet the constant demands of the market, but for this, it is necessary to make the best decisions and deal with various adversities related to the economy, competition, management, among others. The success of investment projects is determined by a set of techniques that must be applied so as not to compromise the viability of the project. When this viability is surrounded by uncertainties, a useful alternative to knowing the risks is the use of the Monte Carlo method. The present work aims to address the risk factors in a company of the furniture sector, using the Monte Carlo simulation to analyze the viability of this project. The methodology adopted was developed from a case study, through an exploratory research. The results showed that the investment project is viable, estimating a return between the 4th and 5th year of the project, in addition, the balance after the 10 years of investment would be around R$ 4,128,211.63, a value that represents 161.25% of the initial investment.

A Simplified Software for Uncertainty Estimation Using Monte Carlo Method

2020 ◽  
Vol 12 (8) ◽  
pp. 1050-1053
Author(s):  
Jasveer Singh ◽  
L. A. Kumaraswamidhas ◽  
Neha Bura ◽  
Kapil Kaushik ◽  
Nita Dilawar Sharma
Keyword(s):  
Monte Carlo ◽  
Standard Deviation ◽  
Monte Carlo Method ◽  
Measurement Uncertainty ◽  
Standard Uncertainty ◽  
Uncertainty Estimation ◽  
End Points ◽  
The Monte Carlo Method ◽  
Adaptive Trials ◽  
Coverage Interval

The current paper discusses about the application of Monte Carlo method for the evaluation of measurement uncertainty using in-house developed program on C++ platform. The Monte Carlo method can be carried out by fixed trials as well as adaptive trials using this program. The program provides the four parameters viz. estimate of measurand, standard uncertainty in the form of standard deviation and end points of coverage interval as an output.

scholarly journals Interpreting and propagating the uncertainty of the standard atomic weights (IUPAC Technical Report)

2018 ◽  
Vol 90 (2) ◽  
pp. 395-424 ◽  
Author(s):  
Antonio Possolo ◽  
Adriaan M. H. van der Veen ◽  
Juris Meija ◽  
D. Brynn Hibbert
Keyword(s):  
Probability Distribution ◽  
Isotopic Composition ◽  
Probability Distributions ◽  
Atomic Weight ◽  
Relative Molecular Mass ◽  
Detailed Knowledge ◽  
Technical Report ◽  
Other Information ◽  
Isotopic Abundances ◽  
Molecular Masses

AbstractIn 2009, the Commission on Isotopic Abundances and Atomic Weights (CIAAW) of the International Union of Pure and Applied Chemistry (IUPAC) introduced the interval notation to express the standard atomic weights of elements whose isotopic composition varies significantly in nature. However, it has become apparent that additional guidance would be helpful on how representative values should be derived from these intervals, and on how the associated uncertainty should be characterized and propagated to cognate quantities, such as relative molecular masses. The assignment of suitable probability distributions to the atomic weight intervals is consistent with the CIAAW’s goal of emphasizing the variability of the atomic weight values in nature. These distributions, however, are not intended to reflect the natural variability of the abundances of the different isotopes in the earth’s crust or in any other environment. Rather, they convey states of knowledge about the elemental composition of “normal” materials generally, or about specific classes of such materials. In the absence of detailed knowledge about the isotopic composition of a material, or when such details may safely be ignored, the probability distribution assigned to the standard atomic weight intervals may be taken as rectangular (or, uniform). This modeling choice is a reasonable and convenient default choice when a representative value of the atomic weight, and associated uncertainty, are needed in calculations involving atomic and relative molecular masses. When information about the provenance of the material, or other information about the isotopic composition needs to be taken into account, then this distribution may be non-uniform. We present several examples of how the probability distribution of an atomic weight or relative molecular mass may be characterized, and also how it may be used to evaluate the associated uncertainty.

scholarly journals The Influence of the Accuracy of Statistical Data on the Results of a Classification of Eu Countries in Terms of Innovation

2020 ◽  
Vol 20 (1) ◽  
pp. 408-420
Author(s):  
Małgorzata Stec
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
European Commission ◽  
Research Methodology ◽  
Statistical Data ◽  
Eu Countries ◽  
A Value ◽  
The Monte Carlo Method ◽  
Diagnostic Variables

AbstractResearch background: The article attempts to include the accuracy of statistical data in a synthetic evaluation and classification of EU countries in terms of innovation.Purpose: The aim of the article is to evaluate an influence of the accuracy of statistical data on a classification of EU countries in terms of innovation.Research methodology: The research employed diagnostic variables determining the innovation of EU countries and a methodology proposed by the European Commission in the European Innovation Scoreboard 2019. The influence of the uncertainty of the measurement of the diagnostic variables on the Summary Innovation Index of EU countries was evaluated. In order to do this, a procedure employing the Monte Carlo method was proposed.Results: Taking into account the uncertainty of the measurement of variables in the evaluation of the innovation of EU countries resulted in qualifying one of the countries to another innovation group.Novelty: The article draws attention to an important but often neglected problem related to the accuracy of statistical data used in research, and the evaluation of their influence on the calculation of a value of synthetic measure (based on the innovation of EU countries).

Assessment of the Uncertainty in the Measurement of Depth of Decarburization of Steel Rail

2012 ◽  
Vol 524-527 ◽  
pp. 1989-1992
Author(s):  
Yi Qiang Sun ◽  
Li Xin Wu ◽  
Zhi Fen Wang ◽  
Ping Zhang
Keyword(s):  
Cross Section ◽  
Standard Uncertainty ◽  
Expanded Uncertainty ◽  
Steel Rail ◽  
Uncertainty In Measurement ◽  
The Cross ◽  
Expression Of Uncertainty

In order to analysis the factors effect the uncertainty in the measurement of depth of decarburization and characterized the dispersity of the measuring results, according to the theory of the uncertainty in measurement and JJF1059-1999 Evaluation and Expression of Uncertainty in Measurement, the uncertainty in the measurement of depth of decarburization of steel rail was assessed, which was caused by the uneven of decarburization and the repetitiveness of the measure, the obliquity of the cross section, the accurate degree of the measure instrument, the approximate of the value. The combined standard uncertainty and the expanded uncertainty was calculated, and the report of the uncertainty was given.

Monte Carlo Analysis as a Tool for Characterizing Uncertainty in Optical Calibration of End Standards

2010 ◽  
Vol 3 ◽  
pp. 18-27
Author(s):  
Niveen Farid
Keyword(s):  
Monte Carlo ◽  
Statistical Analysis ◽  
Conventional Method ◽  
Monte Carlo Analysis ◽  
Uncertainty In Measurement ◽  
M 10 ◽  
Optical Calibration ◽  
Expression Of Uncertainty ◽  
Probability Density Function Pdf ◽  
Good Agreement

In this paper, Monte Carlo method (MCM) is used to analyze the uncertainty of optical calibration of end standards using both contact and non-contact techniques to validate the uncertainty values obtained by the conventional method, Guide to the expression of Uncertainty in Measurement (GUM). Number of trials (M=104) is simulated with the probability density function (pdf) for each quantity, and the comparison between the results of the MCM and the GUM shows good agreement which in turn validates the uncertainty values obtained by the conventional method. The statistical analysis, variables' distributions, and the output of each technique are discussed in detail.

Ein neues Verfahren zur strömungstechnischen Simulation von Gasnetzen

2017 ◽  
Author(s):  
Andreas Hielscher
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Uncertainty In Measurement ◽  
Expression Of Uncertainty

Seit einigen Jahren werden zunehmende Schwankungen der Gasbeschaffenheit, insbesondere des Brennwerts, in Erdgasverteilnetzen beobachtet und damit die korrekte Abrechnung von Endkunden erschwert. In dieser Arbeit wird ein neues Verfahren zur strömungstechnischen Simulation von Erdgasverteilnetzen entwickelt, welches sich auch für instationäre Strömungen eignet. Dieses Verfahren wird zur Brennwertverfolgung eingesetzt und zeichnet sich durch hohe Genauigkeit sowie kurze Rechenzeit aus. Eine Validierung des Rechenmodells erfolgt sowohl auf Basis von Messungen mit Prozessgaschromatografen als auch durch einen Vergleich mit etablierter Simulationssoftware. Zusätzlich wird erstmals eine Unsicherheitsberechnung für die an den Ausspeisestellen des Gasnetzes ermittelten Brennwerte auf Basis einer Monte-Carlo-Simulation nach dem „Guide to the Expression of Uncertainty in Measurement“-Leitfaden durchgeführt. Der Vergleich mit einer Sensitivitätsanalyse bestätigt die Ergebnisse der M...

Determination of Turboprop Reduction Gearbox System Fatigue-Life and Reliability From Computer Generated Tests

2005 ◽  
Author(s):  
Michael Savage ◽  
Erwin V. Zaretsky ◽  
David G. Lewicki
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Fatigue Life ◽  
Field Data ◽  
Computational Models ◽  
A Value ◽  
The Monte Carlo Method ◽  
Life Analysis ◽  
Two Parameter

Two computational models for the fatigue life and reliability of a turboprop gearbox are compared with each other and with field data. The two models are (1) Monte Carlo simulation of randomly selected lives of individual bearings and gears comprising a gearbox and (2) life analysis of the bearings and gears in the gearbox using the two-parameter Weibull distribution and the Lundberg-Palmgren life theory. These results were compared with field life results from 75 gearbox failures. Field data for the gearbox resulted in an L10 life of 2100 hrs. and a Weibull slope of 1.3. The Lundberg-Palmgren method resulted in a calculated L10 life of 1735 hours and a Weibull slope of 1.17. For the life estimation produced by the Monte Carlo method, the median L10 life approached 1775 hours and the Weibull slope approached a value of 1.21. There is reasonably good engineering correlation between the life results obtained from the field data and those predicted from the Lundberg-Palmgren analysis and the Monte Carlo simulation.

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