Measurement Uncertainty And Probability
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Measurement Uncertainty And Probability
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Author : Robin Willink
language : en
Publisher: Cambridge University Press
Release Date : 2013-02-14
Measurement Uncertainty And Probability written by Robin Willink and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-02-14 with Science categories.
A measurement result is incomplete without a statement of its 'uncertainty' or 'margin of error'. But what does this statement actually tell us? By examining the practical meaning of probability, this book discusses what is meant by a '95 percent interval of measurement uncertainty', and how such an interval can be calculated. The book argues that the concept of an unknown 'target value' is essential if probability is to be used as a tool for evaluating measurement uncertainty. It uses statistical concepts, such as a conditional confidence interval, to present 'extended' classical methods for evaluating measurement uncertainty. The use of the Monte Carlo principle for the simulation of experiments is described. Useful for researchers and graduate students, the book also discusses other philosophies relating to the evaluation of measurement uncertainty. It employs clear notation and language to avoid the confusion that exists in this controversial field of science.
Uncertainty Calibration And Probability
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Author : C.F Dietrich
language : en
Publisher: Routledge
Release Date : 2017-07-12
Uncertainty Calibration And Probability written by C.F Dietrich and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-12 with Science categories.
All measurements are subject to error because no quantity can be known exactly; hence, any measurement has a probability of lying within a certain range. The more precise the measurement, the smaller the range of uncertainty. Uncertainty, Calibration and Probability is a comprehensive treatment of the statistics and methods of estimating these calibration uncertainties. The book features the general theory of uncertainty involving the combination (convolution) of non-Gaussian, student t, and Gaussian distributions; the use of rectangular distributions to represent systematic uncertainties; and measurable and nonmeasurable uncertainties that require estimation. The author also discusses sources of measurement errors and curve fitting with numerous examples of uncertainty case studies. Many useful tables and computational formulae are included as well. All formulations are discussed and demonstrated with the minimum of mathematical knowledge assumed. This second edition offers additional examples in each chapter, and detailed additions and alterations made to the text. New chapters consist of the general theory of uncertainty and applications to industry and a new section discusses the use of orthogonal polynomials in curve fitting. Focusing on practical problems of measurement, Uncertainty, Calibration and Probability is an invaluable reference tool for R&D laboratories in the engineering/manufacturing industries and for undergraduate and graduate students in physics, engineering, and metrology.
Measurement Uncertainty And Probability
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Author : Robin Willink
language : en
Publisher:
Release Date : 2014-05-14
Measurement Uncertainty And Probability written by Robin Willink and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-14 with Electronic books categories.
Useful for researchers and graduate students, this book examines the practical meaning of probability.
Measurement Uncertainties
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Author : S. V. Gupta
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-01-13
Measurement Uncertainties written by S. V. Gupta and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-01-13 with Technology & Engineering categories.
This book fulfills the global need to evaluate measurement results along with the associated uncertainty. In the book, together with the details of uncertainty calculations for many physical parameters, probability distributions and their properties are discussed. Definitions of various terms are given and will help the practicing metrologists to grasp the subject. The book helps to establish international standards for the evaluation of the quality of raw data obtained from various laboratories for interpreting the results of various national metrology institutes in an international inter-comparisons. For the routine calibration of instruments, a new idea for the use of pooled variance is introduced. The uncertainty calculations are explained for (i) independent linear inputs, (ii) non-linear inputs and (iii) correlated inputs. The merits and limitations of the Guide to the Expression of Uncertainty in Measurement (GUM) are discussed. Monte Carlo methods for the derivation of the output distribution from the input distributions are introduced. The Bayesian alternative for calculation of expanded uncertainty is included. A large number of numerical examples is included.
Measurement Uncertainty
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Author : Simona Salicone
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-06-04
Measurement Uncertainty written by Simona Salicone and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-06-04 with Mathematics categories.
It is widely recognized, by the scienti?c and technical community that m- surements are the bridge between the empiric world and that of the abstract concepts and knowledge. In fact, measurements provide us the quantitative knowledge about things and phenomena. It is also widely recognized that the measurement result is capable of p- viding only incomplete information about the actual value of the measurand, that is, the quantity being measured. Therefore, a measurement result - comes useful, in any practicalsituation, only if a way is de?ned for estimating how incomplete is this information. The more recentdevelopment of measurement science has identi?ed in the uncertainty concept the most suitable way to quantify how incomplete is the information provided by a measurement result. However, the problem of how torepresentameasurementresulttogetherwithitsuncertaintyandpropagate measurementuncertaintyisstillanopentopicinthe?eldofmetrology,despite many contributions that have been published in the literature over the years. Many problems are in fact still unsolved, starting from the identi?cation of the best mathematical approach for representing incomplete knowledge. Currently, measurement uncertainty is treated in a purely probabilistic way, because the Theory of Probability has been considered the only available mathematical theory capable of handling incomplete information. However, this approach has the main drawback of requiring full compensation of any systematic e?ect that a?ects the measurement process. However, especially in many practical application, the identi?cation and compensation of all s- tematic e?ects is not always possible or cost e?ective.
Measurement Uncertainty And Probability
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Author : Robin Willink
language : en
Publisher: Cambridge University Press
Release Date : 2013-02-14
Measurement Uncertainty And Probability written by Robin Willink and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-02-14 with Mathematics categories.
Useful for researchers and graduate students, this book examines the practical meaning of probability.
Probability And Bayesian Modeling
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Author : Jim Albert
language : en
Publisher: CRC Press
Release Date : 2019-12-06
Probability And Bayesian Modeling written by Jim Albert and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-12-06 with Mathematics categories.
Probability and Bayesian Modeling is an introduction to probability and Bayesian thinking for undergraduate students with a calculus background. The first part of the book provides a broad view of probability including foundations, conditional probability, discrete and continuous distributions, and joint distributions. Statistical inference is presented completely from a Bayesian perspective. The text introduces inference and prediction for a single proportion and a single mean from Normal sampling. After fundamentals of Markov Chain Monte Carlo algorithms are introduced, Bayesian inference is described for hierarchical and regression models including logistic regression. The book presents several case studies motivated by some historical Bayesian studies and the authors’ research. This text reflects modern Bayesian statistical practice. Simulation is introduced in all the probability chapters and extensively used in the Bayesian material to simulate from the posterior and predictive distributions. One chapter describes the basic tenets of Metropolis and Gibbs sampling algorithms; however several chapters introduce the fundamentals of Bayesian inference for conjugate priors to deepen understanding. Strategies for constructing prior distributions are described in situations when one has substantial prior information and for cases where one has weak prior knowledge. One chapter introduces hierarchical Bayesian modeling as a practical way of combining data from different groups. There is an extensive discussion of Bayesian regression models including the construction of informative priors, inference about functions of the parameters of interest, prediction, and model selection. The text uses JAGS (Just Another Gibbs Sampler) as a general-purpose computational method for simulating from posterior distributions for a variety of Bayesian models. An R package ProbBayes is available containing all of the book datasets and special functions for illustrating concepts from the book. A complete solutions manual is available for instructors who adopt the book in the Additional Resources section.
An Introduction To Uncertainty In Measurement
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Author : L. Kirkup
language : en
Publisher: Cambridge University Press
Release Date : 2006-06-01
An Introduction To Uncertainty In Measurement written by L. Kirkup and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-06-01 with Science categories.
Measurement shapes scientific theories, characterises improvements in manufacturing processes and promotes efficient commerce. In concert with measurement is uncertainty, and students in science and engineering need to identify and quantify uncertainties in the measurements they make. This book introduces measurement and uncertainty to second and third year students of science and engineering. Its approach relies on the internationally recognised and recommended guidelines for calculating and expressing uncertainty (known by the acronym GUM). The statistics underpinning the methods are considered and worked examples and exercises are spread throughout the text. Detailed case studies based on typical undergraduate experiments are included to reinforce the principles described in the book. This guide is also useful to professionals in industry who are expected to know the contemporary methods in this increasingly important area. Additional online resources are available to support the book at www.cambridge.org/9780521605793.
Measurement Uncertainty
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Author : Ronald H. Dieck
language : en
Publisher: ISA
Release Date : 2007
Measurement Uncertainty written by Ronald H. Dieck and has been published by ISA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
Literally an entire course between two covers, Measurement Uncertainty: Methods and Applications, Fourth Edition, presents engineering students with a comprehensive tutorial of measurement uncertainty methods in a logically categorized and readily utilized format. The new uncertainty technologies embodied in both U.S. and international standards have been incorporated into this text with a view toward understanding the strengths and weaknesses of both. The book is designed to also serve as a practical desk reference in situations that commonly confront an experimenter. The text presents the basics of the measurement uncertainty model, non-symmetrical systematic standard uncertainties, random standard uncertainties, the use of correlation, curve-fitting problems, and probability plotting, combining results from different test methods, calibration errors, and uncertainty propagation for both independent and dependent error sources. The author draws on years of experience in industry to direct special attention to the problem of developing confidence in uncertainty analysis results and using measurement uncertainty to select instrumentation systems.
The Uncertainty In Physical Measurements
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Author : Paolo Fornasini
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-09-18
The Uncertainty In Physical Measurements written by Paolo Fornasini and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-09-18 with Technology & Engineering categories.
The scienti c method is based on the measurement of di erent physical qu- tities and the search for relations between their values. All measured values of physical quantities are, however, a ected by uncertainty. Understanding the origin of uncertainty, evaluating its extent, and suitably taking it into account in data analysis, are fundamental steps for assessing the global accuracy of physical laws and the degree of reliability of their technological applications. The introduction to uncertainty evaluation and data analysis procedures is generally made in laboratory courses for freshmen. During my long-lasting teaching experience, I had the feeling of some sort of gap between the ava- able tutorial textbooks, and the specialized monographs. The present work aims at lling this gap, and has been tested and modi ed through a feedback interaction with my students for several years. I have tried to maintain as much as possible a tutorial approach, that, starting from a phenomenolo- cal introduction, progressively leads to an accurate de nition of uncertainty and to some of the most common procedures of data analysis, facilitating the access to advanced monographs. This book is mainly addressed to - dergraduate students, but can be a useful reference for researchers and for secondary school teachers. The book is divided into three parts and a series of appendices. Part I is devoted to a phenomenological introduction to measurement and uncertainty. In Chap.