Download or read book Measurement Uncertainty and Probability written by Robin Willink and published by Cambridge University Press. This book was released on 2013-02-14 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Uncertainty Calibration and Probability written by C.F Dietrich and published by Routledge. This book was released on 2017-07-12 with total page 554 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Probability and Bayesian Modeling written by Jim Albert and published by CRC Press. This book was released on 2019-12-06 with total page 553 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Measurement Uncertainty and Probability written by Robin Willink and published by Cambridge University Press. This book was released on 2013-02-14 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: Useful for researchers and graduate students, this book examines the practical meaning of probability.
Download or read book Measurement Uncertainty written by Simona Salicone and published by Springer Science & Business Media. This book was released on 2007-06-04 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: The expression of uncertainty in measurement poses a challenge since it involves physical, mathematical, and philosophical issues. This problem is intensified by the limitations of the probabilistic approach used by the current standard (the GUM Instrumentation Standard). This text presents an alternative approach. It makes full use of the mathematical theory of evidence to express the uncertainty in measurements. Coverage provides an overview of the current standard, then pinpoints and constructively resolves its limitations. Numerous examples throughout help explain the book’s unique approach.
Download or read book Measurement Uncertainty written by Ronald H. Dieck and published by ISA. This book was released on 2007 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Measurements and their Uncertainties written by Ifan Hughes and published by OUP Oxford. This book was released on 2010-07-02 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: This hands-on guide is primarily intended to be used in undergraduate laboratories in the physical sciences and engineering. It assumes no prior knowledge of statistics. It introduces the necessary concepts where needed, with key points illustrated with worked examples and graphic illustrations. In contrast to traditional mathematical treatments it uses a combination of spreadsheet and calculus-based approaches, suitable as a quick and easy on-the-spot reference. The emphasis throughout is on practical strategies to be adopted in the laboratory. Error analysis is introduced at a level accessible to school leavers, and carried through to research level. Error calculation and propagation is presented though a series of rules-of-thumb, look-up tables and approaches amenable to computer analysis. The general approach uses the chi-square statistic extensively. Particular attention is given to hypothesis testing and extraction of parameters and their uncertainties by fitting mathematical models to experimental data. Routines implemented by most contemporary data analysis packages are analysed and explained. The book finishes with a discussion of advanced fitting strategies and an introduction to Bayesian analysis.
Download or read book An Introduction to Uncertainty in Measurement written by L. Kirkup and published by Cambridge University Press. This book was released on 2006-06-01 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Measurement Uncertainties written by S. V. Gupta and published by Springer Science & Business Media. This book was released on 2012-01-13 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book An Introduction to Measurement Uncertainty written by Blair D Hall and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: "This introduction to measurement uncertainty is intended for metrology professionals working in calibration laboratories and metrology institutes, as well as students in tertiary-level science and engineering programmes. The subject matter is presented with an emphasis on developing models of the physical measurement process. The level of mathematics and statistics used is basic and is typically covered by high school studies"--Distributor's website.
Download or read book Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results rev Ed written by Barry N. Taylor and published by DIANE Publishing. This book was released on 2009-11 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt: Results of measurements and conclusions derived from them constitute much of the technical information produced by the National Institute of Standards and Technology (NIST). In July 1992 the Director of NIST appointed an Ad Hoc Committee on Uncertainty Statements and charged it with recommending a policy on this important topic. The Committee concluded that the CIPM approach could be used to provide quantitative expression of measurement that would satisfy NIST¿s customers¿ requirements. NIST initially published a Technical Note on this issue in Jan. 1993. This 1994 edition addresses the most important questions raised by recipients concerning some of the points it addressed and some it did not. Illustrations.
Download or read book Measurement Errors and Uncertainties written by Semyon G. Rabinovich and published by Springer Science & Business Media. This book was released on 2006-12-26 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: A practical reference on theory and methods of estimating measurement errors and uncertainty for both scientists and engineers in industry and experimental research. Building on the fundamentals of measurement theory, this book offers a wealth of practial recommendations and procedures. It differs from the majority of books in that it balances coverage of probabilistic methods with detailed information on the characterization, calibration, standardization and limitations of measuring instruments, with specific examples from both electrical and mechanical systems. In addition to a general updating to reflect current research, new material in this edition includes increased coverage of indirect measurements, with a new, simpler, more efficient method for this class of measurements.
Download or read book The Uncertainty of Measurements written by Shri Krishna Kimothi and published by Quality Press. This book was released on 2001-11-01 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: The uncertainty of measurement results is drawing attention of managers, metrologists and customers. The accuracy of measurements affects all of us in trade, commerce, safety, health care environmental protection and more. The quality of these measurements are regulated by a variety of government agencies. Measurement also plays an important role in manufacturing and service organizations. Use this book to learn more about metrology and the need for reliable measurements. You can also learn about measurement system and quality of measurement systems, objectives and methods. Statistical techniques in metrology are also explained. Examples of measurement data and random variables, probability density functions, sampling distribution, statistical estimation degrees of freedom and regression are included. An entire chapter is devoted to measurement errors. The book goes in-depth into explaining national and international measurement systems and standards, and includes a complete chapter on calibration and measurement trace ability. Measurement Uncertainty will show how to evaluate various uncertainties in measurements using several approaches including international consensus. Calibration laboratories can look specifically at the chapter on that profession to guide them in their measurement improvements. Kimothi also looks at specific industries and their measurement capabilities and includes examples of R&R studies. A great resource for the CQE, CQT, CCT, CSSBB certification exams!
Download or read book The Uncertainty in Physical Measurements written by Paolo Fornasini and published by Springer Science & Business Media. This book was released on 2008-09-18 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Science and Judgment in Risk Assessment written by National Research Council and published by National Academies Press. This book was released on 1994-01-01 with total page 668 pages. Available in PDF, EPUB and Kindle. Book excerpt: The public depends on competent risk assessment from the federal government and the scientific community to grapple with the threat of pollution. When risk reports turn out to be overblownâ€"or when risks are overlookedâ€"public skepticism abounds. This comprehensive and readable book explores how the U.S. Environmental Protection Agency (EPA) can improve its risk assessment practices, with a focus on implementation of the 1990 Clean Air Act Amendments. With a wealth of detailed information, pertinent examples, and revealing analysis, the volume explores the "default option" and other basic concepts. It offers two views of EPA operations: The first examines how EPA currently assesses exposure to hazardous air pollutants, evaluates the toxicity of a substance, and characterizes the risk to the public. The second, more holistic, view explores how EPA can improve in several critical areas of risk assessment by focusing on cross-cutting themes and incorporating more scientific judgment. This comprehensive volume will be important to the EPA and other agencies, risk managers, environmental advocates, scientists, faculty, students, and concerned individuals.
Download or read book Integration Measure and Probability written by H. R. Pitt and published by Courier Corporation. This book was released on 2012-01-01 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introductory treatment develops the theory of integration in a general context, making it applicable to other branches of analysis. More specialized topics include convergence theorems and random sequences and functions. 1963 edition.
Download or read book Probability and Statistics written by Michael J. Evans and published by Macmillan. This book was released on 2004 with total page 704 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unlike traditional introductory math/stat textbooks, Probability and Statistics: The Science of Uncertainty brings a modern flavor based on incorporating the computer to the course and an integrated approach to inference. From the start the book integrates simulations into its theoretical coverage, and emphasizes the use of computer-powered computation throughout.* Math and science majors with just one year of calculus can use this text and experience a refreshing blend of applications and theory that goes beyond merely mastering the technicalities. They'll get a thorough grounding in probability theory, and go beyond that to the theory of statistical inference and its applications. An integrated approach to inference is presented that includes the frequency approach as well as Bayesian methodology. Bayesian inference is developed as a logical extension of likelihood methods. A separate chapter is devoted to the important topic of model checking and this is applied in the context of the standard applied statistical techniques. Examples of data analyses using real-world data are presented throughout the text. A final chapter introduces a number of the most important stochastic process models using elementary methods. *Note: An appendix in the book contains Minitab code for more involved computations. The code can be used by students as templates for their own calculations. If a software package like Minitab is used with the course then no programming is required by the students.
