Measurement Uncertainty: An Approach via the Mathematical Theory of Evidence (Springer Series in Reliability Engineering)

The expression of uncertainty in measurement is a challenging aspect for researchers and engineers working in instrumentation and measurement because it involves physical, mathematical and philosophical issues. This problem is intensified by the limitations of the probabilistic approach used by the current standard (GUM). This text is the first to make full use of the mathematical theory of evidence to express the uncertainty in measurements. It gives an overview of the current standard, then pinpoints and constructively resolves its limitations through its unique approach. The text presents various tools for evaluating uncertainty, beginning with the probabilistic approach and concluding with the expression of uncertainty using random-fuzzy variables. The exposition is driven by numerous examples. The book is designed for immediate use and application in research and laboratory work. Prerequisites for students include courses in statistics and measurement science. Apart from a classroom setting, this book can be used by practitioners in a variety of fields (including applied mathematics, applied probability, electrical and computer engineering, and experimental physics), and by such institutions as the IEEE, ISA, and National Institute of Standards and Technology. 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.

the Expression Of Uncertainty In Measurement Is A Challenging Aspect For Researchers And Engineers Working In Instrumentation And Measurement Because It Involves Physical, Mathematical And Philosophical Issues. This Problem Is Intensified By The Limitations Of The Probabilistic Approach Used By The Current Standard (gum).

this Text Is The First To Make Full Use Of The Mathematical Theory Of Evidence To Express The Uncertainty In Measurements. It Gives An Overview Of The Current Standard, Then Pinpoints And Constructively Resolves Its Limitations Through Its Unique Approach. The Text Presents Various Tools For Evaluating Uncertainty, Beginning With The Probabilistic Approach And Concluding With The Expression Of Uncertainty Using Random-fuzzy Variables. The Exposition Is Driven By Numerous Examples. The Book Is Designed For Immediate Use And Application In Research And Laboratory Work.

apart From A Classroom Setting, This Book Can Be Used By Practitioners In A Variety Of Fields (including Applied Mathematics, Applied Probability, Electrical And Computer Engineering, And Experimental Physics), And By Such Institutions As The Ieee, Isa, And National Institute Of Standards And Technology.

0387306552......Page 1 Springer Series in Reliability Engineering......Page 2 Measurement Uncertainty......Page 4 Contents......Page 6 Preface......Page 9 1 Uncertainty in Measurement......Page 11 2 Fuzzy Variables and Measurement Uncertainty......Page 25 3 The Theory of Evidence......Page 40 4 Random–Fuzzy Variables......Page 81 5 Construction of Random–Fuzzy Variables......Page 94 6 Fuzzy Operators......Page 106 7 The Mathematics of Random–Fuzzy Variables......Page 132 8 Representation of Random–Fuzzy Variables......Page 202 9 Decision-Making Rules with Random–Fuzzy Variables......Page 204 10 List of Symbols......Page 230 References......Page 232 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. "This text is the first to make full use of the mathematical theory of evidence to express the uncertainty in measurements. It gives an overview of the current standard, then pinpoints and constructively resolves its limitations through its unique approach. The text presents various tools for evaluating uncertainty, beginning with the probabilistic approach and concluding with the expression of uncertainty using random-fuzzy variables. The exposition is driven by numerous examples. The book is designed for immediate use and application in research and laboratory work."--Jacket