Authors:
- Book on error calculation from a theoretical point of view, further developing the approach of Gauss
- Integrates mathematics and its applications to physical measurements
- Serves as a text for graduate students and a reference for researchers
- Includes supplementary material: sn.pub/extras
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Table of contents (25 chapters)
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Front Matter
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Basics of Metrology
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Front Matter
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Generalized Gaussian Error Calculus
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Front Matter
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Error Propagation
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Front Matter
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Essence of Metrology
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Front Matter
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Fitting of Straight Lines
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Front Matter
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About this book
For the first time in 200 years Generalized Gaussian Error Calculus addresses a rigorous, complete and self-consistent revision of the Gaussian error calculus. Since experimentalists realized that measurements in general are burdened by unknown systematic errors, the classical, widespread used evaluation procedures scrutinizing the consequences of random errors alone turned out to be obsolete. As a matter of course, the error calculus to-be, treating random and unknown systematic errors side by side, should ensure the consistency and traceability of physical units, physical constants and physical quantities at large.
The generalized Gaussian error calculus considers unknown systematic errors to spawn biased estimators. Beyond, random errors are asked to conform to the idea of what the author calls well-defined measuring conditions.
The approach features the properties of a building kit: any overall uncertainty turns out to be the sum of a contribution due to random errors, to be taken from a confidence interval as put down by Student, and a contribution due to unknown systematic errors, as expressed by an appropriate worst case estimation.
Reviews
From the reviews:
“This book is aimed at the metrology community. … The approach elaborated in this book assesses unknown systematic errors via intervals of estimated lengths. … the author proposes the generalized Gaussian approach presented here as one which produces reliable measurement uncertainties meeting the demands of traceability.” (Rainer Schlittgen, Zentralblatt MATH, Vol. 1210, 2011)Authors and Affiliations
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Braunschweig, Germany
Michael Grabe
About the author
1967 Graduation in Physics at the Technical University of Stuttgart
1970 Doctorate at the Technical University of Braunschweig
1970 – 1975 Scientific assistant and lecturer at the Technical University of Braunschweig
1975 – 2004 Member of Staff at the Physikalische Technischer Bundesanstalt Braunschweig, commissioned to legal metrology, computerized interferometric measurment of length, measurement uncertainties and the adjustment of physical constants
Bibliographic Information
Book Title: Generalized Gaussian Error Calculus
Authors: Michael Grabe
DOI: https://doi.org/10.1007/978-3-642-03305-6
Publisher: Springer Berlin, Heidelberg
eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2010
Hardcover ISBN: 978-3-642-03304-9Published: 26 February 2010
Softcover ISBN: 978-3-642-42436-6Published: 13 December 2014
eBook ISBN: 978-3-642-03305-6Published: 04 February 2010
Edition Number: 1
Number of Pages: XIII, 301
Topics: Mathematical Methods in Physics, Systems Theory, Control, Engineering, general