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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.
List of contents
Basics of Metrology.- True Values and Traceability.- Models and Approaches.- Generalized Gaussian Error Calculus.- The New Uncertainties.- Treatment of Random Errors.- Treatment of Systematic Errors.- Error Propagation.- Means and Means of Means.- Functions of Erroneous Variables.- Method of Least Squares.- Essence of Metrology.- Dissemination of Units.- Multiples and Sub-multiples.- Founding Pillars.- Fitting of Straight Lines.- Preliminaries.- Straight Lines: Case (i).- Straight Lines: Case (ii).- Straight Lines: Case (iii).- Fitting of Planes.- Preliminaries.- Planes: Case (i).- Planes: Case (ii).- Planes: Case (iii).- Fitting of Parabolas.- Preliminaries.- Parabolas: Case (i).- Parabolas: Case (ii).- Parabolas: Case (iii).- Non-Linear Fitting.- Series Truncation.- Transformation.
About the author
Michael Grabe studierte Physik in Braunschweig und Stuttgart, Diplom in Stuttgart, Doktorand - Stipendium der Deutschen Forschungsgemeinschaft an der University of Colorado in Boulder, Promotion zum Dr. rer. nat. in Braunschweig, Wissenschaftlicher Assistent und Lehrbeauf tragter für Physikalische Chemie und Datenverarbeitung. Wissenschaftlicher Mitarbeiter der Physikalisch-Technischen Bundesanstalt Braunschweig, beauftragt mit Problemen des gesetzlichen Messwesens, der rechnergesteuerten interferrometrischen Längenmessung, des Schätzens von Messungssicherheiten und der Anpassung von Fundamentalkonstanten der Physik. Publikationen und Vorträge über Verfahren zum Auswerten von Messdaten.
Additional text
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)
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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)
