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.
Author(s): Michael Grabe (auth.)
Edition: 1
Publisher: Springer-Verlag Berlin Heidelberg
Year: 2010
Language: English
Pages: 301
Tags: Mathematical Methods in Physics;Systems Theory, Control;Engineering, general
Front Matter....Pages i-xiii
Front Matter....Pages 1-1
True Values and Traceability....Pages 3-8
Models and Approaches....Pages 9-21
Front Matter....Pages 23-23
The New Uncertainties....Pages 25-29
Treatment of Random Errors....Pages 31-33
Treatment of Systematic Errors....Pages 35-36
Front Matter....Pages 37-37
Means and Means of Means....Pages 39-52
Functions of Erroneous Variables....Pages 53-78
Method of Least Squares....Pages 79-88
Front Matter....Pages 89-89
Dissemination of Units....Pages 91-100
Multiples and Sub-multiples....Pages 101-112
Founding Pillars....Pages 113-114
Front Matter....Pages 115-115
Preliminaries....Pages 117-119
Straight Lines: Case (i)....Pages 121-129
Straight Lines: Case (ii)....Pages 131-140
Straight Lines: Case (iii)....Pages 141-152
Front Matter....Pages 153-153
Preliminaries....Pages 155-156
Planes: Case (i)....Pages 157-163
Planes: Case (ii)....Pages 165-177
Planes: Case (iii)....Pages 179-190
Front Matter....Pages 191-191
Preliminaries....Pages 193-194
Front Matter....Pages 191-191
Parabolas: Case (i)....Pages 195-201
Parabolas: Case (ii)....Pages 203-212
Parabolas: Case (iii)....Pages 213-224
Front Matter....Pages 225-225
Series Truncation....Pages 227-235
Transformation....Pages 237-242
Back Matter....Pages 243-301
