Generalized Gaussian Error Calculus [electronic resource] /
Grabe, Michael.author.
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.
Description based upon print version of record.
Includes bibliographical references (p. [297]-298) and index.
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.
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.
Physics.
System theory.
Engineering.
Mathematical Methods in Physics.
Systems Theory, Control.
Engineering, general.