E-Book, Englisch, 269 Seiten
Grabe Measurement Uncertainties in Science and Technology
1. Auflage 2005
ISBN: 978-3-540-27319-6
Verlag: Springer Berlin Heidelberg
Format: PDF
Kopierschutz: 1 - PDF Watermark
E-Book, Englisch, 269 Seiten
ISBN: 978-3-540-27319-6
Verlag: Springer Berlin Heidelberg
Format: PDF
Kopierschutz: 1 - PDF Watermark
In this book, Grabe illustrates the breakdown of traditional error calculus in the face of modern measurement techniques. Revising Gauß` error calculus ab initio, he treats random and unknown systematic errors on an equal footing from the outset. Furthermore, Grabe also proposes what may be called well defined measuring conditions, a prerequisite for defining confidence intervals that are consistent with basic statistical concepts. The resulting measurement uncertainties are as robust and reliable as required by modern-day science, engineering and technology.
Autoren/Hrsg.
Weitere Infos & Material
1;Preface;6
2;Contents;8
3;Characterization, Combination and Propagation of Errors;11
3.1;1 Basic Ideas of Measurement;12
3.2;2 Formalization of Measuring Processes;19
3.3;3 Densities of Normal Parent Distributions;33
3.4;4 Estimators and Their Expectations;58
3.5;5 Combination of Measurement Errors;68
3.6;6 Propagation of Measurement Errors;78
4;Least Squares Adjustment;98
4.1;7 Least Squares Formalism;99
4.2;8 Consequences of Systematic Errors;107
4.3;9 Uncertainties of Least Squares Estimators;118
5;Special Linear and Linearized Systems;153
5.1;10 Systems with Two Parameters;154
5.2;11 Systems with Three Parameters;178
5.3;12 Special Metrology Systems;205
6;Appendices;233
6.1;A On the Rank of Some Matrices;234
6.2;B Variance–Covariance Matrices;236
6.3;C Linear Functions of Normal Variables;239
6.4;D Orthogonal Projections;241
6.5;E Least Squares Adjustments;245
6.6;F Expansion of Solution Vectors;249
6.7;G Student’s Density;257
6.8;H Quantiles of Hotelling’s Density;260
7;References;261
8;Index;264
