Measurement uncertainties in science and technology:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2005
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 269 S. graph. Darst. |
| ISBN: | 3540209441 |
Internformat
MARC
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| 100 | 1 | |a Grabe, Michael |d 1939- |e Verfasser |0 (DE-588)106779591 |4 aut | |
| 245 | 1 | 0 | |a Measurement uncertainties in science and technology |c Michael Grabe |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2005 | |
| 300 | |a XI, 269 S. |b graph. Darst. | ||
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| 650 | 4 | |a Messgenauigkeit - Messunsicherheit | |
| 650 | 4 | |a Error analysis (Mathematics) | |
| 650 | 4 | |a Instrumental variables (Statistics) | |
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Datensatz im Suchindex
| _version_ | 1804133327181971456 |
|---|---|
| adam_text | Contents
Part I Characterization, Combination
and Propagation of Errors
1 Basic Ideas of Measurement 3
1.1 Sources of Measurement Uncertainty 3
1.2 Quotation of Numerical Values and Rounding 8
1.2.1 Rounding of Estimators 8
1.2.2 Rounding of Uncertainties 8
2 Formalization of Measuring Processes 11
2.1 Basic Error Equation 11
2.2 Random Variables, Probability Densities
and Parent Distributions 18
2.3 Elements of Evaluation 21
3 Densities of Normal Parent Distributions 25
3.1 One Dimensional Normal Density 25
3.2 Multidimensional Normal Density 29
3.3 Chi Square Density and F Density 33
3.4 Student s (Gosset s) Density 36
3.5 Fisher s Density 41
3.6 Hotelling s Density 43
4 Estimators and Their Expectations 51
4.1 Statistical Ensembles 51
4.2 Variances and Covariances 54
4.3 Elementary Model of Analysis of Variance 58
5 Combination of Measurement Errors 61
5.1 Expectation of the Arithmetic Mean 61
5.2 Uncertainty of the Arithmetic Mean 63
5.3 Uncertainty of a Function of One Variable 66
5.4 Systematic Errors of the Measurands 70
X Contents
6 Propagation of Measurement Errors 71
6.1 Taylor Series Expansion 71
6.2 Expectation of the Arithmetic Mean 74
6.3 Uncertainty of the Arithmetic Mean 77
6.4 Uncertainties of Elementary Functions 80
6.5 Error Propagation over Several Stages 87
Part II Least Squares Adjustment
7 Least Squares Formalism 93
7.1 Geometry of Adjustment 93
7.2 Unconstrained Adjustment 97
7.3 Constrained Adjustment 100
8 Consequences of Systematic Errors 101
8.1 Structure of the Solution Vector 101
8.2 Minimized Sum of Squared Residuals 103
8.3 Gauss Markoff Theorem 105
8.4 Choice of Weights 107
8.5 Consistency of the Input Data 109
9 Uncertainties of Least Squares Estimators 113
9.1 Empirical Variance Covariance Matrix 113
9.2 Propagation of Systematic Errors 117
9.3 Overall Uncertainties of the Estimators 119
9.4 Uncertainty of a Function of Estimators 128
9.5 Uncertainty Spaces 130
9.5.1 Confidence Ellipsoids 131
9.5.2 The New Solids 132
9.5.3 EP Boundaries and EPC Hulls 141
Part III Special Linear and Linearized Systems
10 Systems with Two Parameters 151
10.1 Straight Lines 151
10.1.1 Error free Abscissas, Erroneous Ordinates 154
10.1.2 Erroneous Abscissas, Erroneous Ordinates 165
10.2 Linearization 172
10.3 Transformation 173
Contents XI
11 Systems with Three Parameters 175
11.1 Planes 175
11.2 Parabolas 181
11.2.1 Error free Abscissas, Erroneous Ordinates 181
11.2.2 Erroneous Abscissas, Erroneous Ordinates 188
11.3 Piecewise Smooth Approximation 192
11.4 Circles 195
12 Special Metrology Systems 203
12.1 Dissemination of Units 203
12.1.1 Realization of Working Standards 203
12.1.2 Key Comparison 205
12.2 Mass Decades 210
12.3 Pairwise Comparisons 215
12.4 Fundamental Constants of Physics 215
12.5 Trigonometric Polynomials 224
12.5.1 Unknown Model Function 225
12.5.2 Known Model Function 227
Part IV Appendices
A On the Rank of Some Matrices 233
B Variance—Covariance Matrices 235
C Linear Functions of Normal Variables 239
D Orthogonal Projections 241
E Least Squares Adjustments 245
F Expansion of Solution Vectors 249
G Student s Density 257
H Quantiles of Hotelling s Density 261
References 263
Index 267
|
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| discipline | Physik Mathematik Mess-/Steuerungs-/Regelungs-/Automatisierungstechnik Mess-/Steuerungs-/Regelungs-/Automatisierungstechnik / Mechatronik |
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| indexdate | 2024-07-09T20:06:57Z |
| institution | BVB |
| isbn | 3540209441 |
| language | English |
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| physical | XI, 269 S. graph. Darst. |
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| spelling | Grabe, Michael 1939- Verfasser (DE-588)106779591 aut Measurement uncertainties in science and technology Michael Grabe Berlin [u.a.] Springer 2005 XI, 269 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Messgenauigkeit - Messunsicherheit Error analysis (Mathematics) Instrumental variables (Statistics) Measurement Messgenauigkeit (DE-588)4138706-5 gnd rswk-swf Messfehler (DE-588)4133270-2 gnd rswk-swf Fehlerrechnung (DE-588)4153837-7 gnd rswk-swf Fehleranalyse (DE-588)4016608-9 gnd rswk-swf Messunsicherheit (DE-588)4210374-5 gnd rswk-swf Messfehler (DE-588)4133270-2 s Fehlerrechnung (DE-588)4153837-7 s DE-604 Messgenauigkeit (DE-588)4138706-5 s Messunsicherheit (DE-588)4210374-5 s Fehleranalyse (DE-588)4016608-9 s 1\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013148729&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Grabe, Michael 1939- Measurement uncertainties in science and technology Messgenauigkeit - Messunsicherheit Error analysis (Mathematics) Instrumental variables (Statistics) Measurement Messgenauigkeit (DE-588)4138706-5 gnd Messfehler (DE-588)4133270-2 gnd Fehlerrechnung (DE-588)4153837-7 gnd Fehleranalyse (DE-588)4016608-9 gnd Messunsicherheit (DE-588)4210374-5 gnd |
| subject_GND | (DE-588)4138706-5 (DE-588)4133270-2 (DE-588)4153837-7 (DE-588)4016608-9 (DE-588)4210374-5 |
| title | Measurement uncertainties in science and technology |
| title_auth | Measurement uncertainties in science and technology |
| title_exact_search | Measurement uncertainties in science and technology |
| title_full | Measurement uncertainties in science and technology Michael Grabe |
| title_fullStr | Measurement uncertainties in science and technology Michael Grabe |
| title_full_unstemmed | Measurement uncertainties in science and technology Michael Grabe |
| title_short | Measurement uncertainties in science and technology |
| title_sort | measurement uncertainties in science and technology |
| topic | Messgenauigkeit - Messunsicherheit Error analysis (Mathematics) Instrumental variables (Statistics) Measurement Messgenauigkeit (DE-588)4138706-5 gnd Messfehler (DE-588)4133270-2 gnd Fehlerrechnung (DE-588)4153837-7 gnd Fehleranalyse (DE-588)4016608-9 gnd Messunsicherheit (DE-588)4210374-5 gnd |
| topic_facet | Messgenauigkeit - Messunsicherheit Error analysis (Mathematics) Instrumental variables (Statistics) Measurement Messgenauigkeit Messfehler Fehlerrechnung Fehleranalyse Messunsicherheit |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013148729&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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