| Basics of Metrology | |
| True Values and Traceability | p. 3 |
| Metrology | p. 3 |
| Traceability | p. 3 |
| Measurement Errors | p. 4 |
| Precision and Accuracy | p. 6 |
| Measurement Uncertainty | p. 6 |
| Measuring Result | p. 6 |
| Rivaling Physical Approaches | p. 8 |
| Models and Approaches | p. 9 |
| Gaussian Error Model | p. 9 |
| Generalized Gaussian Approach | p. 10 |
| Robust Testing Conditions | p. 14 |
| Linearizations | p. 15 |
| Quiddity of Least Squares | p. 16 |
| Analysis of Variance | p. 20 |
| Road Map | p. 21 |
| Generalized Gaussian Error Calculus | |
| The New Uncertainties | p. 25 |
| Gaussian Versus Generalized Gaussian Approach | p. 25 |
| Uncertainty and True Value | p. 25 |
| Designing Uncertainties | p. 26 |
| Quasi Safeness | p. 29 |
| Treatment of Random Errors | p. 31 |
| Well-Defined Measuring Conditions | p. 31 |
| Multidimensional Normal Model | p. 32 |
| Permutation of Repeated Measurements | p. 33 |
| Treatment of Systematic Errors | p. 35 |
| Repercussion of Biases | p. 35 |
| Uniqueness of Worst-Case Assessments | p. 36 |
| Error Propagation | |
| Means and Means of Means | p. 39 |
| Arithmetic Mean | p. 39 |
| Extravagated Averages | p. 41 |
| Mean of Means | p. 41 |
| Individual Mean Versus Grand Mean | p. 47 |
| Functions of Erroneous Variables | p. 53 |
| One Variable | p. 53 |
| Two Variables | p. 56 |
| More Than Two Variables | p. 61 |
| Concatenated Functions | p. 66 |
| Elementary Examples | p. 68 |
| Test of Hypothesis | p. 74 |
| Method of Least Squares | p. 79 |
| Empirical Variance-Covariance Matrix | p. 79 |
| Propagation of Systematic Errors | p. 82 |
| Uncertainties of the Estimators | p. 83 |
| Weighting Factors | p. 84 |
| Example | p. 87 |
| Essence of Metrology | |
| Dissemination of Units | p. 91 |
| Working Standards | p. 91 |
| Key Comparisons | p. 95 |
| Multiples and Sub-multiples | p. 101 |
| Calibration Chains | p. 101 |
| Pairwise Comparisons | p. 110 |
| Founding Pillars | p. 113 |
| Consistency | p. 113 |
| Traceability | p. 114 |
| Fitting of Straight Lines | |
| Preliminaries | p. 117 |
| Distinction of Cases | p. 117 |
| True Straight Line | p. 118 |
| Straight Lines: Case (i) | p. 121 |
| Fitting Conditions | p. 121 |
| Orthogonal Projection | p. 121 |
| Uncertainties of the Input Data | p. 123 |
| Uncertainties of the Components of the Solution Vector | p. 124 |
| Uncertainty Band | p. 126 |
| EP-Region | p. 127 |
| Straight Lines: Case (ii) | p. 131 |
| Fitting Conditions | p. 131 |
| Orthogonal Projection | p. 132 |
| Uncertainties of the Components of the Solution Vector | p. 132 |
| Uncertainty Band | p. 135 |
| EP-Region | p. 137 |
| Straight Lines: Case (iii) | p. 141 |
| Fitting Conditions | p. 141 |
| Orthogonal Projection | p. 142 |
| Series Expansion of the Solution Vector | p. 143 |
| Uncertainties of the Components of the Solution Vector | p. 145 |
| Uncertainty Band | p. 147 |
| EP-Region | p. 148 |
| Fitting of Planes | |
| Preliminaries | p. 155 |
| Distinction of Cases | p. 155 |
| True Plane | p. 155 |
| Planes: Case (i) | p. 157 |
| Fitting Conditions | p. 157 |
| Orthogonal Projection | p. 157 |
| Uncertainties of the Input Data | p. 158 |
| Uncertainties of the Components of the Solution Vector | p. 159 |
| EPC-Region | p. 161 |
| Planes: Case (ii) | p. 165 |
| Fitting Conditions | p. 165 |
| Orthogonal Projection | p. 166 |
| Uncertainties of the Components of the Solution Vector | p. 166 |
| Confidence Intervals and Overall Uncertainties | p. 168 |
| Uncertainty Bowls | p. 169 |
| EPC-Region | p. 171 |
| Planes: Case (iii) | p. 179 |
| Fitting Conditions | p. 179 |
| Orthogonal Projection | p. 180 |
| Series Expansion of the Solution Vector | p. 181 |
| Uncertainties of the Components of the Solution Vector | p. 183 |
| Uncertainty Bowls | p. 185 |
| EPC-Region | p. 187 |
| Fitting of Parabolas | |
| Preliminaries | p. 193 |
| Distinction of Cases | p. 193 |
| True Parabola | p. 193 |
| Parabolas: Case (i) | p. 195 |
| Fitting Conditions | p. 195 |
| Orthogonal Projection | p. 195 |
| Uncertainties of the Input Data | p. 196 |
| Uncertainties of the Components of the Solution Vector | p. 197 |
| Uncertainty Band | p. 199 |
| EPC-Region | p. 199 |
| Parabolas: Case (ii) | p. 203 |
| Fitting Conditions | p. 203 |
| Orthogonal Projection | p. 294 |
| Uncertainties of the Components of the Solution Vector | p. 204 |
| Uncertainty Band | p. 207 |
| EPC-Region | p. 209 |
| Parabolas: Case (iii) | p. 213 |
| Fitting Conditions | p. 213 |
| Orthogonal Projection | p. 214 |
| Series Expansion of the Solution Vector | p. 215 |
| Uncertainties of the Components of the Solution Vector | p. 217 |
| Uncertainty Band | p. 219 |
| EPC-Region | p. 220 |
| Non-linear Fitting | |
| Series Truncation | p. 227 |
| Homologous True Function | p. 227 |
| Fitting Conditions | p. 228 |
| Orthogonal Projection | p. 228 |
| Iteration | p. 230 |
| Uncertainties of the Components of the Solution Vector | p. 231 |
| Transformation | p. 237 |
| Homologous True Function | p. 237 |
| Fitting Conditions | p. 237 |
| Orthogonal Projection | p. 238 |
| Uncertainties of the Components of the Solution Vector | p. 239 |
| Appendices | |
| Graphical Scale Transformations | p. 245 |
| Expansion of Solution Vectors | p. 251 |
| Special Confidence Ellipses and Ellipsoids | p. 257 |
| Extreme Points of Ellipses and Ellipsoids | p. 261 |
| Drawing Ellipses and Ellipsoids | p. 265 |
| Security Polygons and Polyhedra | p. 267 |
| EP Boundaries and EPC Hulls | p. 277 |
| Student's Density | p. 283 |
| Uncertainty Band Versus EP-Region | p. 287 |
| Quantiles of Hotelling's Density | p. 295 |
| References | p. 297 |
| Index | p. 299 |
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