Dealing with Uncertainties (eBook)

Preface 6
Foreword by the Translator 8
Prolog. Seven Myths in Error Analysis 9
Contents 11
1 Introduction 13
1.1 The Exactness of Science 14
1.2 Data Without Uncertainty 16
2 Basics on Data 18
2.1 What Is a Measurement? 19
2.2 Analog vs. Digital 22
2.3 Dealing With Data (Numerals) 23
3 Basics on Uncertainties (Errors) 26
3.1 Typical Sources of Internal Uncertainties 27
3.2 Definitions 28
3.3 Uncertainty of Data Depending on One Variable 37
3.4 Multiple Uncertainty Components (Quadratic Sum) 38
4 Radioactive Decay, a Model for Random Events 43
4.1 Time Interval Distribution of Radioactive Events 43
4.2 Inductive Approach to Uncertainty (Example) 49
5 Frequency and Probability Distributions 60
5.1 Frequency Distribution (Spectrum) 60
5.2 Probability Distributions 67
5.3 Statistical Confidence 74
5.4 Dealing With Probabilities 75
6 Deductive Approach to Uncertainty 79
6.1 Theoretical Situation 79
6.2 Practical Situation 79
6.3 Regression Analysis (Least-Squares Method) 89
6.4 Data Consistency Within Data Sets 95
7 Correlation 98
7.1 Introduction 98
7.2 Correlated (Systematic) Internal Uncertainties 100
7.3 Differentiation From "Systematic Errors” 111
7.4 Correlation in Cases of Linear Regression 115
7.5 Data Consistency Among Data Sets 120
7.6 Target Shooting as a Model for Uncertainties 125
8 Dealing With Internal Uncertainties 127
8.1 Calculations With Both Types of Uncertainties 130
8.2 Total Uncertainty 138
8.3 Using Internal Uncertainties for Diagnosis 141
9 Presentation and Estimation of Uncertainties 146
9.1 Graphic Presentation, Also of Uncertainties 146
9.2 Correct Presentation of Uncertainties 150
9.3 Finding the Size of Internal Uncertainties 151
9.4 Estimating the Size of (Internal) Uncertainties 153
10 Feedback of Uncertainties on Experiment Design 157
10.1 Optimizing Experiments 157
10.2 Optimizing Background Measurements 159
10.3 Optimizing With Respect to Dead Time 162
10.4 Optimizing in View of the Mathematical Presentation 164
10.5 Achieving the Smallest Overall Uncertainty 166
Solutions 174
Index 182