Measurement Uncertainty: Methods and Applications Book

Preface ix

Unit 1 Introduction and Overview 3

1-1 Course Coverage 3

1-2 Purpose 3

1-3 Audience and Prerequisites 4

1-4 Study Material 4

1-5 Organization and Sequence 4

1-6 Course Objectives/Learning Objectives 5

1-7 Course Length 5

Unit 2 Fundamentals of Measurement Uncertainty Analysis 9

2-1 The Purpose of Engineering, Experimental, or Test Measurements 9

2-2 Measurement Error Definition 10

2-3 Summary 32

Exercises 34

Unit 3 The Measurement Uncertainty Model 39

3-1 The Statement of Measurement Uncertainty 39

3-2 Grouping and Categorizing Error Sources 40

3-3 The Calculation of Measurement Uncertainty (Symmetrical Systematic Uncertainties) 43

3-4 The Uncertainty Statement (Symmetrical Systematic Standard Uncertainties) 48

3-5 Computing the Uncertainty Interval (Symmetrical Systematic Uncertainties) 51

3-6 The Calculation of Measurement Uncertainty (Nonsymmetrical Standard Systematic Uncertainties) 54

3-7 Common Uncertainty Model Summary 59

3-8 Summary 60

Exercises 62

Unit 4 How To Do It Summary 67

4-1 Review of Nomenclature 67

4-2 How To Do It Summary 69

4-3 Calculation of Random Standard Uncertainties 69

4-4 Obtaining and Combining Systematic Standard Uncertainties 73

4-5 Nonsymmetrical Systematic Standard Uncertainties 79

4-6 Step-by-Step Instructions 80

4-7 Treatment of Calibration Errors (Uncertainties) 83

4-8 Simplified Uncertainty Analysis for Calibrations 85

4-9 Business Decisions and the Impact of Measurement Uncertainty 96

4-10 The Timing of an Uncertainty Analysis 99

4-11 Conclusion 103

References 103

Exercises 103

Unit 5 Uncertainty (Error) Propagation 111

5-1 General Considerations 111

5-2 The Needfor Uncertainty Propagation 111

5-3 Theoretical Considerations: Methods for Uncertainty Propagation 113

5-4 Uncertainty Propagation Examples 126

5-5 Detailed Equation for Uncertainty Propagation 141

5-6 Uncertainty of Results Derived from X-Y Plots 142

5-7 Summary 146

References 146

Exercises 147

Unit 6 Weighting Method for Multiple Results 153

6-1 The Purpose of Multiple Measurements of the Same Test Result 153

6-2 Fundamentals of Weighting by Uncertainty 153

References 161

Exercises 161

Unit 7 Applied Considerations 165

7-1 General Considerations 165

7-2 Choice of Error (and Uncertainty) Units 165

7-3 Treatment of Outliers 168

7-4 Curve Fitting 171

7-5 Correlation Coefficients: Their Use and Misuse 181

7-6 Tests for Normality, Probability Plots 183

7-7 Sampling Error 187

7-8 Selecting Instrumentation Based on Vendor Uncertainty Statements 192

References 194

Exercises 195

Unit 8 Presentation of Results 201

8-1 General Considerations 201

8-2 Presentation Content 202

8-3 Illustration 202

8-4 Summary 206

Appendix A Suggested Reading and Study Materials 209

Appendix B Glossary 212

Appendix C Nomenclature 221

Appendix D Student's for 95% Confidence 229

Appendix E 5% Significant Thompson's T 233

Appendix F Areas Under the Normal Curve 237

Appendix G Pressure Instrumentation Selection Example 241

Appendix H Alternate Measurement Uncertainty Analysis Approach 253

Appendix I Solutions to All Exercises 257

Index 273

Prime Equations for Uncertainty Analysis 275