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 Need for 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 В Glossary .......................................... 212
APPENDIX С Nomenclature ...................................... 221
APPENDIX D Student's t for 95% Confidence .................... 229
APPENDIX E 5% Significant Thompson's τ ....................... 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
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