Table of contents : Preface Contents About the Authors Chapter 1: Introduction 1.1 Measurement Uncertainty: Why Do We Care? 1.2 The History of Measurement 1.3 Measurement Science and Technological Development 1.4 Allegations of Deflated Footballs (``Deflategate´´) 1.5 Fatality Rates During a Pandemic 1.6 Summary 1.7 Related Reading References Chapter 2: Basic Measurement Concepts 2.1 Introduction 2.2 Measurement Terminology 2.2.1 General Measurement Terminology 2.2.1.1 Measurand 2.2.1.2 True Value (True Value of a Quantity) 2.2.1.3 Measurement Accuracy 2.2.1.4 Measurement Precision 2.2.1.5 Resolution 2.2.1.6 Measurement Repeatability 2.2.1.7 Measurement Reproducibility 2.2.1.8 Independence of Measurements 2.2.2 Error Approach Terminology 2.2.2.1 Measurement Error 2.2.2.2 Systematic Measurement Error 2.2.2.3 Random Measurement Error 2.2.3 Uncertainty Approach Terminology 2.2.3.1 Measurement Uncertainty 2.2.3.2 Level of Confidence (Coverage Probability) 2.2.3.3 Coverage Interval 2.2.3.4 Measurement Model 2.2.4 Terminology of Calibration 2.2.4.1 Measuring and Test Equipment (M&TE) 2.2.4.2 Metrological Traceability 2.2.4.3 Calibration 2.2.4.4 Tolerance Test 2.2.4.5 Certification Uncertainty 2.3 Types of Measurements 2.3.1 Physical Measurements 2.3.2 Electrical Measurements 2.3.3 Other Types of Measurements 2.4 Sources of Uncertainty 2.4.1 Evaluating Sources of Uncertainty 2.5 Summary 2.6 Related Reading 2.7 Exercises References Chapter 3: The International System of Units, Traceability, and Calibration 3.1 History of the SI and Base Units 3.1.1 SI Constants 3.1.2 Time: Second (s) 3.1.3 Length: Meter (m) 3.1.4 Mass: Kilogram (kg) 3.1.5 Electric Current: Ampere (A) 3.1.6 Temperature: Kelvin (K) 3.1.7 Quantity of Substance: Mole (mol) 3.1.8 Luminous Intensity: Candela (cd) 3.2 Derived Units 3.3 Unit Realizations 3.3.1 Gauge Block Interferometer 3.3.2 Josephson Volt 3.4 Advancements in Unit Definitions 3.4.1 Kibble (Watt) Balance 3.4.2 Intrinsic Pressure Standard 3.5 Metrological Traceability 3.6 Measurement Standards 3.6.1 Certified Reference Materials 3.6.2 Check Standards 3.7 Calibration 3.7.1 The Calibration Cycle 3.7.2 Legal Aspects of Calibration 3.7.3 Technical Aspects of Calibration 3.7.4 Calibration Policies and Requirements 3.7.4.1 ISO 17025 3.7.4.2 ANSI Z540.1 and ANSI/NCSL Z540.3:2006 3.8 Summary 3.9 Related Reading 3.10 Exercises References Chapter 4: Introduction to Statistics and Probability 4.1 Introduction 4.2 Types of Data 4.3 Exploratory Data Analysis 4.3.1 Calculating Summary Statistics 4.3.1.1 Summary Statistics for Continuous Data 4.3.1.2 Summary Statistics for Discrete Data 4.3.2 Graphical Displays of Data 4.3.2.1 Graphical Displays for Continuous Data 4.3.2.2 Graphical Displays for Discrete Data 4.4 Probability Distributions 4.4.1 Identification of Probability Distributions 4.4.1.1 Continuous Distributions 4.4.1.2 Discrete Distributions 4.4.2 Estimating Distribution Parameters 4.4.3 Assessing Distributional Fit 4.5 Related Reading 4.6 Exercises References Chapter 5: Measurement Uncertainty in Decision Making 5.1 Introduction 5.2 Measurement Uncertainty and Risk 5.2.1 Measurement Uncertainty and Risk in Manufacturing 5.2.1.1 Test Uncertainty Ratio 5.2.1.2 Measurement Decisions 5.2.1.3 False Accept and False Reject Risks 5.2.1.4 Guardbanding 5.2.1.5 Risk with Biased Measurements 5.2.2 Measurement Uncertainty and Risk in Calibration 5.2.2.1 Decision Rules in Calibration 5.3 Summary 5.4 Related Reading 5.5 Exercises References Chapter 6: The Measurement Model and Uncertainty 6.1 Introduction 6.2 Uncertainty Analysis Framework 6.2.1 Standard Uncertainty 6.2.2 Type A Uncertainty Evaluation 6.2.3 Type B Uncertainty Evaluation 6.2.4 Combined Standard Uncertainty 6.2.5 Confidence Level and Expanded Uncertainty 6.3 Direct Measurements and the Basic Measurement Model 6.3.1 Case Study: Voltage Measurement 6.3.2 Discussion 6.4 Indirect Measurements and the Indirect Measurement Model 6.4.1 Case Study: Neutron Yield Measurement 6.4.2 Discussion 6.5 Related Reading 6.6 Exercises References Chapter 7: Analytical Methods for the Propagation of Uncertainties 7.1 Introduction 7.2 Mathematical Basis 7.3 The Simple Case: First-Order Terms with Uncorrelated Inputs 7.3.1 Measurement Examples 7.4 First-Order Terms with Correlated Inputs 7.4.1 Covariance, Correlation, and Effect on Uncertainty 7.4.2 Measurement Examples 7.5 Higher-Order Terms with Uncorrelated Inputs 7.5.1 Measurement Examples 7.6 Multiple Output Quantities 7.7 Limitations of the Analytical Approach 7.8 Related Reading 7.9 Exercises References Chapter 8: Monte Carlo Methods for the Propagation of Uncertainties 8.1 Introduction to Monte Carlo Methods 8.1.1 Random Sampling Techniques and Random Number Generation 8.1.1.1 Sampling from Normal and Non-Normal Distributions 8.1.1.2 Generating Correlated Random Samples (Normal Distribution) 8.1.2 Generation of Probability Density Functions Using Random Data 8.1.3 Computational Approaches 8.1.3.1 Linear Congruential Generator 8.1.3.2 Better PRNG Algorithms 8.2 Standard Monte Carlo for Uncertainty Propagation 8.2.1 Monte Carlo Techniques 8.2.1.1 Case Study: Calculating Density 8.2.1.2 Sensitivity Coefficients 8.2.1.3 Convergence Plots and Adaptive Sampling 8.3 Comparison to the GUM 8.3.1 Quantitative GUM Validity Test 8.4 Monte Carlo Case Studies 8.4.1 Case Study: Neutron Yield Measurement 8.4.2 Case Study: RC Circuit 8.5 Summary 8.6 Related Reading 8.7 Exercises References Chapter 9: Design of Experiments in Metrology 9.1 Introduction 9.2 Factorial Experiments in Metrology 9.2.1 Defining the Measurand and Objective of the Experiment 9.2.2 Selecting Factors to Incorporate in the Experiment 9.2.3 Selecting Factor Levels and Design Pattern 9.2.4 Analysis of CMM Errors via Design of Experiments (24 Full Factorial) 9.2.5 Finite Element Method (FEM) Uncertainty Analysis via Design of Experiments (27-3 Fractional Factorial) 9.2.6 Summary of Factorial DOEx Method 9.3 ANOVA Models in Metrology 9.3.1 Random Effects Models 9.3.2 Mixed Effects Models 9.3.3 Underlying ANOVA Assumptions 9.3.4 Gauge R&R Study (Random Effects Model) 9.3.5 Voltage Standard Uncertainty Analysis (Mixed Effects Model) 9.3.6 Summary of ANOVA Method 9.4 Related Reading 9.5 Exercises References Chapter 10: Determining Uncertainties in Fitted Curves 10.1 The Purpose of Fitting Curves to Experimental Data 10.1.1 Resistance vs. Temperature Data 10.1.2 Considerations When Fitting Models to Data 10.2 Methods for Fitting Curves to Experimental Data 10.2.1 Linear Least Squares 10.2.2 Uncertainty in Fitting Parameters 10.2.3 Weighted Least Squares: Non-constant u(y) 10.2.4 Weighted Least Squares: Uncertainty in Both x and y 10.3 Uncertainty of a Regression Line 10.3.1 Uncertainty of Fitting Parameters 10.3.2 Confidence Bands 10.3.3 Prediction Bands 10.4 How Good Is the Model? 10.4.1 Residual Analysis 10.4.2 Slope Test 10.4.3 Quantitative Residual Analysis 10.5 Uncertainty in Nonlinear Regression 10.5.1 Nonlinear Least Squares 10.5.2 Orthogonal Distance Regression 10.5.3 Confidence and Prediction Bands in Nonlinear Regression 10.6 Using Monte Carlo for Evaluating Uncertainties in Curve Fitting 10.6.1 Monte Carlo Approach 10.6.2 Markov-Chain Monte Carlo Approach 10.7 Case Study: Contact Resistance 10.8 Drift and Predicting Future Values 10.8.1 Uncertainty During Use 10.8.2 Validating Drift Uncertainty 10.8.2.1 Type B Uncertainty 10.8.2.2 Type A Measurement Uncertainty 10.8.2.3 Drift Uncertainty 10.8.2.4 Expanded Uncertainty 10.9 Calibration Interval Analysis 10.10 Summary 10.11 Related Reading 10.12 Exercises References Chapter 11: Special Topics in Metrology 11.1 Introduction 11.2 Statistical Process Control (SPC) 11.2.1 Case Study: Battery Tester Uncertainty and Monitoring Via SPC 11.2.2 Discussion 11.3 Binary Measurement Systems (BMS) 11.3.1 BMS Overview 11.3.2 BMS Case Study Introduced 11.3.3 Evaluation of a BMS 11.3.3.1 Within-Operator Agreement 11.3.3.2 Between-Operator Agreement 11.3.3.3 Assessing BMS Correctness 11.3.4 Sample Sizes for a BMS Study 11.4 Measurement System Analysis with Destructive Testing 11.5 Sample Size and Allocation of Samples in Metrology Experiments 11.6 Summary of Sample Size Recommendations 11.7 Bayesian Analysis in Metrology 11.8 Related Reading 11.9 Exercises References Appendix A: Acronyms and Abbreviations Appendix B: Guidelines for Valid Measurements Related Reading: Electrical Measurements Related Reading: Time and Frequency Measurements Related Reading: Physical Measurements Related Reading: Temperature Measurement Related Reading: Radiation Related Reading: General Measurement and Instrumentation Techniques Appendix C: Uncertainty Budget Case Study: CMM Length Measurements Coordinate Measuring Machine (CMM) Measurements Product Acceptance Uncertainty: Dimensional Part Inspection with a CMM Radius of Curvature of a Spherical Mirror The Measurement Model Measurement Considerations Surface Form of the Mirror CMM Probing Force ROC Measurement Uncertainty Analysis CMM Measurement Process Uncertainty CMM Positioning Error (Standards) Fit Uncertainty Combined Standard Uncertainty: u(R) Final Results Related Reading Appendix D: Uncertainty Quick Reference GUM Method for Measurement Uncertainty Percentage Points of the t Distribution Guardbanding Symmetric Specification Limits Asymmetric Specification Limits One-Sided Specification Limits Metrology Reference Table Appendix E: R for Metrology Introduction Installation of R R Packages R for Metrology Summary References Index