Measurement Uncertainty and Probability

A measurement result is incomplete without a statement of its ‘uncertainty’ or ‘margin of error’. But what does this statement actually tell us? By examining the practical meaning of probability, this book discusses what is meant by a ’95 percent interval of measurement uncertainty’, and how such an interval can be calculated. The book argues that the concept of an unknown ‘target value’ is essential if probability is to be used as a tool for evaluating measurement uncertainty. It uses statistical concepts, such as a conditional confidence interval, to present ‘extended’ classical methods for evaluating measurement uncertainty. The use of the Monte Carlo principle for the simulation of experiments is described. Useful for researchers and graduate students, the book also discusses other philosophies relating to the evaluation of measurement uncertainty. It employs clear notation and language to avoid the confusion that exists in this controversial field of science.

Table of Contents

Part I Principles
Chapter 1 Foundational ideas in measurement
Chapter 2 Components of error or uncertainty
Chapter 3 Foundational ideas in probability and statistics
Chapter 4 The randomization of systematic errors
Chapter 5 Beyond the ordinary confidence interval

Part II Evaluation of uncertainty
Chapter 6 Final preparation
Chapter 7 Evaluation using the linear approximation
Chapter 8 Evaluation without the linear approximation
Chapter 9 Uncertainty information fit for purpose

Part III Related topics
Chapter 10 Measurement of vectors and functions
Chapter 11 Why take part in a measurement comparison?
Chapter 12 Other philosophies
Chapter 13 An assessment of objective Bayesian statistics
Chapter 14 Guide to the Expression of Uncertainty in Measurement
Chapter 15 Measurement near a limit – an insoluble problem?

Appendix A The weak law of large numbers
Appendix B The Sleeping Beauty paradox
Appendix C The sum of normal and uniform variates
Appendix D Analysis with one Type A and one Type B error
Appendix E Conservatism of treatment of Type A errors