A practical reference on theory and methods of estimating measurement errors and uncertainty for both scientists and engineers in industry and experimental research. Building on the fundamentals of measurement theory, this book offers a wealth of practial recommendations and procedures. It differs from the majority of books in that it balances coverage of probabilistic methods with detailed information on the characterization, calibration, standardization and limitations of measuring instruments, with specific examples from both electrical and mechanical systems. In addition to a general updating to reflect current research, new material in this edition includes increased coverage of indirect measurements, with a new, simpler, more efficient method for this class of measurements.

This hands-on guide is primarily intended to be used in undergraduate laboratories in the physical sciences and engineering. It assumes no prior knowledge of statistics. It introduces the necessary concepts where needed, with key points illustrated with worked examples and graphic illustrations. In contrast to traditional mathematical treatments it uses a combination of spreadsheet and calculus-based approaches, suitable as a quick and easy on-the-spot reference. The emphasis throughout is on practical strategies to be adopted in the laboratory. Error analysis is introduced at a level accessible to school leavers, and carried through to research level. Error calculation and propagation is presented though a series of rules-of-thumb, look-up tables and approaches amenable to computer analysis. The general approach uses the chi-square statistic extensively. Particular attention is given to hypothesis testing and extraction of parameters and their uncertainties by fitting mathematical models to experimental data. Routines implemented by most contemporary data analysis packages are analysed and explained. The book finishes with a discussion of advanced fitting strategies and an introduction to Bayesian analysis.

Measurement shapes scientific theories, characterises improvements in manufacturing processes and promotes efficient commerce. In concert with measurement is uncertainty, and students in science and engineering need to identify and quantify uncertainties in the measurements they make. This book introduces measurement and uncertainty to second and third year students of science and engineering. Its approach relies on the internationally recognised and recommended guidelines for calculating and expressing uncertainty (known by the acronym GUM). The statistics underpinning the methods are considered and worked examples and exercises are spread throughout the text. Detailed case studies based on typical undergraduate experiments are included to reinforce the principles described in the book. This guide is also useful to professionals in industry who are expected to know the contemporary methods in this increasingly important area. Additional online resources are available to support the book at www.cambridge.org/9780521605793.

Problems after each chapter

The uncertainty of measurement results is drawing attention of managers, metrologists and customers. The accuracy of measurements affects all of us in trade, commerce, safety, health care environmental protection and more. The quality of these measurements are regulated by a variety of government agencies. Measurement also plays an important role in manufacturing and service organizations. Use this book to learn more about metrology and the need for reliable measurements. You can also learn about measurement system and quality of measurement systems, objectives and methods. Statistical techniques in metrology are also explained. Examples of measurement data and random variables, probability density functions, sampling distribution, statistical estimation degrees of freedom and regression are included. An entire chapter is devoted to measurement errors. The book goes in-depth into explaining national and international measurement systems and standards, and includes a complete chapter on calibration and measurement trace ability. Measurement Uncertainty will show how to evaluate various uncertainties in measurements using several approaches including international consensus. Calibration laboratories can look specifically at the chapter on that profession to guide them in their measurement improvements. Kimothi also looks at specific industries and their measurement capabilities and includes examples of R&R studies. A great resource for the CQE, CQT, CCT, CSSBB certification exams!

This book fulfills the global need to evaluate measurement results along with the associated uncertainty. In the book, together with the details of uncertainty calculations for many physical parameters, probability distributions and their properties are discussed. Definitions of various terms are given and will help the practicing metrologists to grasp the subject. The book helps to establish international standards for the evaluation of the quality of raw data obtained from various laboratories for interpreting the results of various national metrology institutes in an international inter-comparisons. For the routine calibration of instruments, a new idea for the use of pooled variance is introduced. The uncertainty calculations are explained for (i) independent linear inputs, (ii) non-linear inputs and (iii) correlated inputs. The merits and limitations of the Guide to the Expression of Uncertainty in Measurement (GUM) are discussed. Monte Carlo methods for the derivation of the output distribution from the input distributions are introduced. The Bayesian alternative for calculation of expanded uncertainty is included. A large number of numerical examples is included.

The expression of uncertainty in measurement poses a challenge since it involves physical, mathematical, and philosophical issues. This problem is intensified by the limitations of the probabilistic approach used by the current standard (the GUM Instrumentation Standard). This text presents an alternative approach. It makes full use of the mathematical theory of evidence to express the uncertainty in measurements. Coverage provides an overview of the current standard, then pinpoints and constructively resolves its limitations. Numerous examples throughout help explain the book’s unique approach.