Metrology is the science of measurements. As such, it deals with the problem of obtaining knowledge of physical reality through its quantifiable properties. The problems of measurement and of measurement accuracy are central to all natural and technical sciences. Now in its second edition, this monograph conveys the fundamental theory of measurement and provides some algorithms for result testing and validation.

Metrology is the science of measurements. As such, it deals with the problem of obtaining knowledge of physical reality through its quantifiable properties. The problems of measurement and of measurement accuracy are central to all natural and technical sciences. Now in its second edition, this monograph conveys the fundamental theory of measurement and provides some algorithms for result testing and validation.

This book focuses on effective methods for assessing the accuracy of both coordinate measuring systems and coordinate measurements. It mainly reports on original research work conducted by Sladek’s team at Cracow University of Technology’s Laboratory of Coordinate Metrology. The book describes the implementation of different methods, including artificial neural networks, the Matrix Method, the Monte Carlo method and the virtual CMM (Coordinate Measuring Machine), and demonstrates how these methods can be effectively used in practice to gauge the accuracy of coordinate measurements. Moreover, the book includes an introduction to the theory of measurement uncertainty and to key techniques for assessing measurement accuracy. All methods and tools are presented in detail, using suitable mathematical formulations and illustrated with numerous examples. The book fills an important gap in the literature, providing readers with an advanced text on a topic that has been rapidly developing in recent years. The book is intended for master and PhD students, as well as for metrology engineers working at industrial and research laboratories. It not only provides them with a solid background for using existing coordinate metrology methods; it is also meant to inspire them to develop the state-of-the-art technologies that will play an important role in supporting quality growth and innovation in advanced manufacturing.

This book provide a comprehensive set of modeling methods for data and uncertainty analysis, taking readers beyond mainstream methods and focusing on techniques with a broad range of real-world applications. The book will be useful as a textbook for graduate students, or as a training manual in the fields of calibration and testing. The work may also serve as a reference for metrologists, mathematicians, statisticians, software engineers, chemists, and other practitioners with a general interest in measurement science.

Measurement plays a fundamental role both in physical and behavioral sciences, as well as in engineering and technology: it is the link between abstract models and empirical reality and is a privileged method of gathering information from the real world. Is it possible to develop a single theory of measurement for the various domains of science and technology in which measurement is involved? This book takes the challenge by addressing the following main issues: What is the meaning of measurement? How do we measure? What can be measured? A theoretical framework that could truly be shared by scientists in different fields, ranging from physics and engineering to psychology is developed. The future in fact will require greater collaboration between science and technology and between different sciences. Measurement, which played a key role in the birth of modern science, can act as an essential interdisciplinary tool and language for this new scenario. A sound theoretical basis for addressing key problems in measurement is provided. These include perceptual measurement, the evaluation of uncertainty, the evaluation of inter-comparisons, the analysis of risks in decision-making and the characterization of dynamical measurement. Currently, increasing attention is paid to these issues due to their scientific, technical, economic and social impact. The book proposes a unified probabilistic approach to them which may allow more rational and effective solutions to be reached. Great care was taken to make the text as accessible as possible in several ways. Firstly, by giving preference to as interdisciplinary a terminology as possible; secondly, by carefully defining and discussing all key terms. This ensures that a wide readership, including people from different mathematical backgrounds and different understandings of measurement can all benefit from this work. Concerning mathematics, all the main results are preceded by intuitive discussions and illustrated by simple examples. Moreover, precise proofs are always included in order to enable the more demanding readers to make conscious and creative use of these ideas, and also to develop new ones. The book demonstrates that measurement, which is commonly understood to be a merely experimental matter, poses theoretical questions which are no less challenging than those arising in other, apparently more theoretical, disciplines.

This book presents a theory of measurement, one that is "abstract" in that it is concerned with highly general axiomatizations of empirical and qualitative settings and how these can be represented quantitatively.

The International System of Units (SI) is the world's most widely used system of measurement, used every day in commerce and science, and is the modern form of the metric system. It currently comprises the meter (m), the kilogram (kg), the second (s), the ampere (A), the kelvin (K), the candela (cd) and the mole (mol)). The system is changing though, units and unit definitions are modified through international agreements as the technology of measurement progresses, and as the precision of measurements improves. The SI is now being redefined based on constants of nature and their realization by quantum standards. Therefore, the underlying physics and technologies will receive increasing interest, and not only in the metrology community but in all fields of science. This book introduces and explains the applications of modern physics concepts to metrology, the science and the applications of measurements. A special focus is made on the use of quantum standards for the realization of the forthcoming new SI (the international system of units). The basic physical phenomena are introduced on a level which provides comprehensive information for the experienced reader but also provides a guide for a more intense study of these phenomena for students.