Description
In writing this book, we address several groups of readers who require an understanding of measurement, and of uncertainty in measurement, in science and technology.
Undergraduates in science, for example, should have texts that set out the concepts and terminology of measurement in a clear and consistent manner. At present, students often encounter texts that are mutually inconsistent in several aspects. For example, some texts use the terms error and uncertainty interchangeably, whilst others assign them distinctly different meanings. Such inconsistency is liable to confuse students, who are consequently unsure about how to interpret and communicate the results of their measurements.
Until recently, a similar lack of consistency affected those whose primary occupation includes measurement, the evaluation of uncertainty in measurement, instrument and artefact calibration and the maintenance of standards of measurement – that is, professional metrologists. International trade, for example, requires mutual agreement among nations on what uncertainty is, how it is calculated and how it should be communicated; for a global economy to work efficiently, lack of such agreement cannot be tolerated. In the mid 1990s, international bodies, charged with the definition, maintenance and development of technical standards and standards of measurement in a variety of fields, published and disseminated the Guide to the Expression of Uncertainty in Measurement – the ‘GUM’. These bodies included the Bureau International des Poids et Mesures (BIPM) or International Bureau of Weights and Measures, the International Standardisation Organisation (ISO) and the International Electrotechnical Commission (IEC). The GUM is being adopted worldwide by organisations representing a diversity of disciplines, such as calibration and testing laboratories in the physical and engineering sciences, in chemical and biochemical analytic work and related specialised areas of medical testing, in the certification of reference materials and, at the highest metrological level, in national measurement institutes.
Despite its prominence in all fields of measurement, theGUMis (in 2005) largely unknown amongst university and college academics. One of our goals in writing this book is to introduce the GUM and its essential statistical background to an undergraduate audience. We believe that adopting the methods described in the GUM at undergraduate level will confer improved clarity and consistency on the teaching and learning of errors and uncertainty, and on their expression. As use of the GUM grows in industrial and commercial laboratories, new generations of graduating students will require aworking knowledge of its methods and vocabulary as well as of the statistical principles that underpin them. In this book we have attempted to anticipate and address these needs.
We include introductory material in the early chapters, the level of which is consistent with first-year university courses. However, the book as a whole is likely to be of greater benefit to second-year students who have already had some exposure to laboratory work as well as a first-year course in calculus and some basic statistics. When dealing with statistical relationships, we have not attempted the rigour normally found in mathematical statistical texts, but have preferred to introduce them in an intuitively plausible way, often by means of figures and graphs.
We have made some use of Monte Carlo simulation (MCS) in the text. One reason is that the GUM, which advocates as a standard practice the law of propagation of uncertainties involving first-order derivatives of the inputs, nonetheless recognises the need for ‘other analytical or numerical methods’ (when a complicated relationship exists between a measurand and its inputs). One such method is MCS, and therefore some exposure to MCS is desirable. Another important reason, in an educational context, is that MCS can make a statistical process, summarised by a theoretical equation, ‘transparent’ to the reader in a way that a standard theoretical approach does not. MCS bears much the same relationship to theoretical statistics as experimental physics does to theoretical physics, and can be a valuable and accessible teaching tool, since all it requires is a personal computer, randomnumber- generating software and some programming or spreadsheet experience.