Basic Theory of Uncertainty Evaluation in Measurements

This chapter illustrates basic concepts necessary to justify and understand the uncertainty evaluations presented throughout this book. The aim is to provide a brief and practically useful explanation of fundamental concepts and equations, not a complete theory of measurement uncertainty (which could easily be the subject of an entire book). The main source for the symbols, terminology, and concepts used in this chapter is the authoritative document “Guide to the Expression of Uncertainty in Measurement”(GUM). The reader is also encouraged to refer to the “International Vocabulary of Metrology” (VIM), which has a more extensive discussion of terminology, sometimes with slight differences with respect to the GUM. Besides the basic elements of the GUM theory, this chapter illustrates how to handle uncertainties due to gain, offset, nonlinearity, and quantization errors. Such knowledge is necessary for understanding the accuracy specifications of many real-world instruments. The chapter concludes with examples, accompanied by relevant explanations, of accuracy specifications of actual instruments.