Abstract
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.
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Notes
- 1.
The GUM uses also the term “level of confidence,” with the warning that it must not be taken as synonymous with the term “confidence level” used in the theory of confidence intervals. “The terms confidence interval (C.2.27, C.2.28) and confidence level (C.2.29) have specific definitions in statistics and are only applicable to the interval defined by U when certain conditions are met” (GUM, 6.2.2). In order to avoid confusion, we will always use the term “coverage probability.”
- 2.
- 3.
The illustrated model does not take into account dynamic errors, due, for example, to the limited bandwidth of the instrument. They can be modeled by a linear system (typically a lowpass filter) at the instrument input. If the bandwidth of the input signal x(t) is conveniently lower than the instrument bandwidth, dynamic errors can be neglected.
- 4.
Time measurements are affected also by “time noise,” commonly known as jitter. Jitter affects instrumentation, telecommunication appliances, etc., also in a complex way. Going deeper into this subject is far beyond the scope of this book.
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Cataldo, A. et al. (2020). Basic Theory of Uncertainty Evaluation in Measurements. In: Basic Theory and Laboratory Experiments in Measurement and Instrumentation. Lecture Notes in Electrical Engineering, vol 663. Springer, Cham. https://doi.org/10.1007/978-3-030-46740-1_1
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