Measurement Models and Uncertainty

Abstract

To understand what measuring means, let's start from the definition of measurement, taken from the International Vocabulary of Metrology (VIM) [1]. MeasurementProcess of experimentally obtaining one or more quantity values that can reasonably be attributed to a quantity.So, a measurement process provides, as a part of the measurement result, one or more quantity values that can be attributed to a quantity intended to be measured, that is also called, always according to the VIM [1], measurand.To fully understand this definition, we have to refer to the definition of quantity. We can find it again in the VIM. QuantityProperty of a phenomenon, body, or substance, where the property has a magnitude that can be expressed as a number and a reference.The VIM states that a reference can be a measurement unit, a measurement procedure, a reference material, or a combination of such.When physical properties are considered, the reference is generally a measurement unit, whilst, when chemical measurement are considered, the reference is quite often a reference material.The quantity values provided by the measurement are therefore a number and a reference together expressing the magnitude of a quantity [1].Is this the measurement result? Or, better, can a measurement result be expressed only by a number and a reference? As we will see later in section 1.5 of this chapter, a measurement procedure cannot provide the "true" value of a measurand, due to a number of factors that we will thoroughly discuss later. This means that a measurement result can only provide a finite amount of information about the measurand, and we must know if that amount is enough for the intended use of the measurement result. Otherwise, the measurement result would be meaningless.Therefore, any measurement result has to be provided with an attribute capable of quantifying how close to the measurand's value the obtained quantity value is. This attribute is called uncertainty, and the correct definition of measurement result, as provided by the VIM, is as follows. Measurement resultSet of quantity values being attributed to a measurand together with any other available relevant information. JWBS163-c01 JWBS163-FerreroJuly 24, 2015 20:45 Printer Name: Trim: 6.125in × 9.25inMEASUREMENT ALONG THE CENTURIES 5In a note to this general definition, the VIM states that:A measurement result is generally expressed as a single measured quantity value and a measurement uncertainty.The above general definitions have introduced a number of concepts (quantity value, reference, relevant information, uncertainty), that will be covered in the next Sections, and show that a measurement is a definitely more complex procedure than simply reading an instrument.The science that includes all theoretical and practical aspects of measurement, regardless to the measurement uncertainty and field of application, is called metrology [1]. Its definition, as provided by the VIM, is as follows. MetrologyScience of measurement and its application As many other sciences that have a deep...

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