Modern Measurements

Fundamentals and Applications

Alessandro Ferrero, Dario Petri, Paolo Carbone, Marcantonio Catelani, Alessandro Ferrero, Dario Petri, Paolo Carbone, Marcantonio Catelani

• Publisher: Wiley-IEEE Press
• Year: 2015
• Print ISBN: 9781118171318
• eBook ISBN: 9781119021339
• Edition: 1
• Topic: Tecnologia e ingegneria
• Subtopic: Ingegneria elettronica e telecomunicazioni

This book is a collection of chapters linked together by a logical framework aimed at exploring the modern role of the measurement science in both the technically most advanced applications and in everyday life

• Provides a unique methodological approach to understanding modern measurements
• Important methods and devices are presented in a synthetic and easy-to-understand way
• Includes end-of-chapter exercises and solutions

PART I
FUNDAMENTALS

CHAPTER 1
MEASUREMENT MODELS AND UNCERTAINTY

ALESSANDRO FERRERO¹ and DARIO PETRI²

¹Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, Milano, Italy

²Dipartimento di Ingegneria Industriale, Università degli Studi di Trento, Povo, Italy

1.1 INTRODUCTION

Nowadays, we are surrounded by measuring instruments and we use them several times a day, very often unconsciously and unaware of their complexity and accuracy. To realize how instruments have become a big part of our life, just think of how many times we read the speed indicator when we drive our car, the fuel indicator to know when we have to refill the tank, or, when we eventually refill it, the meter on the fuel pump.

Interestingly enough, we usually don’t pay too much attention to the accuracy of the instruments we use, even if we rely on their indication to make important decisions, such as, for instance, driving safely or paying the right amount of money for the quantity of good we purchase. Even more strangely, the only instrument we generally adjust to a reference is our watch, which is probably the most accurate instrument we use in our everyday life: even the cheapest ones don’t lag or lead for more than one second a day, which means that their relative accuracy is in the range of 1 · 10^{− 5}!

The above examples give us clear evidence that we do use and read instruments, but they still leave an important question open: are we also making a measurement? Trying to answer this question opens also another fundamental question: which is the difference between reading an instrument and making a measurement?

This chapter is aimed at providing an answer to this question.

1.2 MEASUREMENT AND METROLOGY

To understand what measuring means, let’s start from the definition of measurement, taken from the International Vocabulary of Metrology (VIM) [1].

Measurement

Process 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.

Quantity

Property 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 result

Set of quantity values being attributed to a measurand together with any other available relevant information.

In 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 V...

Table of contents

• Cover
• IEEE Press
• Title page
• Copyright
• PREFACE
• ACRONYMS
• PART I FUNDAMENTALS
• PART II APPLICATIONS
• PROBLEM SOLUTIONS
• INDEX
• EULA