210
alcohol in the tube of the thermometer is chosen, and a Basic Evaluation Scale of
position is built upon it:
for all X i
*
in the given set, X i
*
→ x i
where x i is the ith value in the scale (in millimeters, say). This scale is specific to
the given measuring instrument, and therefore may be called a local scale.
12
The fundamental structure of a direct measurement is in the relation between a
public scale and a local scale:
• The measurand is a property of the same kind as the properties in the public
scale, and measurement needs to produce measured values in the public scale.
• The measuring instrument performs a transduction from the property under measurement to a property of the same kind as the properties in the local scale (e.g.,
for a thermometer, from a temperature to a position), so that indication values are
values in the local scale (say, millimeters).
As we will see, the calibration of a measuring instrument may be interpreted as the
process of connecting a public scale with the local scale of the instrument. It is this
connection that makes it possible for a calibrated instrument to obtain a measurand
value from an instrument indication value, i.e., a value in a public scale from a value
in a local scale, as depicted in Fig. 7.3.
It is upon this idea that our structural model of direct measurement is grounded.
We next describe its components and how they are connected with each other, first
in the simpler case in which uncertainties are not included in the description and
12 By presenting public scales first and then local scales we are following a conceptual sequence
from what is outside the box, i.e., a measuring instrument, to what is inside the box. But in the
historical development public scales may be the outcome of the previous development of multiple
local scales and the assessment of their agreement. In the example of temperature, the first public
thermometric scales (e.g., Celsius and Fahrenheit) were developed only after several thermometers
were discovered to be in substantial agreement in their behavior (Chang, 2007).
Fig. 7.3 Calibration as a relation of a public scale and a local scale
7 Modeling measurement and its quality
alcohol in the tube of the thermometer is chosen, and a Basic Evaluation Scale of
position is built upon it:
for all X i
*
in the given set, X i
*
→ x i
where x i is the ith value in the scale (in millimeters, say). This scale is specific to
the given measuring instrument, and therefore may be called a local scale.
12
The fundamental structure of a direct measurement is in the relation between a
public scale and a local scale:
• The measurand is a property of the same kind as the properties in the public
scale, and measurement needs to produce measured values in the public scale.
• The measuring instrument performs a transduction from the property under measurement to a property of the same kind as the properties in the local scale (e.g.,
for a thermometer, from a temperature to a position), so that indication values are
values in the local scale (say, millimeters).
As we will see, the calibration of a measuring instrument may be interpreted as the
process of connecting a public scale with the local scale of the instrument. It is this
connection that makes it possible for a calibrated instrument to obtain a measurand
value from an instrument indication value, i.e., a value in a public scale from a value
in a local scale, as depicted in Fig. 7.3.
It is upon this idea that our structural model of direct measurement is grounded.
We next describe its components and how they are connected with each other, first
in the simpler case in which uncertainties are not included in the description and
12 By presenting public scales first and then local scales we are following a conceptual sequence
from what is outside the box, i.e., a measuring instrument, to what is inside the box. But in the
historical development public scales may be the outcome of the previous development of multiple
local scales and the assessment of their agreement. In the example of temperature, the first public
thermometric scales (e.g., Celsius and Fahrenheit) were developed only after several thermometers
were discovered to be in substantial agreement in their behavior (Chang, 2007).
Fig. 7.3 Calibration as a relation of a public scale and a local scale
7 Modeling measurement and its quality