206
• (Example 1) The volume of an object is related to its temperature, i.e., the network includes volume and temperature; the definition of the measurand specifies
a reference temperature, and the network allows us to correct the directly measured value of volume by taking into account the difference between the measured temperature and the specified temperature.
• (Example 2) The density of an object is related to its mass and volume, i.e., the
network includes density, mass, and volume, and allows us to compute a value of
density as a function of the measured values of mass and volume.
Hence, both examples refer to the model of the measurand, but only the first has to
do with the possible distinction between the effective property and the intended
property, as generated by some affecting properties (given that we would surely not
think of density as affected by mass and volume). This calls for a model-related
refinement of the characterization of the distinction between direct and indirect
(methods of) measurement proposed above. Hence, we revise Table 7.1 accordingly
by adding a middle column, where the left column is the same as in Table 7.1 and
Examples 1 and 2 are cases for the middle and the right columns, respectively.
It should be noted that all three methods include a mathematical model in the
form of a function by means of which a value for the measurand can be calculated
and its uncertainty evaluated, with the consequence that measurement cannot be a
purely empirical process: none of these methods can provide “pure data”. Only in
an abstract perspective, however, methods A, B, and C may be treated in an undifferentiated way, under the consideration that all of them require calculating a function “among all properties known to be involved in a measurement”, paraphrasing
from the previously quoted VIM definition of “measurement model” (JCGM, 2012:
2.48). Although the same formal rules for, say, uncertainty propagation apply to the
three cases, maintaining the distinctions presented in Table 7.2 seems to be helpful
for a better understanding of the structure of the measurement process and the role
of mathematical models in it.
This analysis shows that measurement methods can be classified according to
two general criteria, related
• (first criterion) to the way in which the measuring instrument is designed and
coupled with the object that carries the measurand and
• (second criterion) to the way in which the measurand is modeled and this model
is exploited to compute the measurement result.
In light of this distinction and in reference to the content of Table 7.2, method A (left
column) and method C (right column) may be acknowledged to be direct and indirect, respectively, according to these characterizations, where parts (i) and (ii) in the
two definitions below are based on the first and the second criteria, respectively:
a measurement is based on a direct method (as in the left column of Table 7.2) when(i) an
instrument is used that is coupled with the object carrying the measurand and is designed
to interact with instances of the general property of the measurand, and(ii) the model of the
measurand is only used in measurement for identifying the measurand
and:
7 Modeling measurement and its quality
• (Example 1) The volume of an object is related to its temperature, i.e., the network includes volume and temperature; the definition of the measurand specifies
a reference temperature, and the network allows us to correct the directly measured value of volume by taking into account the difference between the measured temperature and the specified temperature.
• (Example 2) The density of an object is related to its mass and volume, i.e., the
network includes density, mass, and volume, and allows us to compute a value of
density as a function of the measured values of mass and volume.
Hence, both examples refer to the model of the measurand, but only the first has to
do with the possible distinction between the effective property and the intended
property, as generated by some affecting properties (given that we would surely not
think of density as affected by mass and volume). This calls for a model-related
refinement of the characterization of the distinction between direct and indirect
(methods of) measurement proposed above. Hence, we revise Table 7.1 accordingly
by adding a middle column, where the left column is the same as in Table 7.1 and
Examples 1 and 2 are cases for the middle and the right columns, respectively.
It should be noted that all three methods include a mathematical model in the
form of a function by means of which a value for the measurand can be calculated
and its uncertainty evaluated, with the consequence that measurement cannot be a
purely empirical process: none of these methods can provide “pure data”. Only in
an abstract perspective, however, methods A, B, and C may be treated in an undifferentiated way, under the consideration that all of them require calculating a function “among all properties known to be involved in a measurement”, paraphrasing
from the previously quoted VIM definition of “measurement model” (JCGM, 2012:
2.48). Although the same formal rules for, say, uncertainty propagation apply to the
three cases, maintaining the distinctions presented in Table 7.2 seems to be helpful
for a better understanding of the structure of the measurement process and the role
of mathematical models in it.
This analysis shows that measurement methods can be classified according to
two general criteria, related
• (first criterion) to the way in which the measuring instrument is designed and
coupled with the object that carries the measurand and
• (second criterion) to the way in which the measurand is modeled and this model
is exploited to compute the measurement result.
In light of this distinction and in reference to the content of Table 7.2, method A (left
column) and method C (right column) may be acknowledged to be direct and indirect, respectively, according to these characterizations, where parts (i) and (ii) in the
two definitions below are based on the first and the second criteria, respectively:
a measurement is based on a direct method (as in the left column of Table 7.2) when(i) an
instrument is used that is coupled with the object carrying the measurand and is designed
to interact with instances of the general property of the measurand, and(ii) the model of the
measurand is only used in measurement for identifying the measurand
and:
7 Modeling measurement and its quality