204
us to refine the distinction between direct and indirect (methods of) measurement
introduced above.
Let us then suppose that the measurand is defined as the volume of an iron rod at
the temperature of 293.15 K and that it has been established (by, say, an independent
measurement) that the current temperature is 287.65 K, possibly with some measurement uncertainty, which is not relevant here. There are at least three possible
strategies for coping with this situation:
• S1: Prior to measurement an empirical action is performed for changing the temperature to the specified value, thus operating what could be called an empirical
correction.
8
• S2: The difference between the specified and actual temperatures is taken into
account by suitably increasing definitional uncertainty, thus independently of
the way the measurement is performed; at the end measurement uncertainty is
compared with definitional uncertainty to check that the former is not lower than
the latter (which would mean that some resources were wasted in performing
unnecessarily accurate measurements).
9
• S3: Whether an empirical action is performed for changing the temperature or
not, both the current volume and the current (thus possibly modified) temperature are measured, and then their values are properly combined, by what could be
called a computational correction, to obtain a value for the measurand.
In all three of these strategies the measuring instrument is designed to empirically
interact with properties of the same kind as the measurand, i.e., the temperature of
the iron rod: according to the provisional characterization proposed above, these
cases would then be all classified as direct measurements. However, their analysis
in the light of the comparison proposed in Table 7.1 reveals some significant differences. Let us consider them with respect to one simple question: What if the model
of the measurand (and more generally of the object under measurement) is wrong?
• S1 does not actually rely on the model of the measurand, as all that is required
for justifying the choice of performing the empirical correction is the qualitative
hypothesis that the measurand somehow depends on temperature; were the
model discovered to be wrong—i.e., volume does not depend on temperature as
stated—this strategy would remain effective. When using this strategy, measurement results do not depend on the validity of the model of the measurand: even if
temperature did not depend on another property, such as pressure, as expected,
8 Given the VIM definition of as a “set of operations carried
out on a measuring system so that it provides prescribed [indication values] corresponding to given
values of a quantity to be measured” (JCGM, 2012: 3.11, adapted), this action could be also called
“adjustment of the measurement environment”.
9 As already mentioned in Footnote 14 of Chap. 3, definitional uncertainty is sometimes understood
simply as one of the components of measurement uncertainty, and as such can be combined with
the other components. We follow here the other approach, and consider it as the lower bound of the
result of such a combination.
7 Modeling measurement and its quality
us to refine the distinction between direct and indirect (methods of) measurement
introduced above.
Let us then suppose that the measurand is defined as the volume of an iron rod at
the temperature of 293.15 K and that it has been established (by, say, an independent
measurement) that the current temperature is 287.65 K, possibly with some measurement uncertainty, which is not relevant here. There are at least three possible
strategies for coping with this situation:
• S1: Prior to measurement an empirical action is performed for changing the temperature to the specified value, thus operating what could be called an empirical
correction.
8
• S2: The difference between the specified and actual temperatures is taken into
account by suitably increasing definitional uncertainty, thus independently of
the way the measurement is performed; at the end measurement uncertainty is
compared with definitional uncertainty to check that the former is not lower than
the latter (which would mean that some resources were wasted in performing
unnecessarily accurate measurements).
9
• S3: Whether an empirical action is performed for changing the temperature or
not, both the current volume and the current (thus possibly modified) temperature are measured, and then their values are properly combined, by what could be
called a computational correction, to obtain a value for the measurand.
In all three of these strategies the measuring instrument is designed to empirically
interact with properties of the same kind as the measurand, i.e., the temperature of
the iron rod: according to the provisional characterization proposed above, these
cases would then be all classified as direct measurements. However, their analysis
in the light of the comparison proposed in Table 7.1 reveals some significant differences. Let us consider them with respect to one simple question: What if the model
of the measurand (and more generally of the object under measurement) is wrong?
• S1 does not actually rely on the model of the measurand, as all that is required
for justifying the choice of performing the empirical correction is the qualitative
hypothesis that the measurand somehow depends on temperature; were the
model discovered to be wrong—i.e., volume does not depend on temperature as
stated—this strategy would remain effective. When using this strategy, measurement results do not depend on the validity of the model of the measurand: even if
temperature did not depend on another property, such as pressure, as expected,
8 Given the VIM definition of
out on a measuring system so that it provides prescribed [indication values] corresponding to given
values of a quantity to be measured” (JCGM, 2012: 3.11, adapted), this action could be also called
“adjustment of the measurement environment”.
9 As already mentioned in Footnote 14 of Chap. 3, definitional uncertainty is sometimes understood
simply as one of the components of measurement uncertainty, and as such can be combined with
the other components. We follow here the other approach, and consider it as the lower bound of the
result of such a combination.
7 Modeling measurement and its quality