59
3.2.5 Measurement uncertainty and measurement results
As construed in the uncertainty approach and specified by the GUM, measurement
uncertainty is a quantity associated with measurement results and inversely related
to the quality of the information they convey: the greater the uncertainty, the lower
the quality.
15
There is an open debate about what, specifically, is uncertain when
measurement uncertainty is stated (the measured value? the measurement result?
the estimate of the true value of the measurand? …: see, e.g., the mention in JCGM,
2008a: 2.2.4), but the general agreement seems to be that measurement uncertainty
is an encompassing entity aimed at summarizing the quality (and quantity) of information acquired through the measurement. The components discussed above synthesize the quality-related aspects of a measurement system and, independently of
the way they are evaluated, by either statistical or nonstatistical methods, they can
be in turn synthesized into a single, overall combined standard measurement uncertainty (JCGM, 2012: 2.31).
The model proposed by the GUM on this matter can be first considered as a black
box. By quoting again the BIPM/CIPM recommendation of 1980, “the combined
uncertainty and its components should be expressed in the form of standard deviations” (JCGM, 2008a: 0.7): from a list of standard deviations, one for each identified component, a standard deviation must be computed as result. There is nothing
new in this problem, and in fact the recommendation states that “the combined
uncertainty should be characterized by the numerical value obtained by applying
the usual method for the combination of variances” (JCGM, 2008a: 0.7). This reinterprets, in the context of the uncertainty approach, what is traditionally called the
“law of error propagation” (see, e.g., Bevington, 1969: p. 58; see also Box 3.1),
which is based on a partial sum of the Taylor series expansion of the function by
which a value of the measurand is computed, about the measured value and usually
computed only in its first-order terms under the hypothesis of sufficient linearity of
the function at the measured value.
The conclusion reached in Chap. 2 about how to report the information obtained
by a measurement may be revised accordingly, and then written as
measurand measured value of a property combined measurement
,
u uncertainty
15 Measurement uncertainty is dependent on the quality of measurement results given the available
information, not in any “absolute” sense. As remarked by Ignazio Lira, “at first sight this is intuitively correct: if two results of the same quantity are available, the one having a smaller uncertainty
will be better than the other. However, by itself the uncertainty says nothing about the care put into
modelling the measurand, performing the actual measurements and processing the information
thus obtained. For example, a small uncertainty may be due to the fact that some important systematic effect was overlooked. Hence, the quality of a measurement can be judged on the basis of its
stated uncertainty solely if one is sure that every effort has been taken to evaluate it correctly”
(2002: p. 44).
3.2 The quality of measurement and its results
3.2.5 Measurement uncertainty and measurement results
As construed in the uncertainty approach and specified by the GUM, measurement
uncertainty is a quantity associated with measurement results and inversely related
to the quality of the information they convey: the greater the uncertainty, the lower
the quality.
15
There is an open debate about what, specifically, is uncertain when
measurement uncertainty is stated (the measured value? the measurement result?
the estimate of the true value of the measurand? …: see, e.g., the mention in JCGM,
2008a: 2.2.4), but the general agreement seems to be that measurement uncertainty
is an encompassing entity aimed at summarizing the quality (and quantity) of information acquired through the measurement. The components discussed above synthesize the quality-related aspects of a measurement system and, independently of
the way they are evaluated, by either statistical or nonstatistical methods, they can
be in turn synthesized into a single, overall combined standard measurement uncertainty (JCGM, 2012: 2.31).
The model proposed by the GUM on this matter can be first considered as a black
box. By quoting again the BIPM/CIPM recommendation of 1980, “the combined
uncertainty and its components should be expressed in the form of standard deviations” (JCGM, 2008a: 0.7): from a list of standard deviations, one for each identified component, a standard deviation must be computed as result. There is nothing
new in this problem, and in fact the recommendation states that “the combined
uncertainty should be characterized by the numerical value obtained by applying
the usual method for the combination of variances” (JCGM, 2008a: 0.7). This reinterprets, in the context of the uncertainty approach, what is traditionally called the
“law of error propagation” (see, e.g., Bevington, 1969: p. 58; see also Box 3.1),
which is based on a partial sum of the Taylor series expansion of the function by
which a value of the measurand is computed, about the measured value and usually
computed only in its first-order terms under the hypothesis of sufficient linearity of
the function at the measured value.
The conclusion reached in Chap. 2 about how to report the information obtained
by a measurement may be revised accordingly, and then written as
measurand measured value of a property combined measurement
,
u uncertainty
15 Measurement uncertainty is dependent on the quality of measurement results given the available
information, not in any “absolute” sense. As remarked by Ignazio Lira, “at first sight this is intuitively correct: if two results of the same quantity are available, the one having a smaller uncertainty
will be better than the other. However, by itself the uncertainty says nothing about the care put into
modelling the measurand, performing the actual measurements and processing the information
thus obtained. For example, a small uncertainty may be due to the fact that some important systematic effect was overlooked. Hence, the quality of a measurement can be judged on the basis of its
stated uncertainty solely if one is sure that every effort has been taken to evaluate it correctly”
(2002: p. 44).
3.2 The quality of measurement and its results