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System Accuracy
Accuracy
(Webster)
.
Freedom from error or the absence of
error. Syn. precision, correctness, exactness. (In this
sense, the term is a qualitative, not quantitative, concept.)
Accuracy
(ISA)
.
In process instrumentation, degree of conformity
of an indicated value to a recognized accepted
standard value, or ideal value.
Accuracy, measured
(ISA)
.
The maximum positive and
negative deviation observed in testing a device under
specified conditions and by a specified procedure.
Accuracy of measurement
(NIST)
.
Closeness of the
agreement between the result of a measurement and
the value of the measurand
…
. Because accuracy is
a quantitative concept, one should not use it quantitatively
or associate numbers with it. (NIST also
advises that neither
precision
nor
inaccuracy
should
be used in place of
accuracy
.)
Error
(ISA)
.
In process instrumentation, the algebraic difference
between the indication and the ideal value
of the measured signal. It is the quantity that, algebraically
subtracted from the indication, gives the
ideal value.
Range
(ISA)
.
The region between the limits within which
a quantity is measured, received, or transmitted,
expressed by stating the lower and upper range values.
Rangeability
(recommended by IEH)
.
Rangeability of a
sensor is the measurement range over which the error
statement, in the units of a percentage of actual reading,
is guaranteed.
Repeatability
(ISA)
.
The closeness of agreement among a
number of consecutive measurements of the output
for the same value of the input under the same operating
conditions, approaching from the same direction,
for full-range traverses.
Repeatability
(NIST)
.
Closeness of agreement between
the results of successive measurements of the same
measurand carried out under the same conditions of
measurement .... Repeatability may be expressed
quantitatively in terms of the dispersion characteristics
of the results.
Reproducibility
(ISA)
.
In process instrumentation, the
closeness of agreement among repeated measurements
of the output for the same value of input
made under the same operating conditions over a
period of time, approaching from both directions.
Reproducibility
(NIST)
.
Closeness of agreement between
the results of measurements of the same measurand
carried out under changed conditions of measurement.
Uncertainty
(Webster)
.
A feeling of unsureness about
something.
Uncertainty
(IEH
Section 1.5)
.
Measurement uncertainty is
expressed to a confidence level of 95%, and it is the
limit to which an error may extend.
Language, Terminology, and Reality
The guide titled
International Vocabulary of Basic and General
Terms in Metrology
(commonly referred to as
VIM
) was
published by ISO in the name of seven organizations and
contains the VIM definitions of 24 terms relevant to measurement
and accuracy. So, from a theoretical point of view, we
do have standards and internationally agreed upon definitions.
But the reality in the average industrial plant is different,
and this
Instrument Engineers’ Handbook
is written for the
average instrumentation and control (I&C) engineer in those
plants. Therefore, when we quantify an error herein, which
one should expect when making a measurement with a particular
instrument, we will not (yet) use terms such as
uncertainty
but will try to stay on familiar grounds. On the other
hand, we will try to take a step in the right direction by
improving the clarity of our language.
When an instrument is specified to have
±
1% accuracy,
people do not expect it to have 99% error! The intended meaning
of that statement is
±
1% inaccuracy or a
±
1% error relative
to some reference standard. It is important to emphasize the
role of a reference standard in all measurements, as we humans
are incapable of measuring anything in the absolute. All we
can do is compare an unknown quantity to a known one and
determine which is larger or smaller and by how much. The
presence of a reference also means that a measurement can be
in error not only because the sensor is inaccurate but also
because the reference has drifted or was inaccurate to start with.
CLARIFYING THE “ACCURACY” STATEMENT
In a volume dealing with process measurement, no subject
is more deserving of in-depth evaluation than the error that
is inherent in all measurement. Good control is possible only
if the controlled variable is precisely measured. Yet the term
accuracy
(or, more precisely,
inaccuracy
or
uncertainty
)
itself is poorly defined, frequently misunderstood, and often
used as a sales gimmick. Consequently, use of this term cries
out for international standardization and, as was noted above,
ISO has already prepared such standards. The need for clarity
of language and standardization exists for the following
reasons:
1. When the error or inaccuracy of an instrument is stated
to be
±
1%, one would assume that this statement refers
to the actual measurement—the actual reading. One
would assume that, if this particular instrument happens
to read 100, the true value of that measurement
must fall between 99 and 101, but this frequently is
not the case. Some manufacturers express their error
statements (inaccuracy percentages) on the basis of
“percent of actual span,” while others might base it on
“percent of full scale,” “percent of range,” or “percent
of upper range value,” and so on. This inconsistency
is undesirable, because it is confusing. It would be
better if all measurement error statements always
referred to the
actual measurement.
2. To make error statements expressed as percentages of
the actual measurement truly meaningful, the statement
should also specify the measurement range over
which the statement holds true. This would be a simple
matter if all manufacturers agreed to define
rangeability
as the
measurement range over which their error
statement (as a percentage of actual reading units) is
guaranteed
. This approach would allow all sensor inaccuracies
to be stated on the same basis and therefore
would eliminate the confusion. If all detector inaccuracies
were stated as “
x
% of actual reading throughout
the range of
y
,” users could be “comparing apples with
apples” when comparing bids, and the room for “creative
specmanship” would at least be reduced.
3. Further confusion occurs because different manufacturers
include different factors in their error statements.
Most suppliers include only linearity, rangeability, and
hysteresis errors in their total error statement; they list
the error contributions caused by drift, temperature
effects, overrange, power supply, humidity, RFI, and
vibration separately. Actually, some manufacturers
claim an apparent increase in accuracy not by improving
precision but by considering fewer and fewer effects in
the total error statement. Naturally, to reverse this trend,
international agreement is needed with regard to the
amount of variation (in ambient temperature, power
supply, and others) that the manufacturer’s error statements
must include.
4. Yet another source of confusion is the fact that, when
the error of 100 sensors is tested, the results fall onto
a “bell curve” (Figure 1.4a). It would be desirable to
reach international agreement so that all error statements
would always be based on the performance of at
least 95% of the units tested. In addition, an error statement
should always state if it is based on self-evaluation
performed by the supplier or on an evaluation by an
independent testing laboratory and, in the latter case, if
the test report is available for review.
If the above four recommendations were universally
accepted, the subject of sensor error and inaccuracy would
be much less confusing. While this is not likely to occur soon,
a better understanding of the factors that cause the present
state of confusion should be helpful, because it can speed
the development of universal standards for sensor error and
performance.
TERMINOLOGY OF INACCURACY AND REPEATABILITY
The purpose of all measurement is to obtain the true value
of the quantity being measured, and error is thought of as
the difference between the measured and the true quantity.
Because it is impossible to measure a value without some
uncertainty, it is equally impossible to know the exact size
of the error. What is possible is to state the limits within
which the true value of a measurement will fall.
The accuracy-related terminology used in the process
control industry can be illustrated by an example of target
shooting (
Figure 1.4b). The spread of the nine shots fired into
the upper right-hand corner of the target in a tight pattern
represents the random error of the shooter. Looking at the
penetration of the bullets, one can say that his shooting is
repeatable and precise, but precision alone does not guarantee
accuracy; it is only the measure of the ability of the shooter,
which is called
random error
.
FIG. 1.4a
In any measurement, the total uncertainty (total error) is the sum of
the sensor’s random error (precision) and its systematic error (bias).
http://abzardaghigh.ir/duh/doc_download/137-system-accuracy.html
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