3.1 Introduction
Errors in measurement systems can be
divided into those that arise during the measure[1]ment
process and those that arise due to later corruption of the measurement signal
by induced noise during transfer of the signal from the point of measurement to
some other point. This chapter considers only the first of these, with
discussion on induced noise being deferred to Chapter 5.
It is extremely important in any
measurement system to reduce errors to the minimum possible level and then to
quantify the maximum remaining error that may exist in any instrument output
reading. However, in many cases, there is a further complication that the final
output from a measurement system is calculated by combining together two or
more measurements of separate physical variables. In this case, special consid[1]eration must also
be given to determining how the calculated error levels in each separate
measurement should be combined together to give the best estimate of the most
likely error magnitude in the calculated output quantity. This subject is
considered in section 3.6.
The starting point in the quest to reduce the
incidence of errors arising during the measurement process is to carry out a
detailed analysis of all error sources in the system. Each of these error
sources can then be considered in turn, looking for ways of eliminating or at
least reducing the magnitude of errors. Errors arising during the measurement
process can be divided into two groups, known as systematic errors and random
errors.
Systematic errors describe errors in the
output readings of a measurement system that are consistently on one side of
the correct reading, i.e. either all the errors are positive or they are all
negative. Two major sources of systematic errors are system disturbance during
measurement and the effect of environmental changes (modifying inputs), as
discussed in sections 3.2.1 and 3.2.2. Other sources of systematic error
include bent meter needles, the use of uncalibrated instruments, drift in
instrument characteristics and poor cabling practices. Even when systematic
errors due to the above factors have been reduced or eliminated, some errors remain
that are inherent in the manufacture of an instrument. These are quantified by
the accuracy figure quoted in the published specifications contained in the
instrument data sheet.
Random errors are perturbations of
the measurement either side of the true value caused by random and
unpredictable effects, such that positive errors and negative errors occur in
approximately equal numbers for a series of measurements made of the same
quantity. Such perturbations are mainly small, but large perturbations occur
from time to time, again unpredictably. Random errors often arise when measure[1]ments are taken
by human observation of an analogue meter, especially where this involves
interpolation between scale points. Electrical noise can also be a source of
random errors. To a large extent, random errors can be overcome by taking the
same measurement a number of times and extracting a value by averaging or other
statistical techniques, as discussed in section 3.5. However, any
quantification of the measure[1]ment value and
statement of error bounds remains a statistical quantity. Because of the nature
of random errors and the fact that large perturbations in the measured quan[1]tity occur from
time to time, the best that we can do is to express measurements in probabilistic
terms: we may be able to assign a 95% or even 99% confidence level that the
measurement is a certain value within error bounds of, say, ลก1%, but we can
never attach a 100% probability to measurement values that are subject to
random errors.
Finally, a word must be said about
the distinction between systematic and random errors. Error sources in the
measurement system must be examined carefully to deter[1]mine
what type of error is present, systematic or random, and to apply the
appropriate treatment. In the case of manual data measurements, a human
observer may make a different observation at each attempt, but it is often
reasonable to assume that the errors are random and that the mean of these
readings is likely to be close to the correct value. However, this is only true
as long as the human observer is not intro[1]ducing
a parallax-induced systematic error as well by persistently reading the
position of a needle against the scale of an analogue meter from one side
rather than from directly above. In that case, correction would have to be made
for this systematic error (bias) in the measurements before statistical
techniques were applied to reduce the effect of random errors.
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