2.2 Error Analysis
All measurements have some degree of uncertainty that may come from a
variety of sources. The process of evaluating the uncertainty associated
with a measurement result is often called error analysis. In flow
measurement terminology, the error is the difference between the true
value of a measurement and the recorded value of a measurement, which
can be classified into two broad categories.
A systematic error (or bias) refers to deviations that are not
due to the changes in flow. It occurs with a measuring device that is
faulty or improperly calibrated so that it consistently overestimates
(or underestimates) the measurements by X units. Systematic errors
cannot be reduced by taking more measurements. To reduce the systematic
error of a data set, researchers must identify the source of the error
and remove it. For example, the errors can be reduced by recalibrating
the flow meter. In other circumstances, the error could be due to the
inherent nature of the measuring technique. Hamouda et al (2016)
reported a scenario where an ultrasound flow meter measured fluid flow
rate based on transit time principle. This difference can be as low as a
few picoseconds, which give rise to technical difficulties in measuring
such a small time-difference with a given accuracy. This type of
systematic errors can be reduced by using more sensitive sensors or
avoiding conducting measurement in low flow range accuracy.
A random error is a deviation that randomly fluctuates over a
mean value. It has no preferred direction. It occurs because there are a
very large number of parameters beyond the control of the instrument
that may interfere with the results of the measurement. For example, a
random error occurs due to the instrument resolution (CDL 2020) and the
way it is affected by changes in the surroundings (Kalla 2009).
Nevertheless, the readings may be imprecise, but not inaccurate, as the
averaging over large number of observations will yield a net effect of
zero deviation.
According to definitions found in literature (CPL 2020),accuracy is defined as the closeness of agreement between a
measured value and a true or accepted value. Accuracy is often reported
quantitatively by using relative error:
\(Relative\ Error=\frac{Measured\ value-Expected\ value}{\text{expected\ value}}\)… (5)
Meanwhile, precision is the degree of consistency among
independent measurements of the same quantity; also described as the
reliability or reproducibility of the result (CPL 2020). Precision is
often reported quantitatively by using relative or fractional
uncertainty:
\(Relative\ Uncertainty=\left|\frac{\text{Uncertainty}}{\text{measured\ quantity}}\right|\)…. (6)
Uncertainty analyses are essential to determine whether
measurement systems are capable of meeting performance targets.
According to ISO-5168, the uncertainty of a flow measurement should be
specified at a confidence level of 95%, which corresponds to two
standard deviations.
\(v=\overset{\overline{}}{v}\pm 2\sigma_{v}\) …. (7)
where \(\overset{\overline{}}{v}\) is mean velocity and \(\sigma_{v}\)is the standard deviation of flow data.
In summary, random error corresponds to imprecision (or repeatability),
and bias to inaccuracy.