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GP 112 – Engineering Measurements
Lecture 3: Performance Indicators
by
Dr. S.K. Navaratnarajah
Department of Civil Engineering
Faculty of Engineering
Precision: - “spread of readings”
The precision is the repeatability of the measuring process.
- closeness of agreement between independent measurements of a
quantity under the same conditions.
It refers to the group of measurements taken for the same
characteristics under identical conditions.
If the instrument is not precise, it will give different (widely varying)
results for the same dimension when measured repeatedly.
The precision of a measuring instrument is determined by the
smallest unit to which it can measure.
High-precision instrument may have a low accuracy.
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Precision:
Precision refers to the reproducibility of a measurement
• Requires several measurements Precise
(notice multiple arrow holes)
• Has nothing to do with the true value Dart Board
(none of the values are close to the
target but all the holes are close)
Accuracy:
The accuracy is a measure of how
close the result of the measurement
comes to the ‘true values’.
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Precision and Accuracy:
Accurate Not Accurate
Precise
Precise and Accurate Precise but Not Accurate
Not Precise
Not Precise but Accurate Not Precise and Not Accurate
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Ex:
The speed of light is measured using different methods and the
results of the trials are shown in m/s.
(Actual value= 3.0 x 108 m/s)
Method A Method B Method C Method D
4.5 x 108 3.1 x 108 1.0 x 108 2.1 x 108
4.9 x 108 2.9 x 108 4.1 x 108 4.3 x 108
4.6 x 108 3.0 x 108 4.9 x 108 2.7 x 108
Which one of the methods has high accuracy and low precision?
Avg: 4.67 x 108 3.0 x 108 3.33 x 108 3.03 x 108
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Example:
In a calibration test, 10 measurements using a thermocouple have been made
of the temperature at the inlet of small steam turbine. The true temperature is
4000C. The readings are 400, 401, 398, 402, 402, 401, 399, 403, 402 and
3990C.
Estimate the systematic and maximum random errors caused by the
thermocouple.
Avg. = 400.7 0C; systematic error= (400.7-400)= 0.7 0C;
Max. Random Error = (400.7-398) = 2.7 0C
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Accuracy & Uncertainity - The most important concept:
accuracy /error is defined as the difference between the measured
value and the true value. In this sense, its definition is close to
uncertainty.
Manufacturers give usually the accuracy/error of their measurement
system.
Uncertainty in Hawk‐Eye Ball Tracking Technology used in DRS
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Accuracy/error is usually given as percentage of the full scale
output.
This is normal since the manufacturer cannot guarantee the same
error if the measurement system is used out of its range.
Full Scale Deflection (FSD)
Accuracy or error of an instrument is generally expressed as a %
of FSD (Full range).
- this means the same error or uncertainty can be applied to
any measurement, from every small value to all the way up
to full scale.
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For example, when you read 5% accuracy of the full scale and the
range of your system is 0 to 5 V, the uncertainty is ±0.25 V.
This is whatever the value you get in the range of the measurement
system.
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Example: An instrument is quoted as having an accuracy
(uncertainty) of 1.5% of FSD. The FSD is 150.
- Compute the error/uncertainty value at FS.
- Calculate the % errors of the instrument when it reads the
values of 75, 50, 25 and 10.
Answer:
i) Error value at FS = 1.5/100 x 150 = 2.25
ii) Possible error at 75 is still 2.25 which equates to an error of
2.25
100 3.0%
75
50 4.5%
25 9.0%
10 22.5% 12
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Ways to improve accuracy in measurements
1. Make the measurement with an instrument that has the highest
level of precision. The smaller the unit, or fraction of a unit, on the
measuring device, the more precisely the device can measure.
2. Know your tools!. Apply correct techniques when using the
measuring instrument and reading the value measured. (Avoid
parallax error).
3. Repeat the same measurement several times to get a good
average value.
4. Measure under control conditions. If the object you are
measuring could change size depending upon climatic conditions
(swell or shrink), be sure to measure it under the same conditions
each time. This may apply to your measuring instrument as well.
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Repeatability
The repeatability of a measuring system is its ability to display the
same reading for repeated measurement of the same quantity
(closely related to precision).
Reproducibility
The reproducibility or stability of a measuring system is its ability to
display the same reading when it is used to measure the same
quantity over a period of time or at different occasions.
Reliability
Reliability of a measuring system is the probability that it will operate
to an agreed level of performance under the conditions specified for
its use.
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Sensitivity
It is the ratio of the linear movement of the pointer on the instrument to the
change in the measured variable causing this motion or is the ratio of the
magnitude of output quantity(response) to the magnitude of the input
quantity.
d (output ) output
Sensitivity
d (input ) input
For ex, a 1 mV recorder might have a 10 cm scale. Its sensitivity would be
10 cm/mV, assuming that the measurement is linear all across the scale.
The static sensitivity of an
instrument can be defined as the
slope of the calibration curve.
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Resolution
Resolution is defined as the smallest increment of input signal that a
measuring system is capable of displaying.
Range (or Span)
The range/span of a measuring system defines the minimum and
maximum values of a quantity between which measurements are
intended to be made by the measuring system.
• The input range defines the minimum and maximum value of the
variable to measure.
I MAX I MIN
• The output range defines the minimum and maximum value of the
signal given by the transducer.
OMAX OMIN
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Threshold
The threshold of a measuring system is the smallest value of the
quantity being measured for which the system responds and gives
a detectable reading when the measured quantity is increased
from zero value.
Dead space
Output
The dead space of a measuring reading
system is the range of values of the
quantity being measured for which
there is no measurable response on
Measured
the measuring system. variable
The range of dead space is from Dead space
zero to threshold.
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Least count
The least count of an instrument is the smallest value it can measure.
Obviously, smaller the least count, larger the accuracy in the
measured value.
An instrument with a given least count cannot measure a value with an
error smaller than half the least count.
Instrument limit of error (ILE)
The instrument limit of error is the precision to which a measuring
device can be read, and is always equal to or smaller than the least
count.
The Instrument Limit of Error is generally taken to be the least count or some fraction (1/2, 1/5, 1/10)
of the least count). No hard and fast rules are possible, instead you must be guided by common sense.
If the space between the scale divisions is large, you may be comfortable in estimating to 1/5 or 1/10
of the least count. If the scale divisions are closer together, you may only be able to estimate to the
nearest 1/2 of the least count, and if the scale divisions are very close you may only be able to estimate
to the least count.
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Example: For each gray rod below, Determine the least count,
Instrument limit of error (ILE) and the length of the grey rod
(The scales are in centimeters)
Least Count (cm) ILE (cm) Length (cm)
(a) 1 0.2 9.6
(b) 0.5 0.1 8.5
(c) 0.2 0.05 11.90
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Lag
Lag
Thermometer Reading
The lag is the time required for the
measuring system to respond adequately Temperature
to the quantity being measured.
Linearity Time
• It is normally desirable that the output Gradient of the line =
reading of an instrument is linearly sensitivity of measurement
Omax
proportional to the quantity being
measured.
• An instrument is considered linear, if
the relationship between output and
input can be fitted in a line.
O OMIN Omin
O OMIN MAX I I MIN Imax
I MAX I MIN Imin
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Instrument Drift
• This is caused by variations taking place in the parts of the
instrumentation over time.
• Prime sources occur as chemical, structural changes and changing
mechanical stresses.
• Drift is a complex phenomenon for which the observed effects are
that the sensitivity and offset values vary.
• It also can alter the accuracy of the instrument differently at the
various amplitudes of the signal present.
• As a result of instrument drift, the measurements will be biased to
different values.
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Classification of Drift
EX:
A voltmeter has a least count of 0.5 V, an accuracy of
±0.5% at FSD of 100 V and a bias of +0.3 V.
What are possible readings of the voltmeter when measuring
a voltage of 10 V? 22
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Calibration of a Measuring System
Calibration is a comparison between a known
measurement (the standard) and the measurement
using your instrument under a specified
environmental condition.
A calibration may be carried out against a standard
device which should in general, be more accurate
than the measurement system.
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Why calibration is important?
The accuracy of all measuring devices degrade over time.
This is typically caused by normal wear and tear (‘aging’).
However, changes in accuracy can also be caused by electric or
mechanical shock.
Depending on the type of instrument and the environment in
which it is being used, it may degrade very quickly or over a long
period of time.
However, the calibration improves the accuracy of measuring
devices. Accurate measuring devices improve product quality.
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When should you calibrate
your measuring device?
A measuring device should be calibrated:
• According to recommendation of the
manufacturer.
• After any mechanical or electrical shock.
• Periodically (annually, quarterly, monthly)
Hidden costs and risks associated with the un-calibrated measuring
device could be much higher than the cost of calibration.
Therefore, it is recommended that the measuring instruments are
calibrated regularly to ensure that errors associated with the
measurements are in the acceptable range.
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Linear behaviour Non-linear behaviour
Calibration process may also create errors, if it is not properly done.
Such calibration errors might come from the fact that we mainly try to
force a linear behavior instead of truly non-linear behavior during
calibration process.
- systematic error
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Hysteresis errors
It should be noted that the accuracy of a measurement system can
be affected by hysteresis errors.
These errors are usually due to friction or electrical capacitance, for
example.
This will result in a lower precision, i.e. the measurement system will
not give the same value dependent on if the measurand was
increased or decreased prior to recording the measurand.
The hysteresis error is
considered as a ‘systematic
error’.
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