The document discusses various types of errors in instrumentation and measurements, including gross errors, blunders, and systematic errors such as instrumental, environmental, observational, and theoretical errors. It provides methods for reducing systematic errors and outlines the statistical analysis of measurements subject to random errors, emphasizing that averages can help mitigate these errors. Additionally, it covers the aggregation of errors from separate measurement system components.

1. Instrumentation
& Measurements
Engr. Taimoor Muzaffar Gondal
taimoor.muzaffar@superior.edu.pk
Faculty of Engineering & Technology
The Superior University Lahore
Spring-2022
Lecture-04
4/6/2022 LECTURE 04 1
Errors During the
Measurement Process

2. In this lecture
1
• Types of Errors in Instrumentation and Measurements
2
• Reduction of Systematic Errors
3
• Quantification of Systematic Errors
4
• Aggregation of measurement System Errors
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3. A. Types of Errors in Instrumentation
and Measurements
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Gross Errors Blunders
Measurement
Errors
Random Errors
Systematic
Error
Instrumental
Errors
Environmental
Errors
Observational
Errors
Theoretical
Errors

4. 1. Gross Errors
Gross errors are caused by mistake in using instruments or meters, calculating
measurement and recording data results.
The best example of these errors is a person or operator reading pressure gage 1.01N/m2
as 1.10N/m2.
This may be the reason for gross errors in the reported data, and such errors may end up
in calculation of the final results, thus deviating results.
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5. 2. Blunders
Blunders are final source of errors, and these errors are caused by faulty recording or due
to a wrong value while recording a measurement or misreading a scale or forgetting a digit
while reading a scale.
These blunders should stick out like sore thumbs if one person checks the work of another
person. It should not be comprised in the analysis of data.
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6. 3. Measurement Errors
The measurement error is the result of the variation of a measurement of the true value.
Measurement error consists of a random error and systematic error.
The best example of the measurement error is, if electronic scales are loaded with 1kg
standard weight and the reading is 10002 grams, then
The measurement error is = (1002 grams-1000 grams) = 2 grams
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7. 3.1: Systematic Errors
The Systematic errors that occur due to
fault in the measuring device are known
as systematic errors.
Usually, they are called as Zero Error: a
positive or negative error.
These errors can be detached by
correcting the measurement device.
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8. 3.1.1. Instrumental Errors
Instrumental errors occur due to wrong construction of the measuring instruments.
These errors may occur due to hysteresis or friction.
These types of errors include loading effect and misuse of the instruments.
In order to reduce the gross errors in measurement, different correction factors must be
applied and in the extreme condition instrument must be recalibrated carefully.
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9. 3.1.2. Environmental Errors
The environmental errors occur due to some external conditions of the instrument.
External conditions mainly include pressure, temperature, humidity or due to magnetic
fields.
In order to reduce the environmental errors
Try to maintain the humidity and temperature constant in the laboratory by making
some arrangements.
Ensure that there shall not be any external electrostatic or magnetic field around the
instrument.
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10. 3.1.3. Observational Errors
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These types of errors occurs due to wrong
observations or reading in the instruments
particularly in case of energy meter reading.
The wrong observations may be due to
PARALLAX (Eye Displacement Angle).
In order to reduce the PARALLAX error highly
accurate meters are needed: meters provided
with mirror scales.

11. 3.1.4. Theoretical Errors
Theoretical errors are caused by simplification of the model system.
For example, a theory states that the temperature of the system surrounding will not
change the readings taken when it does.
Then this factor will begin a source of error in measurement.
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12. 3.2. Random Errors
Random errors are caused by the sudden change in experimental conditions and noise and
tiredness in the working persons.
These errors are either positive or negative.
An example of the random errors is during changes in humidity, unexpected change in
temperature and fluctuation in voltage. These errors may be reduced by taking the average
of many readings.
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13. Errors in Electrical Circuits
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14. Example:
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15. B. Reduction
of systematic
errors
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CAREFUL
INSTRUMENT
DESIGN
METHOD OF
OPPOSING INPUTS
HIGH-GAIN
FEEDBACK
CALIBRATION MANUAL
CORRECTION OF
OUTPUT READING
INTELLIGENT
INSTRUMENTS

16. About Feedback System
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Open Loop System:
Close Loop System:

17. C. Quantification of systematic
errors
Unfortunately, it is not always possible to quantify exact values of a systematic error,
particularly if measurements are subject to unpredictable environmental conditions.
The usual course of action is to assume mid-point environmental conditions and specify
the maximum measurement error as +x% or –x% of the output reading to allow for the
maximum expected deviation in environmental conditions away from this mid-point.
Data sheets supplied by instrument manufacturers usually quantify systematic errors in
this way.
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18. D. More on Random errors
Random errors in measurements are caused by unpredictable variations in the
measurement system.
Therefore, random errors can largely be eliminated by calculating the average of several
repeated measurements.
The degree of confidence in the calculated mean/median values can be quantified by
calculating the standard deviation or variance of the data
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19. D.1: Statistical analysis of measurements
subject to random errors
Mean and median
values
Standard deviation and
variance
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20. D.2: Standard deviation and
variance
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Gaussian
distribution
Standard Gaussian
tables
Standard error of
the mean
Estimation of
random error in a
single
measurement
Distribution of
manufacturing
tolerances
Goodness of fit to
a Gaussian
distribution
Rogue data points
Special case when
the number of
measurements is
small

21. More about Statistical Analysis
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22. D.3: Aggregation of errors from separate
measurement system components
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Error in a
sum
Error in a
difference
Error in a
product
Error in a
quotient

23. End of Lecture-04
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