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Error in Measurement
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Course: AECE-408
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ectronicsInstrumentationIslamicUnive
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rsity.
Submitted to:
Md. Khalid Hossain Jewel
Lecturer
Dept of AECE.
Islamic University, Kushtia.
Submitted by:
Sharat Chandra Barman
Roll: 0715029
Reg:1075
Sess:2007-2008
Dept of AECE.
ERROR
Error is defined as a difference between the desired and actual performance or behavior of a
system or object. Thus the deviation of the true value from the desired value in instrumentation
is called error.
ERROR IN MEASUREMENT
Measurement is the process of comparing an unknown quantity with an accepted standard
quantity. It involves connecting a measurement instrument into the system under
consideration and observing the resulting response on the instrument. The measurement thus
obtained is a quantitative measure of the so- called “true value” (since it is very difficult to
define the true value, the term “expected value” is used). Any measurement is affected by
many variables, therefore the results rarely reflect the expected value. For example, connecting
a measuring instrument into the circuit under consideration always disturbs value.
Some factors that affect the measurements are related to the measuring instruments
themselves. Other factors that are related to the person using the instrument .The degree to
which a measurement nears the expected value is expressed in terms of the error of
measurement.
Error may be defined as the absolute or as percentage of error.
Absolute error may be defined as the difference between the expected value of the variable
and the measured value of the variable, or
e=Yn-Xn
where
e=absolute error
Yn=expected value
Xn=measured value
Therefore % Error= (absolute value expected value) ×100
= ×100
Therefore % error = (
) ×100
It is more frequently expressed as a accuracy rather than error.
Therefore
A = 1-|
|, where A is the relative accuracy.
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Accuracy is expressed as % accuracy
a= 100%-%error,
a=A×100%,
where a is the % of accuracy.
TYPES OF ERROR
There are generally two types of error in measurement as static error and dynamic error. Static
error of a measuring instrument is the numerical difference between the true value of a quality
and its value of quantity and by measurement, i.e. repeated measurement of the same quantity
gives different indication. Dynamic error is the difference between the true value of a quantity
changing with time and the value indicated by the instrument.
Static errors are categorized as gross errors or human error, systematic error and random
errors.
1. GROSS ERROR
These errors are mainly due to human mistakes in reading or in using instruments or error in
recording observations. Error may also occur due to incorrect adjustment of instruments and
computational mistakes. These errors cannot be treated mathematically.
The complete elimination of gross error is not possible, but one can minimize them. Some
errors are easily detected while others may be elusive.
One of the basic gross errors that occur frequently is the improper use of an instrument. The
error can be minimized by taking proper care in reading and recording the measurement
parameter.
In general, indicating instruments change ambient conditions to some extent when connected
into a complete circuit. Due to minimizing this error one should be taken at least three separate
reading instead of being depended on one reading only.
2. SYSTEMATIC ERROR
Systematic errors are biases in measurement which lead to the situation where the mean of
many separate measurements differs significantly from the actual value of the measured
attribute. These errors occur due to shortcomings of the instrument, such as defective or worn
parts, or ageing or effects of the environment on the instrument. Therefore A constant uniform
deviation of the operation of an instrument is known as systematic error.
Some sources of systematic error are:
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• Errors in the calibration of the measuring instruments.
• Incorrect measuring technique: For example, one might make an incorrect scale Reading
because of parallax error.
• Bias of the experimenter. The experimenter might consistently read an instrument
incorrectly, or might let knowledge of the expected value of a result influence the
measurements.
There are basically three types of systematic errors:a. Instrumental errors.
b. Environmental errors.
c. Observational errors.
a. INSTRUMENTAL ERRORS
Instrumental error refers to the combined accuracy and precision of a measuring instrument,
or the difference between the actual value and the value indicated by the instrument.
These errors are inherent in measuring instruments, because of their mechanical structure. For
example, in the D’Arsonval movement, friction in the bearings of various moving components,
irregular spring tensions, stretching of the spring or reduction in tension due to improper
handling or over loading of the instrument.
Instrumental errors can be avoided by:i.
Selecting a suitable instrument for the particular measurement applications.
ii.
Appling correction factors after determining the amount of instrumental error.
iii.
Calibrating the instrument against a standard.
b. ENVIRONMENTAL ERRORS
An environmental error is an error in calculations that are being a part of observations due to
environment. Any experiment performing anywhere in the universe has its surroundings, from
which we cannot eliminate our system. The study of environmental effects has primary
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advantage of being able us to justify the fact that environment has impact on experiments and
feasible environment will not only rectify our result but also amplify it.
The environmental errors have different causes, which are widening with the passage of time,
as the research works telling us, including; temperature, humidity, magnetic field, constantly
vibrating earth surface, wind and improper lightening.
In high precision laboratories, where a slightest bug can destroy the whole system, removal or
at least minimizing the environmental errors proved to be very fruitful.
c. OBSERVATIONAL ERRORS
Observational errors are error introduced by the observer. The most common error is the
parallax error introduced in reading a meter scale, and the error of estimation when obtaining a
reading from a meter scale.
These errors are caused by the habit of individual observers. For example, an observer may
always introduce and error by consistently holding his head too far to the left while reading a
needle and scale reading.
In general, systematic errors can also be subdivided into static and dynamic errors. Static errors
are caused by limitations of the measuring device or the physical laws governing its behavior.
Dynamic errors are caused by the instrument not responding fast enough to follow the changes
in a measured variable.
3. RANDOM ERROR
Random errors are errors that remain after gross and systematic errors have been substantially
reduced or at least accounted for. Random errors are generally an accumulation of a large
number of small effects and may be of real concern only in measurements requiring a high
degree of accuracy. Such errors can be analyzed statically.
These errors are due to unknown causes, not determinable in the ordinary processor
making measurements. Such errors are normally small and follow the laws of probability.
Random errors can thus be treated mathematically.
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For example, suppose a voltage is being monitored by a voltmeter which is read at 15
minutes intervals. Although the instrument operates under ideal environmental conditions and
accurately calibrated before measurements, it still gives that vary slightly over the period of
observation. This variation cannot be corrected by any method of calibration or any other
known method of control.
SOURCES OF RANDOM ERROR:
The sources of error, other than the inability of a piece of hardware to provide true
measurements, are as follows:
1. Insufficient knowledge of process parameters and design conditions
2. Poor design.
3. Change in process parameters, irregularities, upsets, etc.
4. Poor maintenance.
5. Errors caused by person operating the instrument or equipment.
6. Certain design limitations.
ESTIMATING RANDOM ERRORS:There are several ways to make a reasonable estimate of the random error in a Particular
measurement. The best way is to make a series of measurements of a given Quantity (say, x)
and calculate the mean x , and the standard deviation σx from this data.
The mean is defined as
x=
i
Where xi is the result of the ith measurement and N is the number of measurements.
There are also other types of error:-.



limiting error
Parallax error.
Quantization error.
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 LIMITING ERRORS
Most manufacturers of measuring instruments specify accuracy within a certain % of a full
scale reading. For example, the manufacturer of a certain voltmeter may specify the instrument
to be accurate within
with full scale deflection .This specification is called the limiting
error. This means that a full scale deflection reading is guaranteed to be within the limit of 2%
of a perfectly accurate reading; however, with a reading less full scale, the limiting error
increases.
 PARALLAX ERROR
Parallax is an apparent displacement or difference in the apparent position of an object viewed
along two different lines of sight, and is measured by the angle or semi-angle of inclination
between those two lines.
Therefore A change in apparent position of an object, with respect to the reference marks(s) on
an instrument, caused by imperfect adjustment of the instrument or by a change in the position
of the observer or both called parallax error. It is also called instrumental parallax or error of
parallax.
To avoid this error separated everywhere by the same distance. The term is used, in particular,
in respect of lines and surfaces.
 QUANTIZATION ERROR
In analog to digital conversion, the difference between the actual analog value and
quantized digital value is called quantization error or quantization distortion. This error is either
due to rounding or truncation. The error signal is sometimes considered as an additional
random signal called quantization noise because of its stochastic behavior.
Book Ref:
Electronic Instrumentation
-By Kalsi, H.S.
The End
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