Discussion about errors during measurement by instruments

1. Submittedto:
Mr. Umesh Rathore
Professor
Dept of EIE
SLIET Longowal,Punjab(INDIA)
Submittedby:
Munesh Kumar Singh
Reg:PG-
Assignment On
Errors in Measuring Instrument
Course:ICE-8101

2. ICE/136323
M.Tech(ICE)-Ist
year
SLIET
Punjab(INDIA)
ERROR
Error is defined as a difference between the desired and actual performance or behavior of a systemor 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 systemunder 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
=
𝑒
𝑌𝑛
×100

3. Therefore % error = (
𝑌𝑛−𝑋𝑛
𝑌𝑛
) ×100
It is more frequently expressed as a accuracy rather than error.
Therefore A = 1-|
𝑌𝑛−𝑋𝑛
𝑌𝑛
|, where A is the relative accuracy.
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.

4. Some sources of systematic error are:
• 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 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.

5. 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
Randomerrors 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.
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.

6. 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=
1
𝑁
∑ 𝑥𝑁
𝑖=0 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.
 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 ±2%
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

7. 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.