Instrumentation and process control
Chapter-01
(Error)
-Asiqur Rahman Milon,EETE-DIU,EEE-IEB(Con)
What is Error?
- Instrument 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 (error). Measuringinstruments are usually
calibrated on some regular frequency against a standard.
Types
of Error?
- Types of Error
Error can be classified into three types:
1. Gross error
2. Systematic error
3. Random error
1. Gross error
2. Systematic error
3. Random error
1. Gross error-
These error are mainly
covers-
a)Human Error
b)Misreading of
instrument
c)Incorrect adjustment
d)Improper application
e)Computational
mistakes
These Error can be
minimized by adopting this two steps-
1)Great
care should be taken in reading and recording the data
2)Two or three more reading should be taken
for the quantity under measurement.
2. Systematic error
The systematic error can be classified into three types
• Instrumental error
• Environmental error
• Observation error
Instrumental
error:
The instrumental error occurs due to three reasons
• Due to inherent short comings of the instruments
• Due to the misuse of the instruments
• Due to the loading effect.
Inherent
shortcomings
These errors are due to construction, calibration and operation of instruments or measuring devices. Due to this error the instruments may read too high or too low.
For example, if the spring of permanent magnet has become very weak, then the instrument will always read very high.
To avoid these types of error
• The procedure of measurement must be carefully planned.
• Correction factors must be applied after determining the instrument errors
• An instrument can be re-calibrated carefully.
Misuse
of the instrument
When a good instrument is used in a unintelligent manner then it results in misuse of the instruments, thereby producing poor initial adjustment and zero adjustments.
Loading
effect
The loading effect occurs due to improper use of the instrument for measuring work.
For e.g. a well calibrated voltmeter may well mislead voltage when connected across a high resistance circuit. Similarly when the same voltmeter is connected across a low resistance value then it may give more dependable reading.
3.Environmental Errors-
These Error are due to external conditions during measurement.
a)Dusty Environment
b)Temperature change
c)Humidity
d)Vibrations
e)External magnetic fields
f)External Electrostatic field
As the name suggests, 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. In order to reduce the PARALLAX
error highly accurate meters are needed: meters provided with mirror scales.
3. Random error
These types of error remain after gross error and systematic error which can be totally reduced. These errors are due to small factors which changes very often from instrument to the other instrument. These errors are also due to unknown cases which are also called residual error.
Different
Types of Errors in Measurement and Measurement Error Calculation
Error
Formula
The measurement of an amount is based on some international standards
which are completely accurate compared with others. Generally, measurement of
any quantity is done by comparing it with derived standards with which they are
not completely accurate. Thus, the errors in measurement are not only due to error in methods, but
are also due to derivation being not done perfectly well. So, 100% measurement
error is not possible with any methods.
It is very important for the operator to take proper care of the experiment
while performing on industrial instruments so
that the error in measurement can be reduced. Some of the errors are constant
in nature due to the unknown reasons, some will be random in nature, and
the other will be due to gross blunder on the part of the experimenter.
Errors in Measurement System
An error may be defined as the difference between the measured value and
the actual value. For example, if the two operators use the same device or
instrument for finding the errors in measurement, it is not necessary that they
may get the similar results. There may be a difference between both
measurements. The difference that occurs between both the measurements is
referred to as an ERROR.
Sequentially, to understand the concept of errors in measurement, you
should know the two terms that define the error. They are true value and
measured value. The true value is impossible to find out the truth of quantity
by experimental means. It may be defined as the average value of an infinite
number of measured values. Measured value can be defined as the estimated value
of true value that can be found by taking several measured values during an
experiment.
Types of Errors in
Measurement System
Generally errors are classified into three types: systematic errors,
random errors and blunders.
1) Gross Errors
2) Blunders
3) Measurement Errors
2) Blunders
3) Measurement Errors
Systematic
Errors
- Instrumental
Errors
- Environmental Errors
- Observational Errors
- Theoretical
Errors
Random
Errors
Types
of Errors in Measurement System
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. It may be due to the person’s bad habit of not properly remembering
data at the time of taking down reading, writing and calculating, and then
presenting the wrong data at a later time. 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.
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.
3)
Measurement Error
The measurement error is
the result of the variation of a measurement of the true value. Usually,
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 10002grams, then
The measurement error is = (1002grams-1000grams) =2grams
Measurement Errors are classified into two types: systematic error and
random errors
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. These errors may be classified into different
categories.
Systematic
Errors
In order to understand the concept of systematic errors, let us classify
the errors as:
- Instrumental
Errors
- Environmental
Errors
- Observational
Errors
- Theoritical
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.
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.
Observational
Errors
As the name suggests, 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. In order to reduce the PARALLAX error
highly accurate meters are needed: meters provided with mirror scales.
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 actually does, then this factor will
begin a source of error in measurement.
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 a
large number of readings.
Random
Errors
Measurement Error Calculation
There are several ways to make a reasonable measurement error
calculation such as estimating random errors and estimating systematic errors.
Estimating
Random Errors
There are a number of 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 and standard
deviation (x ̅ & σ_x )
from this data.
The mean x ̅ is defined as
Where, Xi is the result of the i th measurements
‘N’ is the number of measurements
The standard variation is given by
If a measurement is repeated many times, then 68% of the measured valves
will drop in the range x ̅ ± σ_x
We become more positive that , is an accurate representation of the true
value of the quantity x ̅ . The standard deviation of the mean σ_x is defined as
σ_(x ̅ )=σ_x⁄√N
The quantity σ_x is a good estimate of our uncertainty in x ̅. Notice that the measurement precision
increases in proportion to √N as we increase the number of measurements.
The following example will clarify these ideas. Assume you made the following
five measurements of a length:
Error
Calculations
Therefore, the result is 22.84±.08mm
In some cases, it is hardly useful to repeat a measurement many times.
In that situation, you can estimate frequently the error by taking account of
the smallest division of the measuring instrument.
For example, when using a meter stick, one can measure, perhaps a half
or sometimes even a fifth of a millimeter. So, the absolute error would be
estimated to be around 0.5 mm or 0.2 mm.
Thus, this is all about the various types of errors in measurement and
error measurement calculation
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