MEASUREMENTS OF ERROR
Measurement Error
No measurement can be made with perfection and accuracy, but it is important to find out what the
accuracy actually is and how different errors have entered into the measurement. Error occurs due
to several sources like human carelessness in taking reading, calculating and in using instrument
etc. Some of the time error is due to instrument and environment effects.
Errors come from different sources and are classified in three types:
1. Gross Error
2. Systematic Errors
3. Random Errors
Gross Error
The gross error occurs due to the human mistakes in reading or using the instruments. These errors
cover human mistakes like in reading, calculating and recordings etc. It sometimes occurs due to
incorrect adjustments of instruments.
The complete elimination of gross errors is impossible, but we can minimize them by the
following ways:
1. It can be avoided by taking care while reading and recording the measurement data.
2. Taking more than one reading of same quantity. At least three or more reading must be
taken by different persons.
Systematic Errors
A systematic error is divided in three different categories: instrumental errors, environmental errors
and observational errors.
1. Instrumental Errors
The instrument error generate due to instrument itself. It is due to the inherent shortcomings in
the instruments, misuse of the instruments, loading effects of instruments. For example in the
D’ Arsonval movement friction in bearings of various moving components may cause incorrect
readings. There are so many kinds of instrument errors, depending on the type of instrument used.
Instrumental errors may be avoided by
(a) Selecting a suitable instrument for the particular measurement application
(b) Applying correction factors after determining the amount of instrumental error
(c) Calibrating the instruments against a standard.
2. Environmental Errors
Environmental errors arise as a result of environmental effects on instrument. It includes conditions
in the area surrounding the instrument, such as the effects of changes in temperature, humidity,
barometric pressure or of magnetic or electrostatic fields.
For example when making measurements with a steel rule, the temperature when the
measurement is made might not be the same as that for which the rule was calibrated.
Environmental errors may be avoided by
(a) Using the proper correction factor and information supplied by the manufacturer of the
instrument.
(b) Using the arrangement which will keep the surrounding condition constant like use of air
condition, temperature controlled enclosures etc.
(c) Making the new calibration under the local conditions.
3. Observational Errors
These errors occur due to carelessness of operators while taking the reading. There are many
sources of observational errors such as parallax error while reading a meter, wrong scale selection,
the habits of individual observers etc.
To eliminate such observational errors, one should use the instruments with mirrors, knife
edged pointers, etc. Now a day’s digital display instruments are available, which are much more
versatile.
Random Errors
These errors are due to unknown causes and occur even when all systematic errors have been
accounted for. In some experiments some random errors usually occur, but they become important
in high-accuracy work.
These errors are due to friction in instrument movement, parallax errors between pointer and
scale, mechanical vibrations, hysteresis in elastic members etc.
When we measure a volume or weight, you observe a reading on a scale of some kind. Scales
by their very nature are limited to fixed increments of value, indicated by the division marks. The
actual quantities we are measuring, in contrast, can vary continuously. So there is an inherent
limitation in how finally we can discriminate between two values that fall between the marked
divisions of the measuring scale. The same problem remains if we substitute an instrument with
a digital display. There will always be some point at which some value that lies between smallest
divisions must arbitrarily toggle between two numbers on the readout display. This introduces
an element of randomness into the value we observe, even if the true value remains unchanged.
These errors are of variable magnitude and sign and do not obey any known law. The presences
of random errors become evident when different results are obtained on repeated measurements
of one and the same quantity
No measurement can be made with perfection and accuracy, but it is important to find out what the
accuracy actually is and how different errors have entered into the measurement. Error occurs due
to several sources like human carelessness in taking reading, calculating and in using instrument
etc. Some of the time error is due to instrument and environment effects.
Errors come from different sources and are classified in three types:
1. Gross Error
2. Systematic Errors
3. Random Errors
Gross Error
The gross error occurs due to the human mistakes in reading or using the instruments. These errors
cover human mistakes like in reading, calculating and recordings etc. It sometimes occurs due to
incorrect adjustments of instruments.
The complete elimination of gross errors is impossible, but we can minimize them by the
following ways:
1. It can be avoided by taking care while reading and recording the measurement data.
2. Taking more than one reading of same quantity. At least three or more reading must be
taken by different persons.
Systematic Errors
A systematic error is divided in three different categories: instrumental errors, environmental errors
and observational errors.
1. Instrumental Errors
The instrument error generate due to instrument itself. It is due to the inherent shortcomings in
the instruments, misuse of the instruments, loading effects of instruments. For example in the
D’ Arsonval movement friction in bearings of various moving components may cause incorrect
readings. There are so many kinds of instrument errors, depending on the type of instrument used.
Instrumental errors may be avoided by
(a) Selecting a suitable instrument for the particular measurement application
(b) Applying correction factors after determining the amount of instrumental error
(c) Calibrating the instruments against a standard.
2. Environmental Errors
Environmental errors arise as a result of environmental effects on instrument. It includes conditions
in the area surrounding the instrument, such as the effects of changes in temperature, humidity,
barometric pressure or of magnetic or electrostatic fields.
For example when making measurements with a steel rule, the temperature when the
measurement is made might not be the same as that for which the rule was calibrated.
Environmental errors may be avoided by
(a) Using the proper correction factor and information supplied by the manufacturer of the
instrument.
(b) Using the arrangement which will keep the surrounding condition constant like use of air
condition, temperature controlled enclosures etc.
(c) Making the new calibration under the local conditions.
3. Observational Errors
These errors occur due to carelessness of operators while taking the reading. There are many
sources of observational errors such as parallax error while reading a meter, wrong scale selection,
the habits of individual observers etc.
To eliminate such observational errors, one should use the instruments with mirrors, knife
edged pointers, etc. Now a day’s digital display instruments are available, which are much more
versatile.
Random Errors
These errors are due to unknown causes and occur even when all systematic errors have been
accounted for. In some experiments some random errors usually occur, but they become important
in high-accuracy work.
These errors are due to friction in instrument movement, parallax errors between pointer and
scale, mechanical vibrations, hysteresis in elastic members etc.
When we measure a volume or weight, you observe a reading on a scale of some kind. Scales
by their very nature are limited to fixed increments of value, indicated by the division marks. The
actual quantities we are measuring, in contrast, can vary continuously. So there is an inherent
limitation in how finally we can discriminate between two values that fall between the marked
divisions of the measuring scale. The same problem remains if we substitute an instrument with
a digital display. There will always be some point at which some value that lies between smallest
divisions must arbitrarily toggle between two numbers on the readout display. This introduces
an element of randomness into the value we observe, even if the true value remains unchanged.
These errors are of variable magnitude and sign and do not obey any known law. The presences
of random errors become evident when different results are obtained on repeated measurements
of one and the same quantity
Comments
Post a Comment