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Metrology General Measurement Concept

MEEG 219 Previous Lecture
• Metrology
• Measurement
• Measurand
• Standard
Module I : General Measurement Concept – Primary
– Secondary
Lecture 2 : Error, Accuracy and Precision
– Working
Bijendra Shrestha • Errors
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What about Errors? Absolute Error

True absolute error : Difference between the result of the
• Difference between the true value of measurement and the conventional true value of the
measurand and measured value quantity measured.
• Error = True value – Measured value = Result of measurement – True Value
Apparent Absolute error: If series of measurement are
made then Algebraic difference between one of the
results of measurement and the arithmetical mean

Error in measurement expressed or evaluated either as an

= Result of measurement – Arithmetic Value
absolute error or as a relative error.
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Relative Error
“No matter, how modern is the measuring instrument, how skillful
•Defined as results of the absolute error and the value of
is the operator, how accurate the measurement process, there
comparison used. would always be some error.”

•Value of comparison may be true value or arithmetic

•To minimize the error, a number of observations are made and their average is
mean for series of measurement taken as the value of that measurement.

The accuracy of measurement, and hence the error depends upon Single Sample Test:
many factor such as: if observation made under identical condition – Same observer, same
instrument and similar working conditions
•Calibration standard : caused due to the variation in the
calibrated scale from it’s normal value.
Multi Sample Test
•Environment: caused due to humidity condition, if observation made using alternate test condition – Different observer,
Temperature and altitude. different instrument, etc
•Workpiece • it avoids many controllable errors eg. Personal error, instrument error
•Instruments
•Person
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Types of Errors Gross Errors

• Gross Errors • Occur due to Human mistakes
• Systematic Errors • During reading instruments, recording &
– Instrumental Errors calculating results
– Environmental Errors • Probably impossible to eliminate the gross
– Observational Errors errors completely
– Avoidable Errors
• Random Errors

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Gross Errors Systematic Errors

I asked him to
weigh a box full
of water, he
• Errors related to equipment
weighed a box
full of wood chips
• Due to inaccuracy in system
• Predictable and expected

If properly analyzed they can be determined and

reduced.

Also called as controllable errors.

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Systematic Errors Systematic Errors

• Instrumental Errors • Environmental Errors

Due to Caused due to
– Inherent shortcomings in the – Variation in atmospheric condition at the place of
instruments measurement
– Misuse of instruments – eg: effect of pressure, temperature, humidity, dust,
– Assembly error vibrations, external magnetic or electrostatic fields

Note: Temperature is most significant factor which causes error in measurement due to
expansion or contraction of component being measured or of the instrument used for
measurement.

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Systematic Errors
Avoidable Errors

• Observational errors •Occur due to parallax, non alignment of work piece centers, improper
location of measuring instrument
Due to
– Carelessness of For eg: Placing thermometer in sunlight while measuring temperature
operators
– Parallax
– Less chance of
observational error in
instruments with digital
display

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Random Errors Accuracy vs. Precision

• Occur randomly and accidental in nature

• Unpredictable
• Difficult to eliminate but the results can be
corrected

• These include errors caused due to variation in

position of setting standard and work piece,
errors due to displacement of lever joints of Precise but not accurate Accurate but not precise
instruments, etc.
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Precision:
•It is the repeatability of the measuring process.
Methods of Measurement
•It indicates to what extent the identically performed measurements
agree with each other.
• Direct method of measurement
“If instrument is not precise it will give different results for the same
dimension when measured again and again.”
– no mathematical calculation
• Indirect method of measurement
– Parameters measured
Accuracy
•It is degree to which the measured value of the quality characteristic – Final value derived by mathematical relation
agrees with the true value. – eg.: Area = Length x Breadth
“Practically difficult to measure exactly true value and therefore
set of observation is made whose mean value is taken as the true
value of the quality measured.”
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Other methods of Measurement Instruments

• Serves as an extension of human faculties and enables to
determine the value of unknown quantity or variable which
• Fundamental method
his unaided human faculties cannot measure.
• Comparison method
• Substitutional method
• Transportation method • Measuring instrument provides information about the
• Differential method physical value of some variable being measured.
• Co incidence method
• Null method • Instrument would sense a physical parameter (e.g. velocity,
• Deflection method pressure, temperature, etc), process and translate it into
• Complimentary method format and range which can be interpreted by the observer.
• Composite method
• Element method • Instrument must also provide the controls by which the
• Contact and contactless method operator can obtain, manipulate and response to the
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Classification of Instrument
• The performance of an instrument is
The instruments may be classified as follows: described by means of quantitative qualities
• Absolute and secondary instruments termed as characteristics.
• Analog and Digital instruments – Static Characteristics : Quantities to be measured
are constant or vary slowly with time (accuracy,
• Mechanical, Electrical and Electronic instruments error, etc)
• Manual and automatic instruments – Dynamic Characteristics: measure a time varying
• Self-contained and remote indicating instruments process variable (Speed)
• Self operated and power operated instruments

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Static Characteristics Repeatability/Reproducibility

Important Parameter
• Repeatability describes the closeness of output readings
• Accuracy and Precision when the same input is applied repetitively over a short
• Repeatability/Reproducibility period of time, with the same measurement conditions,
• Tolerance same instrument and observer, same location and same
conditions of use maintained throughout.
• Range or span
• Linearity
• Reproducibility describes the closeness of output readings
• Sensitivity of measurement for the same input when there are changes in the method
• Threshold of measurement, observer, measuring instrument, location,
• Resolution conditions of use and time of measurement.
• Sensitivity to disturbance
• Hysteresis effects • Both terms thus describe output readings for the same
• Dead space input.

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Tolerance Linearity
• Defined as the maximum error expected in an instrument.
• Ability to reproduce the input characteristics symmetrically
• Explains the maximum deviation of an output component at
a certain value. • measurement system has a linear relationship between input
and output
• Change in output is proportional to the change in the value of
the measurand.
• Expressed by the straight line equation
Range or span
• Defined as the range of reading between minimum value and
maximum value for the measurement of an instrument.
Example: 0-20 V range of a multimeter

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Assignment I
Threshold
• The minimum value below which no output change can be
• Principle of measurement • Measuring Range
detected when the input of an instrument is increased gradually
• Method of measurement • Sensitivity
from zero is called the Threshold of the instrument.
• Nominal size • Scale Interval
• True size • Readability
• Threshold defines the minimum value of input which is • Actual size • Calibration
necessary to cause a detectable change from zero output. • Exact size • Magnification
• Approximate size • Repeatability
• Error of measurement • Reproducibility
• Correction • Hysteresis
• Reliability of measurement • Response time
• Verification • Bias
• Calibration • Inaccuracy
• Measuring Instrument • Uncertianity

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