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Unit 1
Concept of Measurement





A.Shanmugam M.Tech., MBA., (PhD)
Syllabus
General concept – Generalized measurement
system-Units and standards-measuring
instruments- sensitivity, readability, range of
accuracy, precision-static and dynamic response
repeatability- systematic and random errors-
correction, calibration, interchangeability
Definition
• Metrology is the name given to the science of
pure measurement.
• Engineering Metrology is restricted to
measurements of length & angle
• Measurement is defined as the process of
numerical evaluation of a dimension or the
process of comparison with standard
measuring instruments
Why measure things?
• Check quality?
• Check tolerances?
• Allow statistical process control (SPC)?
Need of Measurement
• Quality Control
• Establish standard
• To find fault
• Customer Satisfaction
• Validate the design
• Physical parameter into meaningful number
• True dimension
• Evaluate the Performance

Methods of Measurement
• Direct method
• Indirect method
• Comparative method
• Coincidence method
• Contact method
• Deflection method
• Complementary method

Direct method
• Measurements are directly obtained
– Ex: Vernier Caliper, Scales

Indirect method
• Obtained by measuring other quantities
– Ex : Weight = Length x Breadth x Height x Density


Comparative Method
• It’s compared with other known value
– Ex: Comparators
Coincidence method
• Measurements coincide with certain lines and
signals
Fundamental method
• Measuring a quantity directly in related with
the definition of that quantity
Contact method
• Sensor/Measuring tip touch the surface area
Complementary method
• The value of quantity to be measured is
combined with known value of the same
quantity
– Ex:Volume determination by liquid displacement
Deflection method
• The value to be measured is directly indicated
by a deflection of pointer
– Ex: Pressure Measurement
GENERALIZED MEASURING SYSTEM
Common elements of system
• Primary sensing element
• Variable conversion element
• Variable manipulation element
• Data transmission element
• Data processing element
• Data presentation element
Primary sensing
element
Variable conversion
element
Variable
manipulation element
Data transmission
element
Data processing
element
Data presentation
element
Temperature
Observer
Units and standards
SI: fundamental Units
Physical Quantity Unit Name Symbol
length meter m
mass kilogram kg
time second s
electric current ampere A
temperature Kelvin K
amount of substance mole mol
luminous intensity candela cd
SI: Derived Units
Physical Quantity Unit Name Symbol
area square meter m
2

volume cubic meter m
3

speed
meter per
second
m/s
acceleration
meter per
second squared
m/s
2

weight, force newton N
pressure pascal Pa
energy, work joule J
Supplementary units
Physical Quantity Unit Name Symbol
Plane angle Radian
rad
Solid angle Steradian
sr
Standards
• International standards
• Primary standards
• Secondary standards
• Working standards

International
International Organization of Legal Metrology, Paris
International Bureau of Weights and Measures at
Sevres, France
India
National Physical Laboratory
Dr. K.S. Krishnan Marg
New Delhi - 110012
India
Phone: 91-11-45609212
Fax: 91-11-45609310
Email: [email protected] or [email protected]




Measuring Instruments
• Deflection and null type instruments
• Analog and digital instruments
• Active and passive instruments
• Automatic and manually operated
instruments
• Contacting and non contacting instruments
• Absolute and secondary instruments
• Intelligent instruments.
DEFLECTION AND NULL TYPE
• Physical effect generated by the measuring
quantity
• Equivalent opposing effect to nullify the physical
effect caused by the quantity
ANALOG AND DIGITAL
INSTRUMENTS
• Physical variables of interest in the form of
continuous or stepless variations
• Physical variables are represented by digital
quantities
ACTIVE AND PASSIVE INSTRUMENTS
• Instruments are those that require some source
of auxiliary power
• The energy requirements of the instruments are
met entirely from the input signal
Automatic and manually operated
• Manually operated – requires the service of
human operator
• Automated – doesn't requires human
operator
Contacting And Non Contacting Instruments
• A contacting with measuring medium
• Measure the desired input even though they
are not in close contact with the measuring
medium
Absolute and Secondary Instruments
• These instruments give the value of the electrical
quantity in terms of absolute quantities
• Deflection of the instruments can read directly
Intelligent instruments
• Microprocessors are incorporated with
measuring instruments
Help topics
• http://www.tresnainstrument.com/education.
html
Characteristics of Measuring Instrument
• Sensitivity
• Readability
• Range of accuracy
• Precision
Definition
• Sensitivity- Sensitivity is defined as the ratio of
the magnitude of response (output signal) to the
magnitude of the quantity being measured
(input signal)
• Readability- Readability is defined as the
closeness with which the scale of the analog
instrument can be read
Definition
• Range of accuracy- Accuracy of a measuring
system is defined as the closeness of the
instrument output to the true value of the
measured quantity
• Precision- Precision is defined as the ability of the
instrument to reproduce a certain set of readings
within a given accuracy


Sensitivity
• If the calibration curve is liner, as shown, the sensitivity
of the instrument is the slope of the calibration curve.
• If the calibration curve is not linear as shown, then the
sensitivity varies with the input.
Sensitivity

This is the relationship between a change in the
output reading for a given change of the input.
(This relationship may be linear or non-linear.)

Sensitivity is often known as scale factor or
instrument magnification and an instrument with a
large sensitivity (scale factor) will indicate a large
movement of the indicator for a small input
change.
Load Cell
Force, F
Output, V
o

Output, V
o
(V)
Input, F
i
(kN)
Slope = 5 V/kN
K
Input, F (kN) Output, V
o
(V)
Sensitivity, K = 5 V/kN
Block Diagram:
Example
(1) A 0.01 W/A meter with 5 A fsd,
R
m
= W/A x A
= 0.01 x 5 = 0.05 W
V
max
across the Meter will be
= 5 A x 0.05 W
= 0.25 V for fsd.
(2) A 0.1 W/A meter with 5 A fsd,will drop 2.5 V
(i.e., it is 10 times less sensitive), which may bias
the results
Readability

• Readability is defined as the ease with which
readings may be taken with an instrument.
• Readability difficulties may often occur due to
parallax errors when an observer is noting the
position of a pointer on a calibrated scale
Readability
What is the value ?


What is the value ?

What is the value ?

Accuracy
• Accuracy = the extent to which a measured
value agrees with a true value
• The difference between the measured value &
the true value is known as ‘Error of
measurement’
• Accuracy is the quality of conformity
Example: Accuracy
• Who is more accurate when measuring a book that
has a true length of 16.5 cm?
A :
17.0 cm, 16.0 cm, 18.0 cm, 15.0 cm

B ::
15.5 cm, 15.0 cm, 15.2 cm, 15.3 cm
Precision
• The precision of a measurement depends on the
instrument used to measure it.
• For example, how long is this block?

How big is the beetle?
Measure between the head
and the tail!

Between 1.5 and 1.6 in

Measured length: 1.54 in

The 1 and 5 are known with
certainty

The last digit (4) is estimated
between the two nearest fine
division marks.
Example: Precision
Who is more precise when measuring the same 17.0
cm book?

A:
17.0 cm, 16.0 cm, 18.0 cm, 15.0 cm

B ::
15.5 cm, 15.0 cm, 15.2 cm, 15.3 cm
Accuracy vs. Precision
High Accuracy
High Precision
High Precision
Low Accuracy
Three targets
with three
arrows each to
shoot.
The person hit the bull's-eye?
Both
accurate
and precise
Precise but
not
accurate
Neither
accurate
nor precise
How do they
compare?
Can you define accuracy vs. precision?
Uncertainty
• The word uncertainty casts a doubt about the
exactness of the measurement results
• True value = Estimated value + Uncertainty
Why Is There Uncertainty?
• Measurements are performed with instruments,
and no instrument can read to an infinite number of
decimal places
•Which of the instruments below has the greatest
uncertainty in measurement?
Reading a Meterstick
. l
2
. . . . I . . . . I
3
. . . .I . . . . I
4
. . cm

First digit (known) = 2 2.?? cm
Second digit (known) = 0.7 2.7? cm
Third digit (estimated) between 0.05- 0.08 cm
Length reported = 2.77 cm
or 2.76 cm
or 2.78 cm
Known + Estimated Digits
In 2.77 cm…

• Known digits 2 and 7 are 100% certain

• The third digit 7 is estimated (uncertain)

• In the reported length, all three digits
(2.77 cm) are significant including the
estimated one
Performance of Instruments
• All instrumentation systems are characterized
by the system characteristics or system
response
• There are two basic characteristics of
Measuring instruments, they are
– Static character
– Dynamic character

Static Characteristics
• The instruments, which are used to measure
the quantities which are slowly varying with
time or mostly constant, i.e., do not vary with
time, is called ‘static characteristics’.
STATIC CHARACTERISTICS OF AN INSTRUMENTS
• Accuracy
• Precision
• Sensitivity
• Resolution
• Threshold
• Drift
• Error
• Repeatability
• Reproducibility

• Dead zone
• Backlash
• True value
• Hysteresis
• Linearity
• Range or Span
• Bias
• Tolerance
• Stability
Resolution

This is defined as the smallest input increment
change that gives some small but definite
numerical change in the output.
Threshold

This minimum value of input below which no
output can be appeared is known as threshold
of the instrument.
input
Output
Drift

Drift or Zero drift is variation in the output of
an instrument which is not caused by any
change in the input; it is commonly caused by
internal temperature changes and component
instability.

Sensitivity drift defines the amount by which
instrument’s sensitivity varies as ambient
conditions change.
input
Output
zero
drift
input
Output
sensitivity drift
input
Output
sensitivity drift
zero
drift
• Error – The deviation of the true value from
the desired value is called Error
• Repeatability – It is the closeness value of
same output for same input under same
operating condition
• Reproducibility - It is the closeness value of
same output for same input under same
operating condition over a period of time

Range
• The ‘Range’ is the total range of values which
an instrument is capable of measuring.
Hysteresis

This is the algebraic difference between the average
errors at corresponding points of measurement
when approached from opposite directions, i.e.
increasing as opposed to decreasing values of the
input.
Actual/ Input
Value
Measured
Value
Ideal
Hysteresis is
caused by
energy
storage/
dissipation in
the system.
Zero stability

The ability of the instrument to return to
zero reading after the measured has returned to
zero
Dead band


This is the range of different input values over
which there is no change in output value.
Linearity- The ability to reproduce the input
characteristics symmetrically and linearly
• Backlash – Lost motion or free play of
mechanical elements are known as backlash
• True value – The errorless value of measured
variable is known as true value
• Bias – The Constant Error
• Tolerance- Maximum Allowable error in
Measurement
Dynamic Characteristics
• The set of criteria defined for the
instruments, which are changes rapidly with
time, is called ‘dynamic characteristics’.
Dynamic Characteristics
• Steady state periodic
• Transient
• Speed of response
• Measuring lag
• Fidelity
• Dynamic error


• Steady state periodic – Magnitude has a
definite repeating time cycle
• Transient – Magnitude whose output does not
have definite repeating time cycle
• Speed of response- System responds to
changes in the measured quantity




• Measuring lag
– Retardation type :Begins immediately after the
change in measured quantity
– Time delay lag : Begins after a dead time after the
application of the input
• Fidelity- The degree to which a measurement
system indicates changes in the measured
quantity without error
• Dynamic error- Difference between the true
value of the quantity changing with time &
the value indicated by the measurement
system

Errors in Instruments
• Error = True value – Measured value
or
• Error = Measured value - True value

Types of Errors
• Error of Measurement
• Instrumental error
• Error of observation
• Based on nature of errors
• Based on control
Error of Measurement
• Systematic error -Predictable way in
accordance due to conditions change
• Random error - Unpredictable manner
• Parasitic error - Incorrect execution of
measurement

Instrumental error
• Error of a physical measure
• Error of a measuring mechanism
• Error of indication of a measuring instrument
• Error due to temperature
• Error due to friction
• Error due to inertia
Error of observation
• Reading error
• Parallax error
• Interpolation error
Nature of Errors
• Systematic error
• Random error
Based on control
• Controllable errors
– Calibration errors
– Environmental (Ambient /Atmospheric Condition)
Errors
– Stylus pressure errors
– Avoidable errors
• Non - Controllable errors
Correction
• Correction is defined as a value which is added
algebraically to the uncorrected result of the
measurement to compensate to an assumed
systematic error.
• Ex : Vernier Caliper, Micrometer


Calibration
• Calibration is the process of determining and
adjusting an instruments accuracy to make
sure its accuracy is with in manufacturing
specifications.

Interchangeability
• A part which can be substituted for the
component manufactured to the small shape
and dimensions is known a interchangeable
part.
• The operation of substituting the part for
similar manufactured components of the
shape and dimensions is known as
interchangeability.


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