This document discusses metrology and measurement. It defines metrology as the field concerned with measurement, including theoretical and practical problems related to measurement. It establishes metrology as including the establishment, reproduction, and transfer of measurement standards. The document outlines the principal fields of metrology, including establishing measurement units and standards, measurement methods and accuracy, measuring instruments, observer capabilities, and gauge design. It describes the types of metrology as scientific, industrial, and legal metrology. Scientific metrology deals with maintaining highest level standards. Industrial metrology ensures adequate functioning of instruments in industry. Legal metrology regulates measuring instruments. The document also discusses measurement units, errors, accuracy, precision, calibration, and factors that affect measurements

1. Metrology & Measurement

2. Definitions of Metrology
 Field of knowledge concerned with Measurement &
includes both theoretical & practical problems related to
measurement.
 Process of making extremely precise measurement.
 It is the documented control that all equipment is suitably
calibrated & maintained in order to perform its function &
give reliable results.
 The science concerned with the establishment,
reproduction & transfer of units of measurements & their
standards.

3. Principle Fields of Metrology & Its Related feilds
a. Establishing units of Measurement & their standards.
b. Measurements, methods, execution & estimation of their
accuracy.
c. Measuring instruments, Properties examined with respect
to their intended purpose.
d. Observers capabilities with reference to making
measurements.
e. Design, manufacturing & testing of gauges of all kinds.

4. Types of Metrology
1. Scientific Metrology:
 It deals with the organization & development of measurement
standards & with their maintenance at the highest level.
2. Industrial Metrology:
 It deals with the ensuring of the adequate functioning of measuring
instruments used in industry as well as in production & testing
Processes.
 It is necessary to work with quality in industrial activities.
3. Legal Metrology:
 It is concerned with the accuracy of measurements where these
have influence on the transparency of economical transactions,
health & safety.
 Its function is to regulate, advise, supervise & control the
manufacturing & calibration of measuring instruments.

5. Types of Metrology
 Fundamental Metrology:
 It may be described as scientific metrology, Supplemented by
those parts of legal & industrial metrology that requires
scientific competence.
 It is divided in accordance with the following eleven fields:
Mass, Electricity, Length, Time, Frequency, Ionizing radiations,
Radioactivity, Photometry, Radiometry, Flow , Acoustics,
Amount of Substance & Interdisciplinary metrology.

6. Need for Inspection
i. To ensure components & parts conform to the
established standards.
ii. To meet the interchangeability of manufacturer.
iii. To provide the means of finding the problem areas.
iv. To produce the parts having acceptable quality level.
v. To judge the possibility of rework of defective parts and
re-engineer the process.
vi. To purchase good quality of raw materials, tools &
equipment.

7. Metrological Terminologies
 Accuracy:
 The closeness of agreement between a test result & the accepted
reference value.
 Bias:
 The difference B/w the expectation of the test result & an accepted
reference value.
 Calibration:
 The set of operations that establish the relationship b/w values
indicated by instruments & the corresponding values given by
standards, under specified conditions.
 Confirmation:
 The set of operations required to ensure that an item of measuring
equipment is in a state of compliance with requirements for its
intended use.

8.  Correction:
 It is equal to the assume systematic error.
 As the systematic error can not be known exactly so correction is
subjected to uncertainty.
 Drift:
 A slow change of metrological characteristics of a measuring
instruments.
 Error:
 The indication of measuring instrument output minus the true value of
the input quantity.
 Expectation:
 The mean value of specified population of measurements.
 Fiducial error:
 The error of measuring instrument divide by Fiducial value specified
for the instrument.
 Fiducial value can be the span or upper limit of nominal range of
measuring instrument.

9.  Group Standard:
 A set of standards of chosen value that individually or in combination,
provide a series of values of the same kind.
 Inspection:
 It involves measurement investigation or testing of one or more
characteristics of a product.
 Magnification:
 The output signal from a measuring device is to be magnified many
times to make it more readable.
 Measurand:
 A particular quantity subjected to measurement.
 Nominal value:
 An approximate value of a measuring instrument that provide a guide to
use it.
 Precision:
 The closeness of agreement b/w independent test results obtained
under stipulated conditions.
 Range:
 The capacity with in which the instrument is capable of measuring.

10.  Readability:
 It refers to the ease with which the readings of a measuring instrument
can be read.
 Reference value:
 The value which agreed on reference for comparison.
 Repeatability conditions:
 Where independent test results are obtained using same methods, items,
place, operator & equipment with short interval of time.
 Reproducibility:
 Precession under reproducibility conditions.
 Reproducibility conditions:
 Where test results are obtained using same method & items but in
different place, operator & equipment.
 Response time:
 The time which elapse after sudden change of the measured quantity
until the instrument gives an indication.
 Resolution:
 The smallest change of the measured quantity which changes the
indication of a measuring instrument.

11.  Sensitivity:
 The smallest change in the value of the measured variable to which the
instrument responds.
 Stability:
 The ability of measuring instrument to constantly maintain its
metrological characteristics with time.
 Standardization:
 A process of formulating & applying rules for orderly approach to a
specific activity for the benefit & with the cooperation of all the
concerned in particular.
 Testing:
 A technical investigation to know whether the product fulfills its
specified performance.
 Traceability:
 Means that a measured result can be related to stated references.
 Trueness:
 The closeness of agreement b/w the average value obtained from a large
series of test results & an accepted reference value.
 It is usually expressed in terms if bias.

12.  Uncertainty:
 It is a parameter associated with the result of a measurement that
characterizes the dispersion of the values that could reasonably be
attributed to the Measurand.
 It can also be expressed as an estimate characterizing the range of
values with in which the true value of a Measurand lies.
 When specifying the uncertainty it is necessary to indicate the principle
on which the calculation has been made.
 Verification:
 An investigation that shows that specified requirements are fulfilled.

13. Principal Aspects of Measurement
 Accuracy:
 It is the degree to which the measured value of the quality
characteristics agree with the true value.
 It is referred to the absence of bias to the conformity of results
to the true value of quality characteristics being measured.
 The measured value is the is the sum of the quantity measured
& the error of the instrument.
 Standard deviation of measured value is:
• 𝜎 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 𝑣𝑎𝑙𝑢𝑒 = 𝜎2
𝑡𝑟𝑢𝑒 + 𝜎2 𝑒𝑟𝑟𝑜𝑟

14. Principal Aspects of Measurement
 Precision:
 It is the degree of repeatability in the measuring process.
 It refers to variability of a method when used to make repeated
measurements under specific conditions.
 It is mainly achieved by selecting a correct instrument
technology for application.
 For determining the right level of precision is that the
measuring device must be en times more precise than the
specified tolerances.

15. Methods of Measurements
1. Direct Method:
 This is the simplest method of measurement in which the value of
the quantity to be measured is obtained directly without any
calculations, e.g. measurements by scale, calipers & micrometers.
 It involves contact or non contact type of inspections.
2. Indirect Method:
 The value of the quantity to be measured is obtained by measuring
other quantities, which are related to required value.
 E.g. density calculation by measuring mass & volume.
3. Absolute Method:
 Also called fundamental method & is based on the measurement of
the base quantities used to define a particular quantity.

16. 4. Comparison Method:
 The value of quantity to be measured is compared with a known value of
a same or related quantity to it.
 E.g. dial indicators & other comparators.
5. Substitution Method:
 The quantity is measured by direct comparison on an indicating device
by replacing the measurable quantity with another which produces the
same effect on the indicating device.
6. Coincidence Method:
 There is a very small difference b/w the value of the quantity to be
measure & the reference.
 It is also called differential method of measurement.
7. Transposition Method:
 In this method the value of the quantity measured is first balanced by an
initial known value P of the same quantity.
 Then the value of the quantity measured is put in place of that known
value & is balanced again by another known value Q.
 Finally the value of the quantity is to be measured by 𝑃𝑄

17. 8. Deflection Method:
 The value of the quantity to be measured is directly indicated by
the deflection of a pointer on a calibrated scale.
 e.g. dial indicator.
9. Complementary Method:
 The value of the quantity measured is combined with a known
value of the same quantity.
 E.g. determining volume of solid by liquid displacement.
10. Method of Null Measurement:
 It is a method of Differential measurement.
 In this method the difference b/w measured & known value is
brought to zero.
 E.g. measurement by potentiometer.

18. Measuring Instruments & Their Selection
i. On the basis of Function:
a. Length Measuring Instruments
b. Angle Measuring Instruments
c. Surface Roughness Measuring Instruments
d. Shape Checking Instruments
ii. On the basis of Accuracy:
a. Most Accurate Instruments
b. Moderate Accurate Instruments
c. Below Moderate Accurate Instruments
iii. On the basis of Precision:
a. Precision Measuring instruments
b. Non Precision Measuring Instruments

19. Factors Affecting Accuracy of Measuring Instruments
1. Standards of Calibration for Setting Accuracy
2. Work piece control during Measurement
3. Inherent Characteristics of measuring instruments
4. Inspector (Human Factor)
5. Environmental Conditions

20. Errors in Measurement
Error in Measurement=Measured value-True Value
 Error may be Absolute or Relative.
1. Absolute Error:
It is divided into two types:
a. True absolute Error:
 It is defined as the algebraic difference b/w the result of measurement & the
conventional true value of the quantity Measured.
b. Apparent Absolute Error:
 It is defined as the algebraic difference b/w the arithmetic mean & one of the
results of measurement when a series of measurements are made.
 Absolute Error = |Actual Value-Approximate value|
If, absolute value = x & approximate value = x+dx, then
Absolute Error = dx

21. Errors in Measurement
2. Relative Error:
 It is the quotient of the absolute error to the true/ actual value
(may be true or arithmetic mean of a series of measurements)
Relative Error =
|𝐴𝑐𝑡𝑢𝑎𝑙 𝑉𝑎𝑙𝑢𝑒 −𝐴𝑝𝑝𝑟𝑜𝑥𝑖𝑚𝑎𝑡𝑒 𝑉𝑎𝑙𝑢𝑒|
|𝐴𝑐𝑡𝑢𝑎𝑙 𝑉𝑎𝑙𝑢𝑒|
Relative Error = dx/x
Percentile Error (Ep) = Relative Error * (100)

22. Errors in Measurement
3. Static Error:
 These are the result of physical nature of the various components of a
measuring system i.e. intrinsic imperfection or limitation
instruments.
 They are further classified as:
a. Reading Error:
 Errors when the line of sight is not perpendicular to the measuring
scale.
 Error = X tan θ
b. Characteristic Error:
 It is the deviation of the system output from
the theoretical predicted performance.
 Linearity, repeatability, hysteresis & resolution
error are its types.

23. Errors in Measurement
c. Alignment error:
 This occurs when the checking of an instrument is not correctly
aligned with the direction of the desired measurement.
= D(1 – cos θ)
 To avoid alignment error Abbe’s Principle has to be followed which
states that:
“the axis or line of measurement should coincide with the axis
of the measuring instrument or the line of the measuring scale”

24. Errors in Measurement
d. Environmental Error:
 The error arising from the effect of the surroundings like pressure,
temperature, humidity, magnetic & electric fields etc.
 It can be controlled by controlling the atmospheric factors.
4. Loading error:
 If the datum surface is not flat or if foreign matters like dirt, chips
etc. get entrapped b/w the datum & work piece then there will be
Loading error.
 Also poor contact b/w instrument & work piece can cause this.
 To avoid such errors an instrument with wide area of contact should
not be used.
5. Dynamic error:
 It is caused by time variation in the Measurand. It is the result of
incapability of the system to respond reliably to time varying
measurement.
 Inertia, damping & friction are causes of dynamic error.

25. Errors in Measurement
 Analysis of accumulation of error by the statistical method categorizes
as controllable & random errors
a. Controllable Error:
 These are controllable in both magnitude & sense.
 They are repetitive in nature & are of similar forms
 These are also called systematic errors. They include the following
errors:
i. Calibration Error:
 Caused due to the variation in the calibrated scale from its
normal indicating value.
ii. Stylus pressure error:
 The too small or too large pressure applied on a work piece while
measuring causes stylus pressure.
iii. Avoidable Error:
 These errors occur due to parallax & non alignment of the work
piece.

26. Errors in Measurement
b. Random Error:
 These errors are accidental, non consistent in nature.
 As they occur randomly they cannot be eliminated since no
definite cause can be located.
 Small variation in the setting standards & the work piece can
cause such errors.

27. Units of Measurements (Base)

28. Units of Measurements (Derived)

29. Units of Measurements (SI Prefixes)