Vocabulary of Metrology
For Understating Uncertainty and
Traceability
Prepared by:
Kim, Sang Ho
Engineering Team Leader
Modal Shop, Inc
A PCB Group Company
SI
National
Metrology
Institute
Secondary
Calibration Lab
Control Standards
Working Standards
Uncertainty
o Quantity – property of a phenomenon, body, or
substance, where the property can be expressed
as a number and a reference
• Kinetic energy (T) - kinetic energy of particle i in a
given system (Ti)
• Heat (Q) -heat of vaporization of sample i of water
(Qi)
• Length (l), radius of a circle (r), wavelength of
sodium D radiation (D; Na)
• Amount of ethanol in wine sample i, ci (C2H5OH)
•
o Quantity in a conventionally chosen subset of a
given system of quantities, where no subset
quantity can be expressed in terms of the others.
o The subset mentioned above is termed the “set of
base quantities.”
o Base quantities are referred to as being mutually
independent since a based quantity cannot be
expressed as a product of powers of the other
base quantities.
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o Quantity, in a system of quantities, defined in
terms of the base quantities of that system
o Example:
• Base Quantity
• length and mass – m & kg
• Derived Quantity
• Volume = length to the third power - m3
• mass density = mass / volume – kg/m3
• mass / volume
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o ISQ is based on the seven base quantities:
• length, mass, time, electric current, thermodynamic
temperature, amount of substance, and luminous intensity
o Published in the ISO 80000 and IEC 80000 series
Quantities and units.
o The International System of Units (SI) is based on
the ISQ.
!
o Expression of the dependence of a quantity on
the base quantities of a system of quantities as a
product of powers of factors corresponding to
the base quantities, omitting any numerical
factor.
o Product: A x B Powers of X: Xm
o Symbol of dimension of base quantities
• Length (L), Mass (M), Time (T), Electrical Current (I),
Thermodynamic Temperature ( ), Amount (N), Luminous
Intensity (J)
o Quantity Dimensions
• Quantity dimension of force: dim F = LMT-2 (kg • m/s2)
• Quantity dimension of mass density: dim = ML-3 (kg/m3)
%
o Designated by conventionally assigned names
and symbols
o Base unit - measurement unit adopted by
convention for a base quantity
o Derived unit - measurement unit for a derived
quantity
o System of units - set of base units and derived
units, together with their multiples and
submultiples, defined in accordance with given
rules, for a given system of quantities
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$
o System of units, based on the International
System of Quantities, their names and symbols,
including a series of prefixes and their names and
symbols, together with rules for their use,
adopted by the General Conference on Weights
and Measures (CGPM)
o The SI is founded on the seven base quantities of
the ISQ and the names and symbols of the
corresponding base units:
• m (length), kg (mass), s (time), A (electrical current), K
(thermodynamic temperature), mol (amount of substance)
and cd (luminous intensity)
$
SI Base Unit
Base quantity
Name
Symbol
Length
meter
m
Mass
kilogram
kg
Time
second
s
Electric current
ampere
A
Thermodynamic temperature
kelvin
K
Amount of substance
mole
Mol
Luminous intensity
candela
cd
&
!
$
o 1 second
• the duration of 9,192,631,770 periods of the radiation
corresponding to the transition between the two hyperfine
levels of the ground state of the caesium 133 atom.[
o 1 meter
• Originally intended to be one ten-millionth of the distance
from the Earth's equator to the North Pole (at sea level)
• Since 1983, it is defined as the length of the path travelled
by light in vacuum in 1 299,792,458 of a second
&
$ !
"
SI Derived Units
Derived quantity
area
volume
speed, velocity
acceleration
wave number
Name
square meter
cubic meter
meter per second
meter per second squared
reciprocal meter
Symbol
m2
m3
m/s
m/s2
m-1
mass density
kilogram per cubic meter
kg/m3
specific volume
cubic meter per kilogram
m3/kg
current density
ampere per square meter
A/m2
magnetic field strength
ampere per meter
amount-of-substance concentration mole per cubic meter
A/m
mol/m3
luminance
candela per square meter
cd/m2
mass fraction
kilogram per kilogram, which may be
represented by the number 1
kg/kg =
1
'
(
)
o HeNe laser is stable and has an accepted
wavelength equal to a constant value of 632.81
nm at standard laboratory temperatures and
pressures.
o Used for Laser Primary Calibration
o Wavelength: a base quantity
o nm = 10-9m (base unit)
o Wavelength = 632.81 nm
o Measurement
• Process of obtaining one or more quantity values
• Reasonably
• Experimentally
o Metrology - science of measurement and its
application
• Metrology includes all theoretical and practical aspects of
measurement, whatever the measurement uncertainty and
field of application.
o Measurand
• Quantity intended to be measured
o Measurement result
• Set of quantity values being attributed to a measurand
together with any other available relevant information
o True quantity value; True value
• Quantity value, consistent with the definition of a quantity
• A true quantity value is considered ‘unique’ and unknowable
in practice.
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o Measurement accuracy
• Closeness of agreement between a measured quantity value
and a true quantity value of the measurand
o Measurement trueness
• Closeness of agreement between the average of an infinite
number of replicate measured quantity values and a
reference quantity value
o Measurement precision
• Closeness of agreement between indications obtained by
replicate measurements on the same or similar objects
under specified conditions
*
" '
o Measurement error
• Difference of measured quantity value and reference
quantity value
o Components of measurement error
• Systematic error - component of measurement error that in
replicate measurements remains constant or varies in a
predictable manner
• Measurement bias - estimate of a systematic
measurement error
• Random error - component of measurement error that in
replicate measurements varies in an unpredictable manner
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o Measurement repeatability
• Measurement precision under a set of repeatability
conditions of measurement
• Repeatability conditions - the same measurement
procedure, same location, and replicate measurements on
the same or similar objects over an extended period of time
o Measurement reproducibility
• Measurement precision under reproducibility conditions of
measurement
• Reproducibility conditions - different locations, operators,
measuring systems, and replicate measurements on the
same or similar objects
o Measurement uncertainty
• Non-negative parameter characterizing the dispersion of the
quantity values being attributed to a measurand, based on
the information used
o Many components - can be evaluated by:
• Type A evaluation of measurement uncertainty from the
statistical distribution of the quantity values from series of
measurements and can be characterized by standard
deviations.
• Type B evaluation of measurement uncertainty, evaluated
from probability density functions based on experience or
other information.
* "
o Type A evaluation
• Evaluated by a statistical analysis of quantity values
obtained under defined measurement conditions,
Characterized by experimental standard deviations
o Measurement conditions
• Repeatability condition of measurement
• Intermediate precision condition of measurement
• Reproducibility condition of measurement
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o Type B evaluation
• Some uncertainty contributors cannot be
evaluated statistically a statistical evaluation would
be impractical, or unnecessary.
• The associated uncertainty has to be estimated
based on
• past experience
• taken from a handbook
• extracted from a calibration report, etc.
• Type B Uncertainty
uncertainty
“systematic” components of
$
o Standard measurement uncertainty
• Measurement uncertainty expressed as a standard
deviation
o Combined standard measurement uncertainty
• Obtained using the individual standard measurement
uncertainties associated with the input quantities in a
measurement model
o Statement of a measurement uncertainty, of the
components of that measurement uncertainty,
and of their calculation and combination
o Uncertainty budget should include:
•
•
•
•
•
•
•
•
Measurement model
Estimates
Measurement uncertainties associated with the quantities in the
measurement model
Covariances
Type of applied probability density functions
Degrees of freedom
Type of evaluation of measurement uncertainty
Coverage factor
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o Mechanical
•
•
•
•
Test apparatus including fixtures
Orientation of device
Mounting
Sensor frequency response
o Electrical
•
•
•
•
•
•
•
•
Signal conditioning gain uncertainty
Signal conditioning frequency response
Resolution of readout device or data acquisition
Equipment warm-up
Equipment stabilization
Type and length of signal cable
Type of electrical connector
Meter settings (range, speed, resolution, etc.)
)
$
$
)
o Acquisition Equipment
•
•
•
•
•
•
•
•
DAQ Resolution
DAQ Card settings (range, gain, coupling, etc.)
Number of samples
Sample rate
Aliasing (related to sample rate)
Windowing (related to non-infinite record length)
Warm-up time
Proper use of DAQ self-cal features
o Miscellaneous
•
•
•
•
•
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Environmental conditions
Operator Technique
Repeatability
Stability of working standards
Uncertainty of working standards
Random variations from other sources (determined statistically from
repeated measurements)
$
o Define the test
•
Well documented calibration procedure.
y = f (ax1functional
, x 2 ,...x n ) relationship between input,
o Write a model function, providing
xi, and the output, y:
o Identify and document error components
•
•
•
Use cal procedure and math model as guide.
Document distribution (normal, rectangular, etc,) and standard deviation of
each error component.
Values from product specs, calibration data, engineering knowledge, physics,
past experience, and other uncertainty estimates.
o Collect data for random influence (Type A Error)
•
Repeatability and reproducibility. Use sensors representative of “best
uncertainty” for “routine” calibration.
o Create uncertainty budget
•
•
Combined standard measurement uncertainty: RSS component uncertainties
Expanded uncertainty: k * (combined standard measurement uncertainty)
,
!
o Probability of population falling in “sigma intervals”
±
1
2
3
4
5
6
%
68.26895
95.44997
99.73002
99.99367
99.999943
99.9999998
)
$
o Population of calibrations is normal. Characterized by
average value and standard deviation (dispersion).
o 1
Combined standard measurement uncertainty
# -.
) "
o 1
Combined standard measurement uncertainty
o Expanded uncertainty = k * (combined standard
measurement uncertainty)
o Coverage factor k = 2 corresponds to ±2 (95%); k= 3
corresponds to ±3 (99.7%); etc.
/
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Calibrated sensitivity = 100 mV/g; Measurement
Uncertainty = 1% (95% confidence level with a coverage
factor of 2)
o This means that there is a 95% probability that the true
value is between 99 mV/g and 101 mV/g.
&
o Excerpt from The Modal Shop’s published ISO
17025 A2LA certified uncertainty budget
+ 0
o Measurement is not exact
o Measurement uncertainty is a method
for qualifying a measurement’s range of
possible results
• With a degree of statistical confidence
o Labs are obligated to report
measurement uncertainty by ISO 17025
• Test results are marginally close to a
specification limit
• May be involved in a dispute and challenged in
a court
1
o Metrological Traceability: Property of a measurement result,
which is related to a reference through a documented unbroken
chain of calibrations, each contributing to the measurement
uncertainty
o A metrological traceability chain is defined through a calibration
hierarchy.
o ILAC considers the elements for confirming metrological
traceability to be an unbroken metrological traceability chain to
an international measurement standard or a national
measurement standard, a documented measurement
uncertainty, a documented measurement procedure, accredited
technical competence, metrological traceability to the SI, and
calibration intervals (see ILAC P-10:2002).
National
Metrology
Institute
Secondary
Calibration Lab
Control Standards
Working Standards
Uncertainty
Traceab
ability
SI
$2 -3456 + 0
o ISO 17025 requires statements of “Uncertainty”
and “Traceability” on a calibration certificate.
o Example from a PCB calibration certificate:
• Calibration is NIST Traceable thru Project 822/277342 and PTB
Traceable thru Project 1254.
• Measurement uncertainty (95% confidence level with coverage
factor of 2) for frequency ranges tested during calibration are as
follows: 5-9 Hz; ±2.0%, 10-99 Hz; ±1.5%, 100-1999 Hz; ±1.0%, 210 kHz; ±2.5%.
$2 744-
0
$2 -3456
o All calibrations of ISO 9001 certified organization
must be performed from an ISO 17025 accredited
calibration labs.
o A few examples of ISO 9001 certified Korean
Companies
• Hyundai Motor Company Ltd. & Hyundai Heavy Industries are
certified to the Quality Management System standard ISO 9001
• SEMITEC KOREA Co.,Ltd. Certified to ISO 9001
• SAMSUNG Semiconductor plants in Korea Certified to ISO
9001 in 1993
• SAMSUNG HEAVY INDUSTRIES CO., LTD.
+
o ISO/IEC GUIDE 99:2007
International Vocabulary of Metrology (VIM) 3rd Edition
• http://www.bipm.org/utils/common/documents/jcgm/JCGM_200_2
008.pdf
o A2LA Guide for Estimation of Measurement Uncertainty In
Testing
• http://www.a2la.org/guidance/est_mu_testing.pdf
o ISO 16063-21
• Methods for the calibration of vibration and shock transducers -Part 21: Vibration calibration by comparison to a reference
transducer
• http://www.modalshop.com/calibration.asp?ID=195
o ISO/IEC GUIDE 98-3:2008
• GUM: Guide to the expression of Uncertainty in Measurement)