Post on 09-Apr-2018
Vocabulary of MetrologyFor Understating Uncertainty and
Traceability
Prepared by:
Kim, Sang Ho
Engineering Team Leader
Modal Shop, Inc
A PCB Group Company
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SI
National Metrology Institute
Secondary Calibration LabCalibration Lab
Control Standards
Working Standards
Uncertainty
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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)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)
•
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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.”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• 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.Quantities and units.
o The International System of Units (SI) is based on
the ISQ.
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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 Product: A x B Powers of X: X
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)
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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 quantityquantity
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)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)
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SI Base Unit
Base quantity Name Symbol
Length meter m
Mass kilogram kg
Time second sTime second s
Electric current ampere A
Thermodynamic temperature kelvin K
Amount of substance mole Mol
Luminous intensity candela cd
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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 • 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
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SI Derived Units
Derived quantity Name Symbol
area square meter m2
volume cubic meter m3
speed, velocity meter per second m/s
acceleration meter per second squared m/s2
wave number reciprocal meter m-1
mass density kilogram per cubic meter kg/m3mass 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 A/m
amount-of-substance concentration mole per cubic meter mol/m3
luminance candela per square meter cd/m2
mass fractionkilogram per kilogram, which may be
represented by the number 1
kg/kg =
1
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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
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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.
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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 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
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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 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
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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 • 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.
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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• 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 � “systematic” components of
uncertainty
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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 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
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• 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
o Mechanical• Test apparatus including fixtures
• Orientation of device
• Mounting
• Sensor frequency response
o Electrical
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• 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
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• Warm-up time
• Proper use of DAQ self-cal features
o Miscellaneous• Environmental conditions
• Operator Technique
• Repeatability
• Stability of working standards
• Uncertainty of working standards
• Random variations from other sources (determined statistically from repeated measurements)
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o Define the test
• Well documented calibration procedure.
o Write a model function, providing a functional relationship between input, 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.
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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)
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o Probability of population falling in “sigma intervals”
± � %
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2 95.44997
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4 99.99367
5 99.999943
6 99.9999998
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o Population of calibrations is normal. Characterized by average value and standard deviation (dispersion).
o 1� � Combined standard measurement uncertainty
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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.
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o Excerpt from The Modal Shop’s published ISO 17025 A2LA certified uncertainty budget
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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• 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
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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.
ILAC considers the elements for confirming metrological 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).
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SI
National Metrology Institute
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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 • 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%, 2-
10 kHz; ±2.5%.
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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 • 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.
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o ISO/IEC GUIDE 99:2007International Vocabulary of Metrology (VIM) 3rd Edition
• http://www.bipm.org/utils/common/documents/jcgm/JCGM_200_2008.pdf
o A2LA Guide for Estimation of Measurement Uncertainty In Testing
• http://www.a2la.org/guidance/est_mu_testing.pdf• 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)