Vocabulary of MetrologyFor 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 LabCalibration 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)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.”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.

! ��" ��������# ������� ��������

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

��� ���������$�� ����������� ���$��������� ��������

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.

�������!�� ������������ ��������

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)

� ���� � ������% ������� ��������

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

��� ���������$�� ��������$�������� ��������

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)

�� ��������$� �� ������������ ��������

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

�&���� ! ���������� �� �������� ��$ ������ � ��

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

�&���� ���$�! ��" ������������� ��������

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

�� ��������'�����(�� �)����������

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.

� ���� � ��*�������'� ������

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

*������"�'� ������

� ���� � �������

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

+ � ���������+ ������������

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 • 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• Repeatability condition of measurement

• Intermediate precision condition of measurement

• Reproducibility condition of measurement

�� "��������

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

$�������� ���� � ����� ������

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

��� ������ ��� �

• 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

$���� ������������������$ ����)����������

• 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

$���� ������������������$ ����)����������

• 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)

$� ����������������� ������

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.

),...,( 21 nxxxfy =

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 68.26895

2 95.44997

�����

�����

����3 99.73002

4 99.99367

5 99.999943

6 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.

�����

�����

����

��� ��������&���� �

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��� �1

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

� �������������� ������������� ��������

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).

� �������������� ������

SI

National Metrology Institute

Secondary

�� ���� ���� �������

ab

ility

Secondary Calibration Lab

Control Standards

Working Standards

Uncertainty

Tra

ce

ab

�$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 • 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%.

�$2744-� 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 • 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 99:2007International 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)