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.
!" # 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 - m 3 mass density = mass / volume kg/m 3 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. 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: X m 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/s 2 ) Quantity dimension of mass density: dim = ML -3 (kg/m 3 )
% 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
$ $ 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 Name Symbol area square meter m 2 volume cubic meter m 3 speed, velocity meter per second m/s acceleration meter per second squared m/s 2 wave number reciprocal meter m -1 mass density kilogram per cubic meter kg/m 3 specific volume cubic meter per kilogram m 3 /kg current density ampere per square meter A/m 2 magnetic field strength ampere per meter A/m amount-of-substance concentration mole per cubic meter mol/m 3 luminance candela per square meter cd/m 2 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 = 10-9 m (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 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
+ + 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
" 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 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
$$) o Mechanical Test apparatus including fixtures Orientation of device Mounting Sensor frequency response o Electrical Signal conditioning gain uncertainty Signal conditioning frequency response Resolution of readout device or data acquisition Equipment warm-up Equipment stabilization Type and length of signal cable Type of electrical connector Meter settings (range, speed, resolution, etc.)
$$) 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 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 y = f ( a x1functional, x2,... xn ) relationship between input, x i, 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 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
+01 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
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).
SI National Metrology Institute Secondary Calibration Lab Control Standards Traceab bility Working Standards Uncertainty
$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 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) 3 rd 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)