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Vocabulary of For Understating and

Prepared by: Kim, Sang Ho Team Leader Modal Shop, Inc A PCB Group Company Vocabulary that helps Understanding Traceability & Uncertainty

SI

National Metrology Institute Secondary Lab

Control Standards

Working Standards

Uncertainty Quantities & Units (International Vocabulary of Metrology 3rd Edition) o Quantity – property of a phenomenon, body, or substance, where the property can be expressed as a 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) • (l), radius of a circle (r), of sodium D radiation  (D; Na) • Amount of ethanol in wine sample i, ci (C2H5OH)

• Base Quantity (VIM 3rd Edition) 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. Derived Quantity - (VIM 3rd Edition) o Quantity, in a system of quantities, defined in terms of the base quantities of that system o Example: • Base Quantity • length and – m & kg • Derived Quantity • Volume = length to the third power - m3 • mass density = mass / volume – kg/m3 • mass / volume International System of Quantities (ISQ) (VIM 3rd Edition) o ISQ is based on the seven base quantities: • length, mass, , , thermodynamic , , and 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. Quantity Dimension (VIM 3rd Edition) 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 : dim F = LMT-2 (kg • m/s2) • Quantity dimension of mass density: dim  = ML-3 (kg/m3) Measurement Unit – (VIM 3rd Edition) o Designated by conventionally assigned names and symbols o - 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 International System of Units SI (VIM 3rd Edition) 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) Base Quantity & SI Base Units (VIM 3rd Edition)

SI Base Unit Base quantity Name Symbol

Length meter m

Mass kg Time s Electric current A

Thermodynamic temperature K

Amount of substance Mol

Luminous intensity cd Example Definition of Base Quantities (Second & Meter) 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 of the caesium 133 atom.[ o 1 meter • Originally intended to be one ten-millionth of the from the Earth's equator to the North Pole (at sea level) • Since 1983, it is defined as the length of the path travelled 1 by light in in Ÿ299,792,458 of a second Examples of SI Derived Units (VIM 3rd Edition)

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/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

kilogram per kilogram, which may be kg/kg = mass fraction represented by the number 1 1 Base Units for Primary Laser Calibration o HeNe laser is stable and has an accepted wavelength equal to a constant value of 632.81 nm at laboratory and pressures. o Used for Laser Primary Calibration o Wavelength: a base quantity o nm = 10-9m (base unit) o Wavelength = 632.81 nm Measurement & Metrology (VIM 3rd Edition) o Measurement • Process of obtaining one or more quantity values • Reasonably • Experimentally o Metrology - of measurement and its application • Metrology includes all theoretical and practical aspects of measurement, whatever the and field of application. Measurement (VIM 3rd Edition) 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. Measurement Accuracy & Precision 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 on the same or similar objects under specified conditions Accuracy vs Precision Measurement Error 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 Repeatability & 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 Measurement Uncertainty 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. Type A evaluation 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 Type B evaluation 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 Standard measurement uncertainty o Standard measurement uncertainty • Measurement uncertainty expressed as a o Combined standard measurement uncertainty • Obtained using the individual standard measurement associated with the input quantities in a measurement model Uncertainty Budget 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 Source of Error in Vibration Sensor Calibration

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 acquisition • Equipment warm-up • Equipment stabilization • Type and length of signal cable • Type of electrical connector • Meter settings (range, speed, resolution, etc.) Source of Error in Vibration Sensor Calibration

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) Steps to Estimating Uncertainty o Define the test • Well documented calibration procedure. = o Write a model function, providingy f (ax 1functional, x2 ,...xn ) 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. • Values from product specs, calibration data, engineering , 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) Normal Distribution

o Probability of population falling in “sigma intervals”

±  % 1 68.26895 2 95.44997 3 99.73002 4 99.99367 99.7% 5 99.999943 6 99.9999998 95.4%

68.3% Combined Standard Measurement Uncertainty - 1.

o Population of is normal. Characterized by average value and standard deviation (dispersion). o 1  Combined standard measurement uncertainty

99.7%

95.4%

68.3% Coverage factor k 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.

99.7%

95.4% 68.3% Uncertainty (Example)

Calibrated sensitivity = 100 mV/g; Measurement Uncertainty = 1% (95% confidence level with a coverage factor of 2) o This that there is a 95% probability that the true value is between 99 mV/g and 101 mV/g.

95.4%

68.3% Examples of Uncertainty Budget o Excerpt from The Modal Shop’s published ISO 17025 A2LA certified uncertainty budget Measurement Uncertainty Required? 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 Metrological Traceability (VIM 3rd Edition) 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). Metrological Traceability

Calibration Hierarchy

SI

National Metrology Institute Secondary Calibration Lab ability

Control Standards Traceab

Working Standards

Uncertainty ISO 17025 Requirements 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%, 2- 10 kHz; ±2.5%. ISO 9001 requires ISO 17025 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 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. References 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)