Vocabulary of Metrology For Understating Uncertainty and Traceability Prepared by: Kim, Sang Ho Engineering Team Leader Modal Shop, Inc A PCB Group Company Vocabulary that helps Understanding Traceability & Measurement Uncertainty SI National Metrology Institute Secondary Calibration 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 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) • ase 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 mass – 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, 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. 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 force: 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 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 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) ase Quantity & SI ase Units (VIM 3rd Edition) 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 Example Definition of ase 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 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 1 by light in vacuum in 299,792,458 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 ase 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 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 Measurement & Metrology (VIM 3rd Edition) 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. 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 measurements 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 & Reproducibility 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 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 standard deviation o Combined standard measurement uncertainty • Obtained using the individual standard measurement uncertainties associated with the input quantities in a measurement model Uncertainty udget 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 data acquisition • Equipment warm-up • Equipment