QUANTITIES AND UNITS
(measurable) quantity :
Attribute of a phenomenon, body or substance that may be distinguished qualitatively and determined quantitatively.
- The term “quantity” may refer to a quantity in a general sense [see example a)] or to a particular quantity [see example b)].
a - Quantities in a general sense: length, time, mass, temperature, electrical resistance, amount-of-substance concentration ;
b - Particular quantities: length of a given rod ; electrical resistance of a given specimen of wire - amount-of-substance concentration of ethanol in a given sample of wine.
- Quantities that can be placed in order of magnitude relative to one another in increasing order (or decreasing order) are called quantities of the same kind.
- Quantities of the same kind may be grouped together into categories of quantities, for example: - work, heat, energy ; thickness, circumference, wavelength.
- Symbols of quantities are given in ISO 31.
Base quantity :
One of the quantities that, in a system of quantities, are conventionally accepted as functionally independent of one another.
The quantities length, mass and time are generally taken to be base quantities in the field of mechanics.
- The base quantities which correspond to the base units of the International System of Units (SI) are given in the NOTE of 1.6.
Derived quantity :
Quantity defined, in a system of quantities, as a function of base quantities of that system.
In a system having base quantities length, mass and time, velocity is a derived quantity defined as: length divided by time.
Unit (of measurement) :
Particular quantity, defined and adopted by convention, with which other quantities of the same kind are compared in order to express their magnitudes relative to that quantity.
- Units of measurement have conventionally assigned names and symbols.
- Units of quantities of the same dimension may have the same names and symbols even when the quantities are not of the same kind.
Symbol of a unit (of measurement) :
Conventional sign designating a unit of measurement.
a) m is the symbol of metre ;
b) A is the symbol of ampere.
International System of Units, SI :
The coherent system of units adopted and recommended by the Conférence Générale des Poids et Mesures (CGPM).
The SI is based at the present on the following seven base units :
||SI base unit
|amount of substance
Base unit (of measurement) :
Unit of measurement of a base quantity in a given system of quantities.
In any given coherent systems of units there is only one base unit for each base quantity.
Derived unit (of measurement) :
Unit of measurement of a derived quantity in a given system of quantities.
Some derived units have special names and symbols ; for example in the SI :
||SI derived unit
Multiple of a unit (of measurement) :
Larger unit of measurement that is formed from a given unit according to scaling conventions.
a) One of the decimal multiples of the metre is the kilometre ;
b) One of the non-decimal multiples of the second is the hour.
Submultiple of a unit (of measurement) v:
Smaller unit of measurement that is formed from a given unit according to scaling conventions.
One of the decimal submultiples of the metre is the millimetre.
Value (of a quantity) :
Magnitude of a particular quantity generally expressed as a unit of measurement multiplied by a number.
a) Length of a rod: 5,34 m or 534 cm ;
b) Mass of a body: 0,152 kg or 152 g ;
c) Amount of substance of a sample of water (H2O): 0,012 mol or 12 mmol.
- The value of a quantity may be positive, negative or zero.
- The value of a quantity may be expressed in more than one way.
- The values of quantities of dimension one are generally expressed as pure numbers.
- A quantity that cannot be expressed as a unit of measurement multiplied by a number may be expressed by reference scale or to a measurement procedure or to both.
Set of operations having the object of determining a value of a quantity.
- The operations may be performed automatically.
Science of measurement.
- Metrology includes all aspects both theoretical and practical with reference to measurements, whatever their uncertainty, and in whatever field of science or technology they occur.
Particular quantity subject to measurement.
Vapour pressure of a given sample of water at 20 °C.
- The specification of a measurand may require statements about quantities such as time, temperature and pressure.
Accuracy of measurement :
Closeness of the agreement between the result of a measurement and a true value of the measurand.
- "Accuracy" a is qualitative concept.
- The term precision should not be used for "accuracy".
Repeatability (of results of measurements):
Closeness of the agreement between the results of successive measurements of the same measurand carried out under the same conditions of measurement.
- These conditions are called repeatability conditions.
- Repeatibility conditions include : the same measurement procedure - the same observer - the same measuring instrument – the same reference standard, used under the same conditions - the same location - repetition over a short period of time.
- Repeatability may be expressed quantitatively in terms of the dispersion characteristics of the results.
Reproducibility (-of results of measurements) :
Closeness of the agreement between the results of measurements of the same measurand carried out under changed conditions of measurement.
- A valid statement of reproducibility requires specification of the conditions changed.
- The changed conditions may include: - principle of measurement - method of measurement - observer - measuring instrument - reference standard – location - conditions of use - time.
- Reproducibility may be expressed quantitatively in terms of the dispersion characteristics of the results.
- Results are here usually understood to be corrected results.
Uncertainty of measurement :
Parameter, associated with the result of a measurement, that characterizes the dispersion of values that could reasonably be attributed to the measurand.
- The parameter may be, for example, a standard deviation (or a given multiple of it), or the half-width of an interval having a stated level of confidence.
- Uncertainty of measurement comprises, in general, many components. Some of these components may be evaluated from the statistical distribution of the results of series of measurements and can be characterized by experimental standard deviations. The other components, which can also be characterized by standard deviations, are evaluated from assumed probability distributions based on experience or other information.
- It is understood that the result of the measurement is the best estimate of the value of the measurand, and that all components of the uncertainty, including those arising from systematic effects, such as the components associated with the corrections and reference standards, contribute to the dispersion.
This definition is that of the "Guide to the expression of uncertainty in measurement" in which its rationale is detailed (see, in particular, 2.2.4 and annex D )
Error (of measurement) :
Result of a measurement minus a true value of the measurand.
- Since a true value cannot be determined, in practice a conventional true value is used.
- When it is necessary to distinguish "error" from "relative error", the former is sometimes called absolute error of measurement. This should not be confused with absolute value of error, which is the modulus of the error.
Value minus its reference value.
Many different terms are employed to describe the artefacts which are used in measurement. This Vocabulary defines only a selection of preferred terms; the following list is more complete and is arranged in an approximate order of increasing complexity. These terms are not mutually exclusive.
- measuring transducer
- measuring device
- reference material
- material measure
- measuring instrument
- measuring chain
- measuring system
- measuring installation
Material measure :
Device intended to reproduce or supply, in a permanent manner during its use, one or more known values of a given quantity.
a) a weight ;
b) a measure of volume (of one or several values, with or without a scale) ;
c) a standard electrical generator ;
d) a gauge block ;
e) a standard signal generator ;
f ) a reference material.
- The quantity concerned may be called the supplied quantity.
CHARACTERISTICS OF MEASURING INSTRUMENTS
Some of the terms used in this chapter to describe the characteristics of a measuring instrument are equally applicable to a measuring device, a measuring transducer or a measuring system and by analogy may also be applied to a material measure or a reference material. Consequently, the term "measuring instrument" must be understood here as a generic term covering all of these possible meanings.
The input signal to a measuring system may be called the stimulus ; the output signal may be called the response.
In this chapter, the term “measurand” means the quantity that is applied to a measuring instrument.
Measuring range, working range :
Set of values of measurands for which the error of a measuring instrument is intended to lie within specified limits.
- Error is determined in relation to a conventional true value.
- In some fields of knowledge, the difference between the greatest and smallest value is called the range.
MEASUREMENT STANDARDS, ETALONS
In science and technology, the English word "standard" is used with two different meanings: as a widely adopted written technical standard, specification, technical recommendation or similar document (in French "norme") and also as a measurement standard (in French "etalon"). This Vocabulary is concerned solely with the second meaning and the qualifier "measurement" is generally omitted for brevity.
(Measurement) standard :
Material measure, measuring instrument, reference material or measuring system intended to define, realize, conserve or reproduce a unit or one or more values of a quantity to serve as a reference.
a) 1 kg mass standard ;
b) 100 Ω standard resistor ;
c) standard amperemeter ;
d) caesium frequency standard ;
e) standard hydrogen electrode ;
f) reference solution of cortisol in human serum having a certified concentration.
- A set of similar material measures or measuring instruments that, through their combined use, constitutes a standard is called a collective standard.
- A set of standards of chosen values that, individually or in combination, provides a series of values of quantities of the same kind is called a group standard.
National (measurement) standard :
Standard recognized by a national decision to serve, in a country, as the basis for assigning values to other standards of the quantity concerned.
Primary standard :
Standard that is designated or widely acknowledged as having the highest metrological qualities and whose value is accepted without reference to other standards of the same quantity.
- The concept of primary standard is equally valid for base quantities and derived quantities.
Secondary standard :
Standard whose value is assigned by comparison with a primary standard of the same quantity.
Reference standard :
Standard, generally having the highest metrological quality available at a given location or in a given organization, from which measurements made there are derived.
Working standard :
Standard that is used routinely to calibrate or check material measures, measuring instruments or reference materials.
- A working standard is usually calibrated against a reference standard.
- A working standard used routinely to ensure that measurements are being carried out correctly is called a check standard.
Transfer standard :
Standard used as an intermediary to compare standards.
- The term transfer device should be used when the intermediary is not a standard.
Property of the result of a measurement or the value of a standard whereby it can be related to stated references, usually national or international standards, through an unbroken chain of comparisons all having stated uncertainties.
- The concept is often expressed by the adjective traceable.
- The unbroken chain of comparisons is called traceability chain or calibration chain.
- The relation to standard is called traceability to standards.
Set of operations that establish, under specified conditions, the relationship between values of quantities indicated by a measuring instrument or measuring system, or values represented by a material measure or a reference material, and the corresponding values realized by standards.
- The result of a calibration permits either the assignment of values of measurands to the indications or the determination of corrections with respect to indications.
- A calibration may also determine other metrological properties such as the effect of influence quantities.
- The result of a calibration may be recorded in a document, sometimes called a calibration certificate or a calibration report.
Reference material (RM) :
Material or substance one or more of whose property values are sufficiently homogeneous and well established to be used for the calibration of an apparatus, the assessment of a measurement method, or for assigning values to materials.
- A reference material may be in the form of a pure or mixed gas, liquid or solid. Examples are water for the calibration of viscometers, sapphire as a heat-capacity calibrant in calorimetry, and solutions used for calibration in chemical analysis.
This definition, including the Note, is taken from ISO Guide 30:1992.
Reference material (CRM) :
Reference material, accompanied by a certificate, one or more of whose property values are certified by a procedure which established traceability to an accurate realization of the unit in which the property values are expressed, and for which each certified value is accompanied by an uncertainty at a stated level of confidence.
- The definition of a “reference material certificate” is given in 4.1 (the term is given in ISO Guide 30:1992)
- CRMs are generally prepared in batches for which the property values are determined within stated uncertainty limits by measurements on samples representative of the whole batch.
- The certified properties of certified reference materials are sometimes conveniently and reliably realized when the material is incorporated into a specially fabricated device , e.g. a substance of known triple-point into a triple-point cell, a glass of known optical density into a transmission filter, spheres of uniform particle size mounted on a microscope slide. Such devices may also be considered as CRMs.
- All the CRMs lie within the definition of “measurement standards” or “etalons” given in the “International Vocabulary of basis and general terms in metrology (VIM)”.
- Some RMs and CRMs have properties which, since they cannot be correlated with an established chemical structure or for other reasons, cannot be determined by exactly defined physical and chemical measurement methods. Such materials include certain biological materials such as vaccines to which an International unit has been assigned by the World Health Organization (WHO).
This definition, including the Note, is taken from ISO Guide 30:1992.