NOTE 1 Measurement does not apply to nominal properties.
NOTE 2 Measurement implies comparison of quantities and includes counting of entities.
NOTE 3 Measurement presupposes a description of the quantity commensurate with the intended use of a measurement result, a measurement procedure, and a calibrated measuring system operating according to the specified measurement procedure, including the measurement conditions.
NOTE Metrology includes all theoretical and practical aspects of measurement, whatever the measurement uncertainty and field of application.
NOTE 1 The specification of a measurand requires knowledge of the kind of quantity, description of the state of the phenomenon, body, or substance carrying the quantity, including any relevant component, and the chemical entities involved.
NOTE 2 In the second edition of the VIM and in IEC 60050‑300:2001, the measurand is defined as the ‘quantity subject to measurement’.
NOTE 3 The measurement, including the measuring system and the conditions under which the measurement is carried out, might change the phenomenon, body, or substance such that the quantity being measured may differ from the measurand as defined. In this case, adequate correction is necessary.
EXAMPLE 1 The potential difference between the terminals of a battery may decrease when using a voltmeter with a significant internal conductance to perform the measurement. The open‑circuit potential difference can be calculated from the internal resistances of the battery and the voltmeter.
EXAMPLE 2 The length of a steel rod in equilibrium with the ambient Celsius temperature of 23 °C will be different from the length at the specified temperature of 20 °C, which is the measurand. In this case, a correction is necessary.
NOTE 4 In chemistry, “analyte”, or the name of a substance or compound, are terms sometimes used for ‘measurand’. This usage is erroneous because these terms do not refer to quantities.
EXAMPLE 1 Thermoelectric effect applied to the measurement of temperature.
EXAMPLE 2 Energy absorption applied to the measurement of amount‑of‑substance concentration.
EXAMPLE 3 Lowering of the concentration of glucose in blood in a fasting rabbit applied to the measurement of insulin concentration in a preparation.
NOTE The phenomenon can be of a physical, chemical, or biological nature.
NOTE Measurement methods may be qualified in various ways such as:
See IEC 60050‑300:2001.
NOTE 1 A measurement procedure is usually documented in sufficient detail to enable an operator to perform a measurement.
NOTE 2 A measurement procedure can include a statement concerning a target measurement uncertainty.
NOTE 3 A measurement procedure is sometimes called a standard operating procedure, abbreviated SOP.
EXAMPLE The volume of water delivered by a 50 ml pipette at 20 °C is measured by weighing the water delivered by the pipette into a beaker, taking the mass of beaker plus water minus the mass of the initially empty beaker, and correcting the mass difference for the actual water temperature using the volumic mass (mass density).
NOTE 1 The Consultative Committee for Amount of Substance — Metrology in Chemistry (CCQM) uses the term “primary method of measurement” for this concept.
NOTE 2 Definitions of two subordinate concepts, which could be termed “direct primary reference measurement procedure” and “ratio primary reference measurement procedure”, are given by the CCQM (5th Meeting, 1999).
NOTE 1 A measurement result generally contains “relevant information” about the set of quantity values, such that some may be more representative of the measurand than others. This may be expressed in the form of a probability density function (PDF).
NOTE 2 A measurement result is generally expressed as a single measured quantity value and a measurement uncertainty. If the measurement uncertainty is considered to be negligible for some purpose, the measurement result may be expressed as a single measured quantity value. In many fields, this is the common way of expressing a measurement result.
NOTE 3 In the traditional literature and in the previous edition of the VIM, measurement result was defined as a value attributed to a measurand and explained to mean an indication, or an uncorrected result, or a corrected result, according to the context.
NOTE 1 For a measurement involving replicate indications, each indication can be used to provide a corresponding measured quantity value. This set of individual measured quantity values can be used to calculate a resulting measured quantity value, such as an average or median, usually with a decreased associated measurement uncertainty.
NOTE 2 When the range of the true quantity values believed to represent the measurand is small compared with the measurement uncertainty, a measured quantity value can be considered to be an estimate of an essentially unique true quantity value and is often an average or median of individual measured quantity values obtained through replicate measurements.
NOTE 3 In the case where the range of the true quantity values believed to represent the measurand is not small compared with the measurement uncertainty, a measured value is often an estimate of an average or median of the set of true quantity values.
NOTE 4 In the GUM, the terms “result of measurement” and “estimate of the value of the measurand” or just “estimate of the measurand” are used for ‘measured quantity value’.
NOTE 1 In the Error Approach to describing measurement, a true quantity value is considered unique and, in practice, unknowable. The Uncertainty Approach is to recognize that, owing to the inherently incomplete amount of detail in the definition of a quantity, there is not a single true quantity value but rather a set of true quantity values consistent with the definition. However, this set of values is, in principle and in practice, unknowable. Other approaches dispense altogether with the concept of true quantity value and rely on the concept of metrological compatibility of measurement results for assessing their validity.
NOTE 2 In the special case of a fundamental constant, the quantity is considered to have a single true quantity value.
NOTE 3 When the definitional uncertainty associated with the measurand is considered to be negligible compared to the other components of the measurement uncertainty, the measurand may be considered to have an “essentially unique” true quantity value. This is the approach taken by the GUM and associated documents, where the word “true” is considered to be redundant.
EXAMPLE 1 Standard acceleration of free fall (formerly called “standard acceleration due to gravity”), gn = 9.806 65 m·s−2.
EXAMPLE 2 Conventional quantity value of the Josephson constant, KJ‑90 = 483 597.9 GHz · V−1.
EXAMPLE 3 Conventional quantity value of a given mass standard, m = 100.003 47 g.
NOTE 1 The term “conventional true quantity value” is sometimes used for this concept, but its use is discouraged.
NOTE 2 Sometimes a conventional quantity value is an estimate of a true quantity value.
NOTE 3 A conventional quantity value is generally accepted as being associated with a suitably small measurement uncertainty, which might be zero.
NOTE 1 The concept ‘measurement accuracy’ is not a quantity and is not given a numerical quantity value. A measurement is said to be more accurate when it offers a smaller measurement error.
NOTE 2 The term “measurement accuracy” should not be used for measurement trueness and the term measurement precision should not be used for ‘measurement accuracy’, which, however, is related to both these concepts.
NOTE 3 ‘Measurement accuracy’ is sometimes understood as closeness of agreement between measured quantity values that are being attributed to the measurand.
NOTE 1 Measurement trueness is not a quantity and thus cannot be expressed numerically, but measures for closeness of agreement are given in ISO 5725.
NOTE 2 Measurement trueness is inversely related to systematic measurement error, but is not related to random measurement error.
NOTE 3 Measurement accuracy should not be used for ‘measurement trueness’ and vice versa.
NOTE 1 Measurement precision is usually expressed numerically by measures of imprecision, such as standard deviation, variance, or coefficient of variation under the specified conditions of measurement.
NOTE 2 The ‘specified conditions’ can be, for example, repeatability conditions of measurement, intermediate precision conditions of measurement, or reproducibility conditions of measurement (see ISO 5725‑3:1994).
NOTE 3 Measurement precision is used to define measurement repeatability, intermediate measurement precision, and measurement reproducibility.
NOTE 4 Sometimes “measurement precision” is erroneously used to mean measurement accuracy.
NOTE 1 The concept of ‘measurement error’ can be used both
NOTE 2 Measurement error should not be confused with production error or mistake.
NOTE 1 A reference quantity value for a systematic measurement error is a true quantity value, or a measured quantity value of a measurement standard of negligible measurement uncertainty, or a conventional quantity value.
NOTE 2 Systematic measurement error, and its causes, can be known or unknown. A correction can be applied to compensate for a known systematic measurement error.
NOTE 3 Systematic measurement error equals measurement error minus random measurement error.
NOTE 1 A reference quantity value for a random measurement error is the average that would ensue from an infinite number of replicate measurements of the same measurand.
NOTE 2 Random measurement errors of a set of replicate measurements form a distribution that can be summarized by its expectation, which is generally assumed to be zero, and its variance.
NOTE 3 Random measurement error equals measurement error minus systematic measurement error.
NOTE 1 A condition of measurement is a repeatability condition only with respect to a specified set of repeatability conditions.
NOTE 2 In chemistry, the term “intra-serial precision condition of measurement” is sometimes used to designate this concept.
NOTE 1 The changes can include new calibrations, calibrators, operators, and measuring systems.
NOTE 2 A specification for the conditions should contain the conditions changed and unchanged, to the extent practical.
NOTE 3 In chemistry, the term “inter-serial precision condition of measurement” is sometimes used to designate this concept.
NOTE Relevant statistical terms are given in ISO 5725‑3:1994.
NOTE 1 The different measuring systems may use different measurement procedures.
NOTE 2 A specification should give the conditions changed and unchanged, to the extent practical.
NOTE Relevant statistical terms are given in ISO 5725‑1:1994 and ISO 5725‑2:1994.
NOTE 1 Measurement uncertainty includes components arising from systematic effects, such as components associated with corrections and the assigned quantity values of measurement standards, as well as the definitional uncertainty. Sometimes estimated systematic effects are not corrected for but, instead, associated measurement uncertainty components are incorporated.
NOTE 2 The parameter may be, for example, a standard deviation called standard measurement uncertainty (or a specified multiple of it), or the half-width of an interval, having a stated coverage probability.
NOTE 3 Measurement uncertainty comprises, in general, many components. Some of these may 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. The other components, which may be evaluated by Type B evaluation of measurement uncertainty, can also be characterized by standard deviations, evaluated from probability density functions based on experience or other information.
NOTE 4 In general, for a given set of information, it is understood that the measurement uncertainty is associated with a stated quantity value attributed to the measurand. A modification of this value results in a modification of the associated uncertainty.
NOTE 1 Definitional uncertainty is the practical minimum measurement uncertainty achievable in any measurement of a given measurand.
NOTE 2 Any change in the descriptive detail leads to another definitional uncertainty.
NOTE 3 In the GUM:1995, D.3.4, and in IEC 60359, the concept ‘definitional uncertainty’ is termed “intrinsic uncertainty”.
NOTE 1 For various types of measurement conditions, see repeatability condition of measurement, intermediate precision condition of measurement, and reproducibility condition of measurement.
NOTE 2 For information about statistical analysis, see e.g. the GUM:1995.
NOTE 3 See also GUM:1995, 2.3.2, ISO 5725, ISO 13528, ISO/TS 21748, ISO 21749.
EXAMPLES Evaluation based on information
NOTE See also GUM:1995, 2.3.3.
NOTE In case of correlations of input quantities in a measurement model, covariances must also be taken into account when calculating the combined standard measurement uncertainty; see also GUM:1995, 2.3.4.
NOTE An uncertainty budget should include the measurement model, estimates, and 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, and any coverage factor.
NOTE 1 The factor depends upon the type of probability distribution of the output quantity in a measurement modeland on the selected coverage probability.
NOTE 2 The term “factor” in this definition refers to a coverage factor.
NOTE 3 Expanded measurement uncertainty is termed “overall uncertainty” in paragraph 5 of Recommendation INC‑1 (1980) (see the GUM) and simply “uncertainty” in IEC documents.
NOTE 1 A coverage interval does not need to be centred on the chosen measured quantity value (see JCGM 101:2008).
NOTE 2 A coverage interval should not be termed “confidence interval” to avoid confusion with the statistical concept (see GUM:1995, 6.2.2).
NOTE 3 A coverage interval can be derived from an expanded measurement uncertainty (see GUM:1995, 2.3.5).
NOTE 1 This definition pertains to the Uncertainty Approach as presented in the GUM.
NOTE 2 The coverage probability is also termed “level of confidence” in the GUM.
NOTE A coverage factor is usually symbolized k (see also GUM:1995, 2.3.6).
NOTE 1 A calibration may be expressed by a statement, calibration function, calibration diagram, calibration curve, or calibration table. In some cases, it may consist of an additive or multiplicative correction of the indication with associated measurement uncertainty.
NOTE 2 Calibration should not be confused with adjustment of a measuring system, often mistakenly called “self‑calibration”, nor with verification of calibration.
NOTE 3 Often, the first step alone in the above definition is perceived as being calibration.
NOTE 1 Measurement uncertainty necessarily increases along the sequence of calibrations.
NOTE 2 The elements of a calibration hierarchy are one or more measurement standards and measuring systems operated according to measurement procedures.
NOTE 3 For this definition, the ‘reference’ can be a definition of a measurement unit through its practical realization, or a measurement procedure, or a measurement standard.
NOTE 4 A comparison between two measurement standards may be viewed as a calibration if the comparison is used to check and, if necessary, correct the quantity value and measurement uncertainty attributed to one of the measurement standards.
NOTE 1 For this definition, a ‘reference’ can be a definition of a measurement unit through its practical realization, or a measurement procedure including the measurement unit for a non-ordinal quantity, or a measurement standard.
NOTE 2 Metrological traceability requires an established calibration hierarchy.
NOTE 3 Specification of the reference must include the time at which this reference was used in establishing the calibration hierarchy, along with any other relevant metrological information about the reference, such as when the first calibration in the calibration hierarchy was performed.
NOTE 4 For measurements with more than one input quantity in the measurement model, each of the input quantity values should itself be metrologically traceable and the calibration hierarchy involved may form a branched structure or a network. The effort involved in establishing metrological traceability for each input quantity value should be commensurate with its relative contribution to the measurement result.
NOTE 5 Metrological traceability of a measurement result does not ensure that the measurement uncertainty is adequate for a given purpose or that there is an absence of mistakes.
NOTE 6 A comparison between two measurement standards may be viewed as a calibration if the comparison is used to check and, if necessary, correct the quantity value and measurement uncertainty attributed to one of the measurement standards.
NOTE 7 The 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).
NOTE 8 The abbreviated term “traceability” is sometimes used to mean ‘metrological traceability’ as well as other concepts, such as ‘sample traceability’ or ‘document traceability’ or ‘instrument traceability’ or ‘material traceability’, where the history (“trace”) of an item is meant. Therefore, the full term of “metrological traceability” is preferred if there is any risk of confusion.
NOTE 1 A metrological traceability chain is defined through a calibration hierarchy.
NOTE 2 A metrological traceability chain is used to establish metrological traceability of a measurement result.
NOTE 3 A comparison between two measurement standards may be viewed as a calibration if the comparison is used to check and, if necessary, correct the quantity value and measurement uncertainty attributed to one of the measurement standards.
NOTE The expression “traceability to the SI” means ‘metrological traceability to a measurement unit of the International System of Units’.
EXAMPLE 1 Confirmation that a given reference material as claimed is homogeneous for the quantity value and measurement procedure concerned, down to a measurement portion having a mass of 10 mg.
EXAMPLE 2 Confirmation that performance properties or legal requirements of a measuring system are achieved.
EXAMPLE 3 Confirmation that a target measurement uncertainty can be met.
NOTE 1 When applicable, measurement uncertainty should be taken into consideration.
NOTE 2 The item may be, e.g. a process, measurement procedure, material, compound, or measuring system.
NOTE 3 The specified requirements may be, e.g. that a manufacturer's specifications are met.
NOTE 4 Verification in legal metrology, as defined in VIML, and in conformity assessment in general, pertains to the examination and marking and/or issuing of a verification certificate for a measuring system.
NOTE 5 Verification should not be confused with calibration. Not every verification is a validation.
NOTE 6 In chemistry, verification of the identity of the entity involved, or of activity, requires a description of the structure or properties of that entity or activity.
EXAMPLE A measurement procedure, ordinarily used for the measurement of mass concentration of nitrogen in water, may be validated also for measurement in human serum.
EXAMPLE Measurement results, for the distances between the Earth and the Moon, and between Paris and London, are metrologically comparable when they are both metrologically traceable to the same measurement unit, for instance the metre.
NOTE 1 See Note 1 to 2.41 metrological traceability.
NOTE 2 Metrological comparability of measurement results does not necessitate that the measured quantity values and associated measurement uncertainties compared be of the same order of magnitude.
NOTE 1 Metrological compatibility of measurement results replaces the traditional concept of ‘staying within the error’, as it represents the criterion for deciding whether two measurement results refer to the same measurand or not. If in a set of measurements of a measurand, thought to be constant, a measurement result is not compatible with the others, either the measurement was not correct (e.g. its measurement uncertainty was assessed as being too small) or the measured quantity changed between measurements.
NOTE 2 Correlation between the measurements influences metrological compatibility of measurement results. If the measurements are completely uncorrelated, the standard measurement uncertainty of their difference is equal to the root mean square sum of their standard measurement uncertainties, while it is lower for positive covariance or higher for negative covariance.
NOTE 1 A general form of a measurement model is the equation h(Y, X1, …, Xn) = 0, where Y, the output quantity in the measurement model, is the measurand, the quantity value of which is to be inferred from information about input quantities in the measurement model X1, …, Xn.
NOTE 2 In more complex cases where there are two or more output quantities in a measurement model, the measurement model consists of more than one equation.
NOTE 1 If a measurement model h(Y, X1, …, Xn) = 0 can explicitly be written as Y = f(X1, …, Xn), where Y is the output quantity in the measurement model, the function f is the measurement function. More generally, f may symbolize an algorithm, yielding for input quantity values x1, …, xn a corresponding unique output quantity value y = f(x1, …, xn).
NOTE 2 A measurement function is also used to calculate the measurement uncertainty associated with the measured quantity value of Y.
EXAMPLE When the length of a steel rod at a specified temperature is the measurand, the actual temperature, the length at that actual temperature, and the linear thermal expansion coefficient of the rod are input quantities in a measurement model.
NOTE 1 An input quantity in a measurement model is often an output quantity of a measuring system.
NOTE 2 Indications, corrections and influence quantities can be input quantities in a measurement model.
EXAMPLE 1 Frequency in the direct measurement with an ammeter of the constant amplitude of an alternating current.
EXAMPLE 2 Amount-of-substance concentration of bilirubin in a direct measurement of haemoglobin amount-of-substance concentration in human blood plasma.
EXAMPLE 3 Temperature of a micrometer used for measuring the length of a rod, but not the temperature of the rod itself which can enter into the definition of the measurand.
EXAMPLE 4 Background pressure in the ion source of a mass spectrometer during a measurement of amount‑of‑substance fraction.
NOTE 1 An indirect measurement involves a combination of direct measurements, each of which may be affected by influence quantities.
NOTE 2 In the GUM, the concept ‘influence quantity’ is defined as in the second edition of the VIM, covering not only the quantities affecting the measuring system, as in the definition above, but also those quantities that affect the quantities actually measured. Also, in the GUM this concept is not restricted to direct measurements.
NOTE 1 See GUM:1995, 3.2.3, for an explanation of ‘systematic effect’.
NOTE 2 The compensation can take different forms, such as an addend or a factor, or can be deduced from a table.