# Metrology

(Redirected from Metrological)
A scientist stands in front of the Microarcsecond Metrology (MAM) testbed.

Metrology is "the science of measurement, embracing both experimental and theoretical determinations at any level of uncertainty in any field of science and technology" as defined by the International Bureau of Weights and Measures (BIPM).[1] The field of metrology is important for establishing a common understanding of units, which is crucial in linking human activities.[2] Modern metrology has its roots in the French Revolution, with the political motivation to harmonize units all over France, a proposal was made to create a length standard borrowed from a natural source.[3] This led to the creation of the decimal based metric system in 1795 to establish a set of standards for other types of measurements. Several other countries adopted the metric system between 1795 and 1875 and to ensure conformity between the countries, the Bureau International des Poids et Mesures (BIPM) was established by the Metre Convention.[4][5] This has since evolved into the International System of Units (SI) as a result of a resolution made in the 11th Conference Generale des Poids et Mesures (CGPM) in 1960.[6]

Metrology is a broad field divided into three basic, overlapping activities:[7][8]

• Definition of internationally accepted units of measurement
• Realisation of these units of measurement in practice
• Application of chains of traceability linking measurements made in practice to reference standards

Metrology also has three basic subfields that all use the three basic activities to varying degrees:[7]

• Scientific or fundamental metrology
• Applied, technical or industrial metrology
• Legal metrology

In each country a national measurement system (NMS) exists as a network of laboratories, calibration facilities and accreditation bodies that implement and maintain the metrology infrastructure of a country.[9][10] The NMS greatly effects how measurements are undertaken in the country and their subsequent recognition by the international community. This has wide reaching impacts in a variety of different regions of society. It has implications in the area of economies, energy, environment, health, manufacturing, industry, consumer confidence and many others.[11][12] The effects of metrology on trade and the economy are some of the easiest observed societal impacts. In order to facilitate fair and accurate trade between countries there must be an agreed upon system of measurement, without this there is an asymmetry between the buyers and sellers and generally subsequent market failure.[12]

## Overview

Metrology is defined by the International Bureau of Weights and Measures (BIPM) as "the science of measurement, embracing both experimental and theoretical determinations at any level of uncertainty in any field of science and technology."[13] The field of metrology is important for establishing a common understanding of units, which is crucial in linking human activities.[2] For example, trading manufactured goods, the ability to accurately diagnose illnesses, and ensuring consumer confidence during the purchase of goods and services are all dependent on a common confidence in the measurements made during these processes.[13] Establishing this common confidence is achieved through the three basic activities of metrology: the definition of internationally accepted units of measurement, realisation of these units of measurement in practice, and application of chains of traceability linking measurements made in practice to reference standards.[7][2] These base concepts of metrology are propagated by the three main fields of metrology, which are: scientific or fundamental metrology; applied, technical or industrial metrology; and legal metrology.[7]

### Scientific or fundamental metrology

Scientific metrology concerns the establishment of units of measurement, the development of new measurement methods, realization of measurement standards, and the transfer of traceability from these standards to users in society.[2][4] While there is no formal definition of fundamental metrology it is considered to be the top level of scientific metrology that strives for the highest level of accuracy.[4] The BIPM maintains a database of the metrological calibration and measurement capabilities of various institutes around the world. These institutes, whose activities are peer-reviewed, provide the fundamental reference points for metrological traceability. In the area of measurement, the BIPM has identified nine metrology areas, including length, mass, and time.[14]

### Applied, technical or industrial metrology

Applied, technical or industrial metrology concerns the application of measurement science to manufacturing and other processes and their use in society, ensuring the suitability of measurement instruments, their calibration and quality control of measurements.[2] Although the emphasis in this area of metrology is on the measurements themselves, traceability of the calibration of the measurement devices is necessary to ensure confidence in the measurements. Industrial metrology is important to the economical and industrial development of a country and therefore the condition of the industrial metrology program can indicate a countries economic status.[15]

### Legal metrology

Legal metrology "concerns activities which result from statutory requirements and concern measurement, units of measurement, measuring instruments and methods of measurement and which are performed by competent bodies."[16] Such statutory requirements might arise from, amongst others, the needs for protection of health, public safety, the environment, enabling taxation, protection of consumers and fair trade. The International Organization for Legal Metrology (OIML) was established to assist in harmonising such regulations across national boundaries to ensure that legal requirements do not inhibit trade.[17] In Europe WELMEC was established in 1990 to promote cooperation on the field of legal metrology in the European Union and the European Free Trade Association (EFTA) member states.[18] In the United States uniformity of legal metrology is under the authority of the Office of Weights and Measures of National Institute of Standards and Technology (NIST), however enforcement is decided by the individual states.[17]

## Historical development

Throughout history the ability to make measurements has been instrumental in the progress of mankind. The ability to measure alone is not sufficient, rather the ability to compare separate measurements and have agreeability is crucial for the measurements to be meaningful.[3] The first record of a permanent standard is from 2900 BC, when the Royal Egyptian Cubit was created out of black granite.[3] The cubit was decreed to be the length of the Pharaoh's forearm plus the width of his hand and replica standards were given out to builders.[4] The success of standardized length during the building of the pyramids is evidenced by the lengths of the pyramid bases differing by no more than 0.05%.[3]

Other civilizations produced their own measurement standards that were accepted throughout their nations. The architecture of the Roman and Greek empires were based on their own respective systems of measurement.[3] Nonetheless, the fall of these great empires and the rise of the dark ages caused much of measurement knowledge and standardization to be lost. During this time, local systems of measurements became common, however comparability of measurements was complicated as many of local systems did not agree.[3] For example England in 1196 established the Assize of Measures to create standards for the length of measurements, and in 1215 followed with a section in the Magna Carta for the measurement of wine and beer.[19]

Modern metrology has its roots in the French Revolution. With the political motivation to harmonize units all over France, a proposal was made to create a length standard borrowed from a natural source.[3] In March of 1791, the meter was defined so that it was not an arbitrary unit and that it was not related to a single country.[5] This led to the creation of the decimal based metric system in 1795 to establish a set of standards for other types of measurements. Several other countries adopted the metric system between 1795 and 1875 and to ensure conformity between the countries, the Bureau International des Poids et Mesures (BIPM) was established by the Metre Convention.[4][5] The original mission of BIPM was to create international standards for the units of measurements and to compare them to national standards to ensure conformity. Over time its scope has increased to include electrical units, photometric units, and ionizing radiation measurement standards.[5] Modernization of the metric system occurred again in 1960 with the creation of the International System of Units (SI) as a result of a resolution made in the 11th Conference Generale des Poids et Mesures (CGPM).[6]

## Fundamental concepts

### Definition of units

The International System of Units (SI Units), and the definitions on which they are based, was formally established in 1960 at the 11th Conférence Générale des Poids et Mesures (CGPM).[6] SI Units have seven internationally recognized base units: length, mass, time, electric current, thermodynamic temperature, amount of substance, and luminous intensity.[20] By convention, each of these units are considered to be mutually independent of each other; however, in reality they are interdependent given some definitions contain other base SI Units.[21] All of the other SI Units can be derived from a combination of the seven base units.[22] The base SI Units and the current standards are summarized in the table below.

Base Quantity Name Symbol Definition
Length Metre m The length of the path travelled by light in vacuum during a time interval of 1/299792458 of a second[23]
Mass Kilogram kg The mass of the international prototype of the kilogram (IPK)[24]
Time Second s The duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom[25]
Electric Current Ampere A A constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 metre apart in vacuum, would produce between these conductors a force equal to 2 x 10–7 newton per metre of length[26]
Thermodynamic Temperature Kelvin K The fraction 1/273.16 of the thermodynamic temperature of the triple point of water[27]
Amount of Substance Mole mol The amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12[28]
Luminous Intensity Candela cd The luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 x 1012 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian[29]

Since the definitions of the base units are the reference point for all measurements taken in SI units if the reference value was to change then all prior measurements would be incorrect. For example, if a piece of the international prototype of the kilogram was to snap off it would still be defined as a kilogram and then all previous measured values of a kilogram would be heavier.[4] The importance of reproducible SI units has led the Bureau International des Poids et Mesures (BIPM) to begin the process of defining the base SI units in terms of physical constants.[30] By defining the base SI units with respect to physical constants it becomes possible to realise them with a higher level of precision and reproducibility at any place, at any time, by anyone.[30]

### Realisation of units

A computer-generated image of the International Prototype kilogram (IPK), which is made from an alloy of 90% platinum and 10% iridium (by weight)

The realisation of a unit of measure is the conversion of its definition into reality.[31] Three possible methods of realisation are defined by International vocabulary of metrology (VIM). Firstly, a physical realisation of the unit from its definition. Secondly, a production of a highly reproducible measurement as a reproduction of the definition, such as the quantum Hall effect for the ohm. Thirdly, the usage of a material object as the measurement standard, like the international prototype of the kilogram (IPK) picture right.[32]

### Standards

In metrology, a standard (or etalon) is an object, system, or experiment that bears a defined relationship to a unit of measurement of a physical quantity.[33] Standards are the fundamental reference for a system of weights and measures by realising, preserving, or reproducing a unit, which measuring devices can be compared against.[2] A certified reference material (CRM) is an example of a standard this is produced with a stated value and uncertainty value. A CRM provides direct traceability to the realisation of the unit of measure and can be used for direct comparisons of other materials or calibration of a measuring device.[2]

#### Standards hierarchy

There are three levels of standards in the hierarchy of metrology, which are the primary standards, secondary standards, and working standards.[15]

• Primary standards are of the highest quality and do not reference any other standards.
• Secondary standards are standards which are calibrated with reference to a primary standard.
• Working standards are used to calibrate or check measuring instruments or other material measures, and are calibrated with respect to the secondary standards.

The reason a hierarchy exists for standards in metrology is to preserve the quality of the higher standards.[15] When standards are used for calibrations or checks there is a potential for the standard to deteriorate over time. By following the hierarchy, calibrations using the primary standard are done infrequently and therefore preserve the integrity of the primary standard.

### Traceability and calibration

The metrology traceability pyramid

Metrological traceability is defined by the Joint Committee for Guides in Metrology as "property of a measurement result whereby the result can be related to a reference through a documented unbroken chain of calibrations, each contributing to the measurement uncertainty".[34] It permits comparison of measurements, whether the result is compared to the previous result in the same laboratory, a measurement result a year ago, or to the result of a measurement performed anywhere else in the world.[35] The unbroken chain of traceability allows any measurement to be be referenced to higher levels of measurements all the way back to the original definition of the unit.[2] This allows separate measurements to be compared through the common unit definition.

Traceability is most often obtained by calibration, establishing the relation between the indication of a measuring instrument or secondary standard and the value of a measurement standard. Calibration is defined as an "Operation that, under specified conditions, in a first step, establishes a relation between the quantity values with measurement uncertainties provided by measurement standards and corresponding indications with associated measurement uncertainties (of the calibrated instrument or secondary standard) and, in a second step, uses this information to establish a relation for obtaining a measurement result from an indication" by the Joint Committee for Guides in Metrology.[34] The four primary reasons calibrations are undertaken are:[2]

• Provide Traceability
• Ensure instrument/standard is consistent with other measurements
• Determine accuracy
• Establish reliability

### Uncertainty

Uncertainty of a measurement in metrology is a value associated with a measurement that expresses the spread of possible values associated with the measurand.[36] In other words it is a quantitative expression of the doubt that exists in the measurement. There are two components to stating an uncertainty on a measurement, first the width of the uncertainty interval, and secondly the confidence level which states how likely the true value is to fall within the interval.[37] Uncertainty is generally expressed as follows:[2]

${\displaystyle Y=y\pm U}$

Where 'y' is the measurement value and 'U' is the uncertainty.

According to the Guide to the Expression of Uncertainty in Measurement (GUM) each uncertainty value has two components, the type A uncertainty and the type B uncertainty.[36] Type A uncertainty is estimates resulting from statistical analysis, whereas type B uncertainty is from other sources, such as history of the instrument, manufacturers specifications, or from published information.[37] Generally type A measurements are calculated by taking several repeat measurements and determining the standard deviation of the measurements, then using the following equation:

${\displaystyle typeA={\frac {s}{\sqrt {n}}}}$

Where 's' is the standard deviation and 'n' is the number of measurements. The type B uncertainty is determined by estimating the upper and lower limits of uncertainty and selecting what type of distribution the uncertainty follows. Then with the confidence interval the type B uncertainty can be determined.[37] The overall uncertainty is determined to be the root sum of squares of the type A and type B uncertainties.[36]

## International infrastructure

There are several organizations that help maintain and standardise metrology on an international scale.

### Metre Convention

The Metre Convention created three main organizations to facilitate the standardisation of weights and measures around the world. The first, the General Conference on Weights and Measures (CGPM) provided a forum for representative of member states, the second, the International Committee for Weights and Measures (CIPM) was an advisory committee of metrologists of high standing and the third, the International Bureau of Weights and Measures (BIPM) was an institute that provided appropriate secretarial and laboratory facilities in support of the CGPM and CIPM.[38]

#### General Conference on Weights and Measures

The General Conference on Weights and Measures (French: Conférence générale des poids et mesures or CGPM) is the principal decision-making body put on place by the convention. It is made up of delegates from member states and [non-voting] observers from associate states.[39] The conference usually meets every four to six years to receive and discuss a report from the CIPM and to endorse new developments in the SI on the advice of the CIPM though at the 2011 meeting, it agreed to meet again in 2014 rather than 2015 to discuss the maturity of the new SI proposals.[40] It is also responsible for new appointments to the CIPM and decides on major issues concerning the development and financing of the BIPM.

#### International Committee for Weights and Measures

Seal of the BIPM

The International Committee for Weights and Measures (French: Comité international des poids et mesures or CIPM) is made up of eighteen (originally fourteen)[41] individuals from a member state of high scientific standing, nominated by the CGPM to advise the CGPM on administrative and technical matters. It is responsible for the running of ten consultative committees (CCs), each of which investigates different aspects of metrology – one CC discusses the measurement of temperature, another the measurement of mass and so on. The CIPM meets annually at Sèvres to discuss annual reports from the various CCs, to submit an annual report to the governments of member states in respect of the administration and finances of the BIPM and to advise the CGPM on technical matters as and when necessary. Each member of the CIPM is from a different member state – with France, in recognition of its work in setting up the Convention, always having one seat on the CIPM.[42][43]

#### International Bureau of Weights and Measures

The International Bureau of Weights and Measures (French: Bureau international des poids et mesures or BIPM) is an organisation based at Sèvres, France that has custody of the International Prototype Kilogram, provides metrology services for the GCPM and CIPM, houses the secretariat for these organisations and hosts their formal meetings. It also has custody of the former International Prototype Metre which was retired in 1960. Over the years the various international prototype metres and kilograms were returned to BIPM headquarters for recalibration services. The director of the BIPM is ex-officio a member of the CIPM and a member of all consultative committees.

### International Organization of Legal Metrology

The International Organization of Legal Metrology (French: Organisation Internationale de Métrologie Légale or OIML), is an intergovernmental organization, created in 1955 with the objective to promote the global harmonization of the legal metrology procedures that underpin and facilitate international trade.[44] The harmonization of the technical requirements, test procedures and test report formats ensure confidence in measurements completed for trade and reduces the costs from discrepancies and measurement duplications. [45] OIML creates a number of publications that fall within 4 distinct categories:[45]

• International Recommendations: Model regulations to establish metrological characteristics and conformity of measuring instruments
• International Documents: Informative documents with the aim of harmonizing the field of legal metrology
• International Guides: Guidelines to the application of legal metrology
• International Basic Publications: Definitions of the operating rules of the OIML structure and system

While OIML has no legal authority to impose its recommendations and guidelines on its member countries, it provides a standardised legal framework for its member countries to adopt into their policies. This assists members in the development of the appropriate and harmonized legislation regarding certification and calibration.[45]

### International Laboratory Accreditation Cooperation

The International Laboratory Accreditation Cooperation (ILAC) is an international organisation for accreditation bodies that are involved in the certification of various conformity assessment bodies.[46] It standardises the accreditation practices and procedures to recognise competent calibration facilities and provides assistance to countries developing their own accreditation bodies.[2] ILAC has a mutual recognition agreement (MRA) between its members, which allows the work of the members to be automatically accepted by any other signatories, which helps remove some of the technical barriers to trade.[47]

### Joint Committee for Guides in Metrology

The Joint Committee for Guides in Metrology (JCGM) is an committee the created and maintains two metrology guides, the Guide to the expression of uncertainty in measurement (GUM)[48] and the International vocabulary of metrology - basic and general concepts and associated terms (VIM).[49] JCGM is a collaboration of eight different partner organisations, which are as follows:[50]

The JCGM operates through two seperate working groups JCGM-WG1 and JCGM-WG2, where JCGM-WG1 has responsibility for the GUM and JCGM-WG2 has responsibility for the VIM.[51] Each of the member organization appoints one representative and up to two experts to attend each of the meetings, and it allowed to appoint up to three experts to each of the working groups.[50]

## National infrastructure

A national measurement system (NMS) is a network of laboratories, calibration facilities and accreditation bodies that implement and maintain the measurement infrastructure of a country.[52][10] The NMS of a country sets the standards of measurement, ensures accuracy, consistency, comparability, and reliability of measurements conducted within the country.[53] This allows all countries that are part of the CIPM Mutual Recognition Arrangement (CIPM MRA), an agreement between national metrology institutes, to have measurements be recognized by all other member countries.[2]

### National metrology institutes

An overview of a national measurement system

The National Metrology Institute's (NMI) role in the national measurement system is to undertake scientific metrology, realisation of the base units, and maintain the primary national standards.[2] Through realising the base units and holding the primary national standards, a NMI provides the traceability link to international standards for the country and therefore anchors the national calibration/traceability hierarchy.[2] For the national measurement system to be recognized internationally under the CIPM Mutual Recognition Arrangement the NMI is required to participate in international comparisons of its measurement capabilities.[10] The Bureau International des Poids et Mesures maintains a key comparison database of these comparisons and a list of calibration and measurement capabilities (CMCs) of the countries participating the the CIPM MRA.[54] Not all countries have a single centralized metrology institute, some have a lead NMI and several decentralised designated institutes that specialize in specific national standards.[2]

### Calibration laboratories

Calibration laboratories are another important aspect of the national measurement system because they are generally responsible for industrial metrology.[10] Calibration laboratories are accredited and provide calibration services to industry firms, which provides a traceability link back to the national metrology institute. This traceability link is established when calibration laboratories have their standards calibrated against the national standards by a national metrology institute or another designated institute.[2] The calibration laboratories are essential to propagating the measurement standards of the country from a national level to the industrial level.

### Accreditation bodies

Accreditation is when an authoritative body determines that an organization is competent to perform its services by assessing the personnel and management system of the organization.[10] For international recognition, the accreditation body of a country must comply with international requirements, and therefore are generally built from international and regional cooperation.[10] Accreditation is granted by evaluation of the laboratory with regards to international standards, for example ISO/IEC 17025 “General requirements for the competence of testing and calibration laboratories".[2] To ensure impartial, objective, and technically credible accreditation these bodies are independent from other national measurement system institutions.[10]

## Societal impact

Metrology is a very diverse field of science and has wide reaching impacts in a variety of different regions of society. It has implications in the area of economies, energy, environment, health, manufacturing, industry, consumer confidence and many others.[11][12] The effects of metrology on trade and the economy are some of the easiest observed societal impacts. In order to facilitate fair and accurate trade between countries there must be an agreed upon system of measurement, without this there is an asymmetry between the buyers and sellers and generally subsequent market failure.[12] Therefore, the accurate measurement and resulting regulation of essentials such as water, fuel, food and electricity, are critical for consumer protection and to promote the flow of goods and services between trade partners.[55] Common measurement systems and quality standards benefit both the consumer and the manufacturer, as production of goods to a common standard reduces the variety of standard reducing costs, and reduces a consumers risk by ensuring the product meets their requirements without additional quality verification.[12] This impacts trade through the reduction of transaction costs and increasing economy of scale. Several studies have shown that increasing standardization in measurement has a positive impact on GDP. In the United Kingdom it was evaluated that 28.4% of GDP growth between 1921 and 2013 was a result of standardization, in Canada it was demonstrated that between 1981 and 2004 that standardization resulted in 9% of the GDP growth, and in Germany the economic benefit of standardization is 0.72% of GDP per year.[12]

Legal metrology has significant impacts on society aside from the economic impacts. It has been observed that there is a reduction in accidental deaths and injuries as a result of radar speed devices and breathalyzer measuring devices.[55] Also, the legal regulation of measuring devices has improved the efficiency and reliability of the devices, which result in impacts in the health field, environment, and many other fields where advances rely on accurate and reliable measurements.[55] In the health industry measuring the human body is a challenging field with poor repeatability and reproducibility, so advances in metrology field help develop new techniques to improve health care and reduce costs.[56] Environmental policy is based on data from environmental research and having the highest quality measurements is important for understanding things like climate change and regulations needed for pollutants.[57] Aside from regulation, metrology is essential in supporting innovation in nearly all fields, the ability to measure provides a technical infrastructure and tools that can then be used to pursue further innovation. By providing a technical platform which new ideas can be built upon, easily demonstrated, and shared, measurement standards allow new ideas to be explored and expanded upon.[12]

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