Measurement Standards

Measurement Standards

The world around us, first of all, is the world of physical quantities existing in reality in the widest range of their values. This is why, the range of characteristics describing both natural phenomena and the behaviour of devices and instruments produced in this world, is very wide.

Physical quantities are characteristics of the objects of the material world as well as the processes which are characterizing different interactions between these objects or their variation with time. This logically follows from the materiality of the world, which manifests itself in the absolute categories of this world as a whole and the attributes of separate objects around us such as space, time, interactions, dimensions, development, thermal state, displacements, and so on.

People see their destination in cognition of the world. On the way, experience has led them to the quantitative comparison of physical quantities, that is, to the conclusion that a person is to measure something in order to know it. Further logic in this regards is that in order to measure, the person is to choose a measure, establish a single value of the quantity i.e. the unit. Hence, there is a requirement for a standard, material, accurate, and stable embodiment of this unit.

The history of human civilization is closely connected with the development of the measurement culture. This is the process of continuous improvement of methods and means for measurement, and of systems ensuring measurement traceability based on improvements in accuracy and measurement uniformity, motivated by the increasing recognition of the importance of reference measurements as a necessary basis for both economic and state power. In other words, the entire history of human kind reflects the way that people have passed from measurements based on the senses to the scientific fundamentals of measurements which are the most important components of modern metrology, a science of measurements, methods and means for ensuring their traceability, and ways for reaching the required accuracy.

Measurement has the following two different definitions. As per the first definition,’ the measurement in the narrow sense is an experimental comparison of one measure and to another, known one of the same kind (quality), which is established as a unit’. A typical example is the measurement of physical quantities and application of the proportional scales. As per the second definition, ‘measurement in the broad sense is a search for correlations between numbers and states or processes according to a certain rule’.

The wide scope of activities in the field of measurement testifies to their significant role in science and technology in the life of modern society. One can judge the general level of development of a society according to the condition and opportunities of the measuring service and metrological assurance. However, the great masses of measurement data which are obtained through the measurements are socially significant and useful only if their traceability and accuracy, irrespective of the place, time, and conditions under which they are taken, are assured. Measurement traceability is one of the most important tasks of metrology.

The technological significance of measurements is determined by the fact that measurements provide information about an object under control, which is necessary to realize the technological process, to ensure the quality of products, and to control the object.

Measurements play a very important role in the fields of science, engineering and technology. Measurements have been developed over many decades, with a tendency to differentiate the branches of science, engineering, and technology. This meant the accelerated development of separate fields of measurement, as well as of separate types of measuring instruments and equipment. Such developments are continuing. However, because of the development of complex information measuring systems, in some instances the opposite situation occurred. The integration of different fields of metrology began to develop too. These tendencies have been reflected in the working out of the theory of information, measuring systems intended to study physical quantities of different kinds, the fundamentals for the theory of accuracy of measuring devices, the development of methods to process the measurement results, and the theory of scientific experiment.

Measurement standards are those devices, artifacts, procedures, instruments, systems, protocols, or processes which are used to define (or to realize) measurement units and on which all lower level (less accurate) measurements depend. A measurement standard can also be said to store, embody, or otherwise provide a physical quantity which serves as the basis for the measurement of the quantity.

A measurement standard is defined as the physical embodiment of a measurement unit, by which its assigned value is defined, and to which it can be compared for calibration purposes. In general, it is not independent of physical environmental conditions, and it is a true embodiment of the unit only under specified conditions. Another definition of a measurement standard is that it is a unit of known quantity or dimension to which other measurement units can be compared.

History of measurement standards

Many early standards were based on the human body such as the length of the hand of a person, the width of his thumb, the distance between outstretched fingertips, the length of the foot of a person, and a certain number of paces, etc. In the beginning, while groups were small, such standards were convenient and uniform enough to serve as the basis for measurements.

The logical person to impose a single standard was the ruler of the country. Hence, the present 12-inch or other short measuring stick is still called a ‘ruler’. The establishment of measurement standards thus became the prerogative of the government, and this right has since been assumed by all the national governments.

History is replete with examples which show the importance of measurements and standards. It is a known fact that ‘weights and measures are ranked among the necessaries to every individual of human society’. Hence, these were thought to be very important and even in early ages, the national governments used their power to fix uniform standards of weights and measures. The need for weights and measures (standards) dates back to earliest recorded history.

Originally, they were locally decreed to serve the parochial needs of commerce, trade, land division, and taxation. Because the standards were defined by local or regional authorities, differences arose that often caused problems in commerce and early scientific studies. The rapid growth of science in the late 17th century highlighted a number of serious deficiencies in the system of units then in use and, in 1790, led the French National Assembly to direct the French Academy of Sciences to ‘deduce an invariable standard for all measures and all the weights’. The Academy proposed a system of units, the metric system, to define the unit of length in terms of the earth’s circumference, with the units of volume and mass being derived from the unit of length. Additionally, they proposed that all multiples of each unit be a multiple of 10.

In 1875, several countries signed the ‘Treaty of the Meter’, establishing a common set of units of measure. It also established an International Bureau of Weights and Measures (called the BIPM). That bureau is located in the Parisian suburb of Sevres. It serves as the worldwide repository of all the units which maintain our complex international system of weights and measures. It is through this system that compatibility between measurements made thousands of kilometers apart is currently maintained.

In correspondence with the adopted definitions, the standards of the meter and the kilogram were reproduced in the BIPM: the meter as the distance between two lines on a platinum-iridium rod, and the kilogram as a cylindrical weight with diameter and height equal to 39 mm, made of the same alloy. They were manufactured and tested in the BIPM, and from 1889, they were given, according to sortition, to the countries participating in the ‘Convention du Meter’. Two standards were given to each participant (one as a national standard, and the other as its copy), which facilitated the introduction of the metric system throughout the world.

The system of units set up by the BIPM is based on the meter and kilogram instead of the yard and the pound. It is called the ‘Systeme International d’Unites (SI)’ or the International System of Units. It is used in almost all scientific work and is the only system of measurement units in most of the countries of the world today.

However, even a common system of units does not guarantee measurement agreement. And the crux of the problem lies therein. People are to make measurements, and they are to know how accurately (or, to be more correct, with what uncertainty) they have made those measurements. In order to know that standards are required. Even more important, everyone is to agree on the values of those standards and use the same standards.

As the level of scientific sophistication improved, the basis for the measurement system changed dramatically. The earliest standards were based on the human body, and then attempts were made to base them on ‘natural’ phenomena. At one time, the basis for length was supposed to be a fraction of the circumference of the earth but it was ‘maintained’ by the use of a platinum/iridium bar. Time was maintained by a pendulum clock but was defined as a fraction of the day and so on. Today, the metre is no longer defined by an artifact. Now, the metre is the distance which light travels in an exactly defined fraction of a second. Since the speed of light in a vacuum is now defined as a constant of nature with a specified numerical value (299, 792, 458 metres per second), the definition of the unit of length is no longer independent of the definition of the unit of time.

Prior to 1960, the second was defined as 1/86,400 fraction of a mean solar day. Between 1960 and 1967, the second was defined in terms of the unit of time implicit in the calculation of the ephemerides i.e. ‘the second is the fraction 1/31, 556, 925.9747 of the tropical year for January 0 at 12 hours of ephemeris time’. With the advent of crystal oscillators and, later, atomic clocks, better ways were found of defining the second (SI). This, in turn, allowed a better understanding of things about natural phenomena that would not have been possible before. For example, it is now known that the earth does not rotate on its axis in a uniform manner. In fact, it is erratically slowing down. Since the second is maintained by atomic clocks it is necessary to add ‘leap seconds’ periodically so that the solar day does not gradually change with respect to the time used every day. It was decided that a constant frequency standard was preferred over a constant length of the day.


One problem with standards is that they are of several kinds. In addition to ‘measurement standards’, there are ‘standards of practice or protocol standards’ which are produced by the various standards organizations such as the International Organization for Standardization (ISO), the International Electro-technical Commission (IEC), the American National Standards Institute (ANSI), and the Bureau of Indian Standards etc.

Standards of Practice (Protocol Standards)

Standards of Practice (Protocol Standards) are standards (Fig 1) which define everything from the dimensions and electrical characteristics of a flashlight battery to the shape of the threads on a machine screw and from the size and shape of an IBM punched card to the ‘quality assurance requirements’ for measuring equipment. Such standards can be defined as documents describing the operations and processes which are to be performed in order for a particular end to be achieved. They are called a ‘protocol’ by Europeans to avoid confusion with a physical standard.

Fig 1 Standards of Practice (Protocol Standards)

Legal Metrology

The application of measurement standards to the control of the daily transactions of trade and commerce is known as Legal Metrology. It is more commonly known as Weights and Measures. Internationally, coordination among nations on Legal Metrology matters is, by international agreement, handled by a quasi-official body ‘the International Organization for Legal Metrology (OIML)’.

Forensic Metrology

Forensic Metrology is the application of measurements and hence measurement standards to the solution and prevention of crime. It is practiced within the laboratories of law enforcement agencies throughout the world. Worldwide activities in Forensic Metrology are coordinated by Interpol ( International Police, the international agency that coordinates the police activities of the member nations).

Standard Reference Materials

Another type of standards which are used is the Standard Reference Materials (SRM). SRMs are discrete quantities of substances or minor artifacts which have been certified as to their composition, purity, concentration, or some other characteristic useful in the calibration of the measurement devices and the measurement processes normally used in the process control of those substances. SRMs are the essential calibration standards in stoichiometry (the metrology of chemistry). For example, in the USA, the National Institute of Standards and Technology (NIST), through its Standard Reference Materials Program, offers for sale of over 1300 SRMs. These range from ores to pure metals and alloys. They also include many types of gases and gas mixtures as well as and many biochemical substances and organic compounds. Among the artifact devices available are optical filters with precise characteristics and standard lamps with known emission characteristics.

Conceptual Basis of Measurements

Some outstanding scientists, giving a high estimate to the importance of measurements, wrote the following.

  • ‘Count what is countable, measure what is measurable, and make measurable what is not measurable’ (G. Galileo).
  • ‘Science begins when people begin to measure; exact science is impossible without measure’ (D. I. Mendeleyev).
  • ‘Each thing is known only to the extent to which it can be measured’ (W. Kelvin). Lord Kelvin’s oft-quoted statement is ‘I often say that when you can measure what you are speaking about, and can express it in numbers, you know something about it; but when you cannot measure it, cannot express it in numbers, your knowledge is of a meager and unsatisfactory kind; it may be the beginnings of knowledge, but you have scarcely, in your thoughts, advanced to the stage of science, whatever the matter may be. So therefore, if science is measurement, then without metrology there can be no science (William Thomson Kelvin, May 6, 1886).

Lord Kelvin’s statement has been quoted so many times that it has almost become trite, but the Fig 2 shows an interesting hierarchy for valid decision making. In order to achieve quality or ‘to do things right’, it is necessary to make some decisions. The correct decisions cannot be made unless there are good numerical data on which to base those decisions. Those numerical data, in turn, is to come from measurements and if ‘valid’ decisions are really needed, they are to be based on the ‘right’ numbers. The only way to get ‘correct’ numerical data is to make accurate measurements using calibrated instruments which have been properly utilized. Finally, if it is important to compare those measurements to other measurements made at other places and other times, the instruments are to be calibrated using traceable standards.

Fig 2 Hierarchy for valid decision making

Need for Standards

Standards define the units and scales in use, and allow comparison of measurements made in different times and places. For example, buyers of fuel oil are charged by a unit of liquid volume. In some countries, the measure is ‘the gallon’ but in some other countries, the measure is ‘the litre’. It is important for the buyer that the quantity ordered is actually received and the refiner expects to be paid for the quantity shipped. Both parties are interested in accurate measurements of the volume and, hence, need to agree on the units, conditions, and method(s) of measurement to be used.

Persons needing to measure a mass cannot borrow the primary standard maintained in France or even the national standard such as in case of USA, the NIST. They are to use lower-level standards which can be checked against those national or international standards. Everyday measuring devices, such as scales and balances, can be checked (calibrated) against working level mass standards from time to time to verify their accuracy. These working-level standards are, in turn, calibrated against higher-level mass standards. This chain of calibrations or checking is called ‘traceability’. A proper chain of traceability is to include a statement of uncertainty at every step.

Types of standards

There are two types of standards namely (i) basic or fundamental standards, and (ii) derived standards.

Basic or fundamental standards – In the SI system, there are seven basic measurement units from which all other units are derived. All of the units except one are defined in terms of their unitary value. The one exception is the unit of mass. It is defined as 1000 grams (g) or 1 kilogram (kg). It is also unique in that it is the only unit currently based on an artifact. All the standards of mass are based on one particular platinum / iridium cylinder kept at the BIPM in France. If that International Prototype Kilogram is to change, then all other mass standards throughout the world becomes wrong.

The seven basic units are listed in Tab 1.

Tab 1 SI Base Units
Sl. No.Base quantityName of Base UnitSymbol
4Electric currentampereA
5Thermodynamic temperaturekelvinK
6Amount of substancemolemol
7Luminous intensitycandelacd

The International definitions of the SI Base Units are given below. 

Unit of length (meter) – The meter is the length of the path traveled by light in vacuum during a time interval of 1/299,792,458 of a second.

Unit of mass (kilogram) – The kilogram is the unit of mass which is equal to the mass of the international prototype of the kilogram.

Unit of time (second) – The second is 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 cesium-133 atom.

Unit of electric current (ampere) – The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible cross section, and placed 1 meter apart in vacuum, would produce between these conductors a force equal to 0.0000002 newtons per meter of length.

Unit of thermodynamic temperature (kelvin) – The kelvin, unit of thermodynamic temperature, is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water. The unit kelvin and its symbol K is also used to express an interval or a difference in temperature. In addition to the thermodynamic temperature (symbol T), expressed in kelvin, use is also made of Celsius temperature (symbol t) defined by the equation t = T – To where To = 273.15 K by definition. To express Celsius temperature, the unit ‘degree Celsius’ which is equal to the unit ‘kelvin’ is used; in this case ‘degree Celsius’ is a special name used in place of ‘kelvin’. An interval or difference of Celsius temperature can be, however, expressed in kelvins as well as degrees Celsius.

Unit of amount of substance (mole) – The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon-12. When the mole is used, the elementary entities are to be specified and can be atoms, molecules, ions, electrons, other particles, or specified groups of such particles. In the definition of the mole, it is understood that unbound atoms of carbon-12, at rest, and in their ground state, are referred to.

Unit of luminous intensity (candela) – The candela is the luminous intensity, in a given direction, of a source which emits monochromatic radiation of frequency 540 x (10 to the power 12) hertz and which has a radiant intensity in that direction of (1/683) watt per steradian.

Derived Standards

All of the other units are derived from the seven basic units described in Tab 1. Measurement standards are devices which represent the SI standard unit in a measurement. (As an example, one can use a zener diode together with a reference amplifier and a power source to supply a known voltage to calibrate a digital voltmeter. This can serve as a measurement standard for voltage and be used as a reference in a measurement). Tab 2 lists the most common derived SI units, together with the base units which are used to define the derived unit. As an example, the unit of frequency is the hertz; it is defined as the reciprocal of time, i.e., 1 hertz (1 Hz) is one cycle per second.

The Measurement Assurance System

There exists the interrelationship of the various categories of standards throughout the world. Every nation has its own structure for ensuring a Measurement Assurance system. Indeed, a variety of regional organizations exist which help relate measurements made in different parts of the world to each other.

Numbers, dimensions, and units

A measurement is always expressed as a multiple (or sub-multiple) of some unit quantity. That is, both a numeric value and a unit are required. If electric current is the measured quantity, it can be expressed as some number of milli-amperes or even micro-amperes. It is easy to take for granted the existence of the units used, because their names form an indispensable part of the vocabulary.

Multiplication factors

Since it is inconvenient to use whole units in many cases, a set of multiplication factors has been defined that can be used in conjunction with the units to bring a value being measured to a more reasonable size. For example, it is difficult to have to refer to large distances in terms of the meter. Hence, one defines longer distances in terms of kilometers. Short distances are stated in terms of millimeters, micrometers, and nanometers etc.

Defining Terms

Most of the definitions described below are taken from the ‘International Vocabulary of Basic and General Terms in Metrology’, published by the ISO. The balance definitions are the ones which are widely accepted.

Accuracy of measurement – The closeness of the agreement between the result of a measurement and a true value of the measurands. However, it is to be noted that the accuracy is a qualitative concept. The term precision is not to be used for accuracy. Precision only implies repeatability. For example, to say an instrument is accurate to 5 % (a common way of stating it) is wrong. One does not find such an instrument very useful if it, in fact, is only accurate 5 % of the time. When such a statement is made, it is meant that the instrument’s inaccuracy is less than 5 % and it is accurate to better than 95 %. Unfortunately, this statement is almost as imprecise as ‘accurate to 5 %’. An instrument is not useful if it is accurate only 95 % of the time; but this is not what is implied by ‘5 % accuracy’. Here, it is meant that, (almost) all of the time, its indication is within 5 % of the ‘true’ value.

Calibration – A set of operations which 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. However, it is to be noted that the result of a calibration permits either the assignment of values of the measurands to the indicators or the determination of corrections with respect to indications. A calibration can also determine other metrological properties, such as the effect of influence quantities. The result of a calibration can be recorded in a document, sometimes called a ‘calibration certificate’ or a ‘calibration report’.

Calibration laboratory – A work space, provided with test equipment, controlled environment, and trained personnel, established for the purpose of maintaining proper operation and accuracy of measuring and test equipment. Calibration laboratories typically perform many routine calibrations, often on a production-line basis.

Certified Reference Material (CRM) – It is a reference material (RM), 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. CRMs are generally prepared in batches for which the property values are determined within stated uncertainty limits by measurements on samples representative of the entire batch. The certified properties of the CRMs are sometimes conveniently and reliably realized when the material is incorporated into a specifically 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 can also be considered CRMs. All CRMs lie within the definition of ‘measurement standards’ given in the International Vocabulary of basic and general terms in metrology (VIM). Some RMs and CRMs have properties which, because 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.

Coherent (derived) unit (of measurement) – A derived unit of measurement which can be expressed as a product of powers of base units with the proportionality factor ‘one’. Coherency can be determined only with respect to the base units of a particular system. A unit can be coherent with respect to one system but not to another.

Coherent system of units (of measurement) – It is a system of units of measurement, in which all of the derived units are coherent.

Conservation of a (measurement) standard – It is a set of operations, necessary to preserve the metrological characteristics of a measurement standard within appropriate limits. The operations normally include periodic calibration, storage under suitable conditions, and care in use.

Inter-laboratory standard – It is a device which travels between the laboratories for the sole purpose of relating the magnitude of the physical unit represented by the standards maintained in the respective laboratories.

International (measurement) standard – It is a standard recognized by an international agreement to serve internationally as the basis for assigning values to other standards of the quantity concerned.

International System of Units (SI) – It is the coherent system of units adopted and recommended by the General Conference on Weights and Measures (CGPM). The SI is based at present on the seven base units namely (i) meter, (ii) kilogram, (iii) second, (iv) ampere, (v) kelvin, (vi) mole, and (vii) candela.

Measurand – It is a particular quantity subject to measurement. For example, vapour pressure of a given sample of water at 20 deg C. The specification of a measurand can require statements about quantities such as time, temperature, and pressure.

Measurement – It is a set of operations having the object of determining a value of a quantity. The operations can be performed automatically.

Method of measurement – It is a logical sequence of operations, described generically, used in the performance of measurements. Methods of measurement can be qualified in various ways, such as (i) substitution method, (ii) differential method, and (iii) null method.

Metrology – It is the science of measurement. Metrology includes all aspects, both theoretical and practical, with reference to measurements, whatever their uncertainty, and in whatever fields of science or technology they occur.

National (measurement) standard – It is a standard recognized by a national decision to serve, in a country, as the basis for assigning values to other standards of the quantity concerned.

National reference standard – It is a standard maintained by national laboratories, and which are the legal standards of their respective countries.

Primary standard – It is a standard which 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.

Principle of measurement – It is the scientific base of a measurement. Examples are (i) the thermoelectric effect applied to the measurement of temperature, (ii) the Josephson effect applied to the measurement of electric potential difference, (iii) the Doppler effect applied to the measurement of velocity, and (iv) the Raman effect applied to the measurement of the wave number of molecular vibrations.

Reference standard – It is a standard, generally having the highest metrological quality available at a given location or in a given organization, from which measurements made there are derived.

Reference Material – It is a 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. It is a reference material which can 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.

Repeatability (of results of measurements) – It is the 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. Repeatability conditions include (i) the same measurement process, (ii) the same observer, (iii) the same measuring instrument, used under the same conditions, (iv) the same location, and (v) repetition over a short period of time. Repeatability can be expressed quantitatively in terms of the dispersion of characteristics of the results.

Reproducibility (of results of measurements) – It is the closeness of the agreement between the results of measurements of the same measurand carried out under changed conditions of measurement. However, it is to be noted that a valid statement of reproducibility requires specification of the conditions changed. The changed conditions include (i) principle of measurement, (ii) method of measurement, (iii) observer, (iv) measuring instrument, (v) reference standard, (vi) location, (vii) condition of use, and (viii) time. Reproducibility can be expressed quantitatively in terms of the dispersion characteristics of the results. Results here are usually understood to be corrected results.

Secondary standard – It is a standard whose value is assigned by comparison with a primary standard of the same quantity.

Standards laboratory – It is a work space, provided with equipment and standards, a properly controlled environment, and trained personnel, established for the purpose of maintaining traceability of standards and measuring equipment used by the organization it supports. Standards laboratories typically perform fewer, more specialized and higher accuracy measurements than the calibration laboratories.

Tolerance – In metrology, it is the limits of the range of values (the uncertainty) which apply to a properly functioning measuring instrument.

Traceability – It is the 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 is having stated uncertainties. The concept is often expressed by the adjective traceable. The unbroken chain of comparisons is called a traceability chain.

Even though the ISO has published (and accepted) the definition listed above, many people have attempted to make this term more meaningful. They feel that the definition is to introduce the aspect of evidence being presented on a continuing basis, to overcome the idea that if valid traceability is achieved, it could last forever. A definition similar to the following one would meet that requirement.

Traceability is a characteristic of a calibration or a measurement. A traceable measurement or  calibration is achieved only when each instrument and standard, in a hierarchy stretching back to the national (or international) standard was itself properly calibrated and the results properly documented including statements of uncertainty on a continuing basis. The documentation must provide the information needed to show that all the calibrations in the chain of calibrations were appropriately performed.

Transfer standard It is a standard used as an intermediary to compare standards. The term transfer device is to be used when the intermediary is not a standard.

Traveling standard – It is a standard, sometimes of special construction, intended for transport between locations. Example is a portable battery-operated cesium frequency standard.

Uncertainty of measurement – It is a parameter, associated with the result of a measurement, which characterizes the dispersion of the values which can reasonably be attributed to the measurand.

The parameter can 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 can 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 uncertainty (including those arising from systematic effects) such as components associated with corrections and reference standards, contribute to the dispersion.

Value (of a quantity) – The magnitude of a particular quantity generally expressed as a unit of measurement multiplied by a number. Examples are (i) length of a rod: 5.34 m or 534 cm, (ii) Mass of a body: 0.152 kg or 152 g, (iii) amount of substance of a sample of water (H2O): 0.012 mol or 12 mmol. It is to be noted that (i) the value of a quantity can be positive, negative, or zero, (ii) the value of a quantity can be expressed in more than one way, (iii) the values of quantities of dimension one are generally expressed as pure numbers, and (iv) a quantity which cannot be expressed as a unit of measurement multiplied by a number can be expressed by reference to a conventional reference scale or to a measurement procedure or both.

Working standard – It is a standard which is used routinely to calibrated 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 a measurement is being carried out correctly is called a check standard.

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