Metrology

General information

Everyone has concepts of measurement:

My mass is of 70 kg
the sky is partially covered
You measurements 1,80 m
It has 30 year S
Your eyes are blue-green
It is 8 H 30 min
the apparatus consumes 50 Watt S
That costs 15 €

Measurement is thus an essential concept in Science S just like in the life in company. It makes it possible to express a size by a Symbole (a word, a drawing, a number). The numbers can then be handled with the assistance of the Mathématiques. When it uses a statistical digital model, it rests on the theory of measurement.

The attribution of a value quantified with a measurement is related to the definition of a unit based on a standard. For example, the standard of the mass is preserved at the International office of the weights and measures (BIPM, Paris). One compares any quantity of matter with this standard Masse, his multiples or under multiples so that measurement leads to: “the object made N time the standard masses”.

A name called unit is defined for each standard. The unit associated with the mass is the Kilogram (shortened in “kg”), so that the sentence above becomes: “the object made N kilograms”.

A size is thus expressed by its measure to a unit :

Size = measurement × unit

Any measurement is necessarily sullied with errors for various reasons. An experimental measurement thus has value only if one associates to him an estimate of the error (ex: “the beam measures 1 m from length to 5 mm near”). This estimate of the precision is called “absolute error”, “bars error” (because of its chart) or “absolute uncertainty” which one preferably expresses with the same unit as that used to express the measurement of the size.

The evaluation of this error corresponds to the branch of mathematics called Calcul of uncertainty. In the case of the digital models, measurement must be associated with a uncertainty and a interval confidence .

Model of measurement

In a general way, it is necessary to consider the concept of model. A model is an abstracted representation, simplified, of a phenomenon and which is brought back to parameters, sizes; for example in the case of the caused object, the model is a whole of sizes (length, width, depth, thickness, mass, color…). Metrology covers the methods and techniques which make it possible to parameterize a model intended to represent reality. Once this parameterized model, it can be studied and handled in order to

produce knowledge: rather than to build a series of objects having different characteristics, it is simpler to handle the figures, to simulate the effect of a variation on such or such parameter (one will produce objects only at the end of the study, to check the validity of the model);
to act on the reality which it represents: the fact of fixing the intensity of a phenomenon (“piloting” of the phenomenon).

Reality concerned is usually “physical reality”, but can also be an economic reality, sociological, psychological. The models are digital or linguistic models.

Standards

One uses a phenomenon of reference for each measurable size.

History of the standards

Until the European Rebirth, the sizes were evaluated in comparison with human references, like the foot , the inch or the line (1/12ede inch) for the lengths (often bodies of the kings and emperors), the Journal for surface (field gérable by a person being occupied some daily)…

Each country, each area even, had its measuring units. The German Empire did not count less than 19 feet different lengths, the rest of Europe 18 others. This complicated the commercial exchanges and obstructed the diffusion of knowledge (See Measuring units of the Old Mode).

The French scientists, inspired by the spirit of the Lights and the French revolution, conceived a frame of reference based on objects having the same value for all, without reference to a particular person, in short universal - “universal” in the direction “accessible to all and recognized by all”, but it acts at the bottom only of one arbitrary convention. Thus one took the circumference of the Ground like reference length to build the Mètre.

The advantage of the “universal” standard is that the scientists of all the countries can exchange their results without ambiguity.

Determination of the standards

Being possible to express sizes from others, the international Système of units is based on seven sizes to define its basic Unités of the international system (uSI):

Length;
Mass;
Lasted;
Intensity of the electric current;
Temperature;
Quantity of matter;
Luminosity.

The other units are defined without having to use of another physical phenomenon. For example:

starting from the meter (m), one defines the Surface unit, the Square meter (m ²), and the Volume unit, the cubic meter (m ³);
for the Speed, the phenomenon of reference is defined by:
the distance unit traversed in one duration unit (in fact a meter in one second);
for the Acceleration, the phenomenon of reference is defined by:
an increase the speed of a unit during one duration unit (in fact increase of one meter a second in one second);
a force being a phenomenon which causes the acceleration of a material object, the phenomenon of reference is defined by the variation speed of reference (acceleration) and the inertia of reference (mass); the unit of force (the newton) is defined with the mass and time, unit of length.

Universal and specific standards

The “universal” standards are the standards of the Convention of the Meter, defining the units of the international system (SI). If they allow precise determinations, they are not inevitably easily exploitable, usable on the spot where must be made the calibration. One thus needs “specific” standards, more practices of use, which themselves are gauged starting from the universal standards.

For example, the mass standard of the BIPM is used as reference for specific masses standard which are used to calibrate the balances S at manufacturing.

A user of a machine of measurement manufactures sometimes itself his own standards; for example, for the chemical analysis, the users often manufacture solutions starting from pure products to calibrate their apparatuses of analysis. The national and international organizations of standardization often provide specific standards certified by their services.

The standards can be:

an inalterable object, as the mass standard;
a physical phenomenon, like the standard second, the standard measures, the standard intensity of the electric current;
a chemical reaction, like the normal electrode with hydrogen or the calomel electrode saturated with KCl used in electrochemistry.

; Anecdote One will remember that the Martian Space probe Mars Climate Orbiter was crushed on red planet because a team expressed the lengths in Mètre S whereas the other expressed them in feet (see: Exploration of the planet Mars).

Organizations of standardization

So that a standard is recognized, it is necessary that the users of the measuring devices know his existence and accept to use it. This role of selection and recognition of the standards is delegated at organizations of standardization ( standardization in English).

There are two internationally recognized organizations:

the International office of the weights and measures located at the House of Breteuil with Sevres, created by the diplomatic treaty of the Convention of the Meter and to which approximately 50 countries adhere; it is an official organization;
the ISO, which federates the national organizations of standardization.

Each country has thereafter its own organization of standardization: French Association of standardization - AFNOR in France, the National Institute for Science and Technology - NIST in the United States, the Deutsches Institute für Normung - DIN in Germany, the Belgian Institute of standardization - IBN in Belgium, the British Standards Institution - BSI in the United Kingdom, the federal Office of Metrology - METAS in Switzerland… Notons that these national organizations are private (AFNOR for example is a association gathering the industrialists) and that the standards which they publish are not free of right but paying.

Measure of a size

Measurement is done using a Measuring instrument which gives a number.

Measurement can be done by comparison:

to measure the lengths, one can compare the dimension of the object with those of an object of reference, like a scale;
in the same way for the Angle S, one can use a graduated rapporteur;
to measure the mass, one can use a balances Roberval with masses marked out of brass.

This comparison can utilize a device modifying the intensity of the phenomenon, as for example an action leverage in the balances S with plague to measure the mass.

Measurement can transform a physical phenomenon into another more easily measurable; the intensity of the phenomenon to be measured must be connected to the measured phenomenon in a nonambiguous way. For example:

the lengthening of a Ressort is proportional to the force, therefore by measuring a length, one deduces the force.
At a given place of the Earth, the mass is proportional to the weight, therefore by measuring the weight (a force), one can deduced the mass.
an electric current traversing a reel creates a Magnetic field; this field attracts a metal needle which is retained by a return spring. One thus transformed an electric current into force, then a force in angular deviation, the deviation being readable using a compass, it is the principle of the Ampèremètre.
to measure a Speed, the radars of highway (Tachometer S) use the shift of frequency of an electromagnetic wave according to the Effect Doppler; one thus transformed a speed into a difference in frequency.

Many phenomena can be transformed into electric current, for example the luminous intensity (with a Diode photoréceptrice), a force (by a piezoelectric crystal )… Thus, the modern majority of the measuring devices evaluate with final intensity of electric current.

The analog devices are distinguished, for which measurement is read on a dial with a needle, and the digital devices which post a numerical value on a screen or which store it in a Ordinateur.

Calibration, checking and fitting of an apparatus

The calibration is the operation which consists in comparing the values indicated by the apparatus to calibrate with the corresponding values of reference (standards). In certain regulated fields, the calibration is obligatory, for example when the errors can cause accidents, drifts on quality of a product or in the operations of commercial exchanges (legal metrology).

The metrological checking consists in bringing the proof by measurements (calibration) that specified requirements are satisfied. The result of a checking results in a decision of conformity (followed by a start-up) or of nonconformity (followed by a fitting, a repair, a downgrading or a reform of the apparatus).

Fitting consists in bringing back the apparatus in tolerances of exactitude of finer measurement.

Sampling

See the detailed article: Sampling

In certain cases, the phenomenon which one wants to evaluate is not homogeneous, it is thus necessary to make several measurements.

For example, if one wants to measure the thickness of a plate, it should be done in several places because the thickness is not strictly constant. If one wants to know the chemical composition of an crude oil in the compartments of a Pétrolier supertanker , it is necessary to make taking away in several places; in particular, because of the decantation, the heavy products are at the light bottom and products above. In Geology, it is necessary to take rocks in several places to determine the nature of the ground. When the object is rather small and liquid or Pulvérulent, one can be satisfied to brew it (see to crush it for a solid) before taking an minor amount of it.

The case of the sampling more known, and undoubtedly most problematic, is that of the Sondage S of opinion; the organizations of survey attempt to question a sample (or panel) known as representative of the population, in particular with regard to the sex, the age, the incomes, the practiced trade, the place of dwelling…

Error of measurement

See also: Analysis error, Calculation of uncertainty

The precision determines the effectiveness of the method of measurement. But the precision having a cost, it is sometimes harmful to make on precision.

When measurement leads to a valid/invalid selection, good-candidate/bad-candidate (candidate in the broad sense of event), it is necessary to stick to have a method

which eliminates the minimum from good candidates: one speaks about Sensibilité ;
which selects the minimum of bad candidates: one speaks about Sélectivité .

The sensitivity is capacity to select the good “candidates”, the selectivity is the capacity to eliminate the bad “candidates”.

Measurement in software genius

Measure on the code

One can distinguish for example:

textual measurement: it relates to the vocabulary used and the number of occurrences of the elements of the vocabulary in the text of the program (measurement of Halstead).
measurement on the graph of programme testing, for example:

“measurement of McCabe” which uses the cyclomatic number (many linearly independent ways in the program) + 1 (in order to hold account that a program is not modelled by a strongly related graph). The subjacent theory is criticizable: account about the instructions does not hold!
on the structure of the program analyzed in terms of structures of basic control (sequence, alternative, iterative): depth of nichage, etc

measurement on the graph of call

Measure on the specifications

We will quote measurements make on developments with proof. For example, during the developments made with the method B, one counts the number of automatic, interactive evidence. One calculates the relationship between many lines of specification and many lines of generated achievable code.

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