## How to make measurements

Measurement is a set of operations, the purpose of which is to determine the value of a certain value. The result of the measurement is three parameters: number, units and uncertainty. The measurement result is recorded so: Y = (x±u)[M], for example L = (7.4±0.2)m. A unit of measurement is a relative unit that we use as a physical quantity. A number is the number of units of measurement that contains in itself, the measured object. And finally, uncertainty is the degree of approximation of the measured quantity to the measured one.

## Measurement error

Any measurement contains two types of errors: random and systematic. Random errors are caused by probabilistic events that take place in any dimension. Random errors do not have regularities, therefore, with a large number of measurements, the average value of the random error tends to zero. Systematic errors occur with an arbitrarily large number of measurements. Systematic errors they can be reduced only if the reason is known, for example, improper use of the tool.

## Influence of indirect factors

There are factors that indirectly affect the measurement result and are not part of the measured value. For example, when measuring the length of a profile, the length of the profile depends on the temperature of the profile, and the measurement result indirectly depends on the temperature of the micrometer. In this case, the temperature should be described as a result of the measurement, at which the measurement was made. Another example: when measuring the length of the profile with a laser on the measurement result air temperature, atmospheric pressure and humidity are indirectly affected.

Thus, in order for the measurement result to be representative, it is necessary to determine the measurement conditions:
determine the factors influencing the measurement; select the appropriate tools; determine the measured
object; use the appropriate mode of operation. Such measurement conditions are determined by the norms for
in order for the measurement results to be ** reproduced and compared**, such conditions are called
**normal conditions for measurement**.

## Correction of measurement results

In some cases, it is possible to correct the measurement result when
normal conditions cannot be met. The introduction of such an adjustment complicates the measurement and often requires
measurements of other quantities. For example, measuring the length of the profile at a temperature different from normal,
20°C, can be adjusted by the following formula: l'_{20} = l'_{θ}[1+α(20-θ)].
Adjusting the calibration of the measuring device at 20°C - C_{c}. Thus,
the length of the profile is determined by the following relationship: l_{20} = f(l'_{,α,θ,Cc).
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In general, the measurement result will be expressed as a dependence on other measurements: y = f(x_{1},x_{2},...x_{N}),
where f can be an analytical function, a probability distribution, or even be a partially unknown function.
Correcting the results reduces the measurement inaccuracy, but in this way it is impossible to reduce the measurement inaccuracy to zero.

## Metrological Laboratory

The metrology laboratory must control all indirect measurement factors. The conditions depend on the type and accuracy measurements. So, even the measurement department in production can be considered a laboratory. The main requirements for the metrological laboratory will be described below.

#### Location

The metrological laboratory should be located as far as possible from other buildings, located on the lowest floor (preferably in the basement) and have sufficient insulation from noise, temperature difference, vibrations and other sources of irritation.

#### Temperature

In the metrological laboratory, the temperature regime must be observed, which takes into account those who are in the laboratory of employees. It is necessary to have an air conditioning and heating system.

#### Humidity

Humidity should be maintained at the minimum permissible for operation - about 40%.

#### Air purity

Suspensions larger than one micrometer should not be present in the air.

#### Lighting

Lighting should be produced by fluorescent lamps of cold color, the illumination should be from 800 to 1000 lux.

## Uncertainty of the measuring instrument

The uncertainty can be determined by comparing the measurement results with the sample or measuring with a higher precision instrument. During the calibration of the instrument , the output adjustment value and uncertainty.

#### Example of micrometer calibration

By measuring a sample of a pre-known length, we get the correction value, c. Thus, if the length measured by
the length is x_{0}, the actual length will be x_{c} = x_{0} + c.

Let's make n_{c} measurements of the sample and get the deviation s_{c}. Now, with any measurements
with a calibrated micrometer, the uncertainty value u will be equal to:
u = √(u^{2}_{0} +s^{2}_{c}/n_{c} + u^{2}_{m}/n),
u_{m} is the deviation obtained with n measurements.

## Tolerance

In production, the concept of tolerance is used, setting the upper and lower values within which the measured object is not considered a marriage. For example, in the production of capacitors with a capacity of 100±5% UF a tolerance of 5% is set, which means that at the quality control stage when measuring the capacitance of the capacitor, capacitors with a capacity of more than 105 UF and less than 95 UF are considered defective.

During quality control, it is necessary to take into account the uncertainty of the measuring instrument, so if the uncertainty of measuring the capacitance of the capacitor is 2 UF, then the measurement result of 95 UF can mean 93-97 uf. To account for the uncertainty in the measurement results, it is necessary to expand the concept of tolerance: the uncertainty of the measuring device must be taken into account in the tolerance. To do this, you need set the confidence interval, i.e. the percentage of details that must be guaranteed to match the specified parameters.

The confidence interval is based on a normal distribution: it is assumed that the measurement result corresponds to normal distribution μ±kσ. The probability of finding a value within ku depends on the value of k: at k= 1, 68.3% of measurements will fall into the value of σ±u, at k=3 - 99.7%.

## Measurement model

In most cases, the desired value Y is not measured directly, but is defined as a function
some dimensions X_{1}, X_{2}, ... X_{n}. Such a function is called a **model
measurements**, while each value X_{i} can also be a measurement model.