Determination of instrument accuracy. Measurement accuracy What determines the measurement accuracy of this device

Measurement accuracy- this is the degree of approximation of the measurement results to some real value of the physical quantity. The lower the accuracy, the greater the measurement error and, accordingly, the smaller the error, the higher the accuracy.

Even the most accurate instruments cannot show the actual value of the measured value. There is necessarily a measurement error, the causes of which can be various factors.

Errors can be:

systematic, for example, if the strain resistance is poorly glued to the elastic element, then the deformation of its lattice will not correspond to the deformation of the elastic element and the sensor will constantly react incorrectly;

random, caused, for example, by incorrect functioning of the mechanical or electrical elements of the measuring device;

rough, as a rule, they are allowed by the performer himself, who, due to inexperience or fatigue, incorrectly reads the instrument readings or makes mistakes when processing information. Their cause can be a malfunction of measuring instruments, and a sharp change in measurement conditions.

It is practically impossible to completely eliminate errors, but it is necessary to establish the limits of possible measurement errors and, therefore, the accuracy of their implementation.

Classification and metrological characteristics of measuring instruments

Measuring instruments approved by the State Standard of Russia are registered in the State Register of Measuring Instruments, certified by certificates of conformity, and only after that they are allowed for use on the territory of the Russian Federation.

In reference publications, the following structure for describing measuring instruments is adopted: registration number, name, number and validity period of the certificate of approval of the type of measuring instrument, location of the manufacturer and basic metrological characteristics. The latter evaluate the suitability of measuring instruments for measurements in a known range with a known accuracy.

Metrological characteristics of measuring instruments provide:

The possibility of establishing the accuracy of measurements;

Achievement of interchangeability and comparison of measuring instruments among themselves;

Selection of the necessary measuring instruments for accuracy and other characteristics;

Determination of errors in measuring systems and installations;

Assessment of the technical condition of measuring instruments during their verification.

The metrological characteristics established by the documents are considered valid. In practice, the following metrological characteristics of measuring instruments are most common:

measuring range- the range of values ​​of the measured value, for which the permissible error limits of the measuring instrument are normalized;

measurement limit- the largest or smallest value of the measurement range. For measures, this is the nominal value of the reproducible quantity.

Measuring instrument scale- a graduated set of marks and numbers on the reading device of the measuring instrument, corresponding to a series of successive values ​​of the measured quantity

Scale division value- the difference in the values ​​of the quantities corresponding to two adjacent marks on the scale. Devices with a uniform scale have a constant division value, and with an uneven scale - a variable one. In this case, the minimum division price is normalized.

The main normalized metrological characteristic of measuring instruments is error, i.e., the difference between the readings of measuring instruments and the true (actual) values ​​of physical quantities.

All errors depending on external conditions divided into basic and additional.

Basic error - this is the error under normal operating conditions.

In practice, when there is a wider range of influencing quantities, it is normalized and additional error measuring instruments.

The maximum error caused by a change in the influencing quantity, at which the measuring instrument, according to the technical requirements, can be allowed for use, acts as the limit of the permissible error.

Accuracy class - this is a generalized metrological characteristic that determines the various properties of a measuring instrument. For example, for indicating electrical measuring instruments, the accuracy class, in addition to the main error, also includes a variation in indications, and for measures of electrical quantities - the amount of instability (percentage change in the value of the measure during the year).

The accuracy class of the measuring instrument already includes systematic and random errors. However, it is not a direct characteristic of the accuracy of measurements performed using these measuring instruments, since the measurement accuracy also depends on the measurement technique, the interaction of the measuring instrument with the object, measurement conditions, etc.

Objective: learn to determine the price division of the scale of the measuring instrument and the limits of measurement.

Equipment: ruler, beaker, thermometers, stopwatch (Fig. 46).

Rice. 46

Test yourself

Before starting the lab, test your readiness for the lab by answering the following questions.

1. What is the scale division of the instrument and how to determine it?
2. What determines the accuracy of measurements with this device?

Progress:

1. Determine and enter in the table the price of division of the scale shown in Figure 46 of the devices.
2. Determine and enter in the table the lower and upper limits of measurements of the devices shown in Figure 46.
3. Determine and enter in the table the accuracy of measurements by the devices shown in Figure 46.

test questions

Rice. 49

Let's repeat the main thing in the studied

• Physics is the science of nature.
• The stages of scientific knowledge of the world include: observation of phenomena, accumulation of facts, hypotheses, experimental verification of the hypothesis, formulation of laws.
• In physics, any object is called a physical body.
• Changes that occur with physical bodies and fields are called physical phenomena.
• Physical quantities describe the properties of physical bodies and physical phenomena. A physical quantity can be measured using instruments or calculated using a formula.
• To measure a physical quantity means to compare it with a homogeneous quantity taken as a unit.
• Adding, subtracting and comparing physical quantities is possible only if they are homogeneous, that is, they represent the same physical quantity.
• Each physical quantity has a symbolic designation, a numerical value and a unit of measurement.
• The division of the scale of the measuring instrument is the gap between the two nearest strokes on its scale. The division price is the value of the smallest division of the instrument scale.
• If a physical quantity is measured directly by taking data from the scale of the instrument, then such a measurement is called direct.
• If a physical quantity is determined by a formula, that is, indirectly, then such a measurement is called an indirect measurement.
• Measurement limits are the minimum (lower limit) and maximum (upper limit) values ​​of the instrument scale.

Accuracy class is the main metrological characteristic of the device, which determines the permissible values ​​of the main and additional errors that affect the measurement accuracy.

The error can be normalized, in particular, in relation to:

§ measurement result (according to relative error)

in this case, according to GOST 8.401-80 (instead of GOST 13600-68), the numerical designation of the accuracy class (in percent) is enclosed in a circle.

§ length (upper limit) of the instrument scale (according to the given error)

For pointer instruments, it is customary to indicate the accuracy class, written as a number, for example, 0.05 or 4.0. This number gives the maximum possible error of the instrument, expressed as a percentage of the largest value of the quantity measured in a given range of operation of the instrument. So, for a voltmeter operating in the measurement range 0 - 30 V, an accuracy class of 1.0 determines that the indicated error when the arrow is positioned anywhere on the scale does not exceed 0.3 V. Accordingly, the standard deviation s of the device is 0.1 AT.

The relative error of the result obtained using the indicated voltmeter depends on the value of the measured voltage, becoming unacceptably high for low voltages. When measuring a voltage of 0.5 V, the error will be 20%. As a result, such a device is not suitable for studying processes in which the voltage changes by 0.1 - 0.5 V.

Usually the price of the smallest division of the scale of the pointer instrument is consistent with the error of the instrument itself. If the accuracy class of the device used is unknown, the error s of the device is always taken as half the price of its smallest division. It is clear that when reading readings from the scale, it is not advisable to try to determine the division fractions, since the measurement result will not become more accurate from this.

It should be borne in mind that the concept of accuracy class is found in various fields of technology. So in the machine tool industry there is a concept of the accuracy class of a metal-cutting machine, the accuracy class of electroerosive machines (according to GOST 20551).

Accuracy class designations may take the form of capital letters of the Latin alphabet, Roman numerals and Arabic numerals with the addition of conventional signs. If the accuracy class is indicated in Latin letters, then the accuracy class is determined by the limits of the absolute error. If the accuracy class is indicated by Arabic numerals without conventional signs, then the accuracy class is determined by the limits of the reduced error and the largest modulo of the measurement limits is used as the normalizing value. If the accuracy class is indicated by Arabic numerals with a tick, then the accuracy class is determined by the limits of the given error, but the length of the scale is used as a normalizing value. If the accuracy class is indicated by Roman numerals, then the accuracy class is determined by the limits of the relative error.

Devices with an accuracy class of 0.5 (0.2) start working in the class from 5% load. and 0.5s (0.2s) already with 1% load

It should be borne in mind that everyone, even the best device, has some measurement error. According to the degree of accuracy, the devices are divided into 8 classes: 0.05; 0.1; 0.2; 0.5; one; 1.5; 2.5; 4, and the most accurate instrument has a class of 0.05. The error is smaller, the closer the measured value is to the nominal value of the device. Therefore, it is preferable to use such devices, in which, during the measurement, the arrow will be in the second half of the scale.

Measuring instruments (SI) have a large number of various indicators and characteristics. All measuring instruments can be characterized by some common properties - metrological characteristics. There are static and dynamic characteristics of SI. The static characteristics of the SI arise in the static mode of its operation. The static mode of operation is such a mode in which the SI perceives a change in the input value and the dimensions of the measured value do not change in time. The static metrological characteristics of SI include: measurement range; measurable, convertible or reproducible (for measures) value; calibration characteristic; sensitivity (IP conversion factor); sensitivity threshold; power consumption; input and output resistances, etc. The dynamic characteristics of the IP occur in the dynamic mode of its operation. The dynamic mode of operation is such a mode in which the PI means perceives a change in the input value, and the dimensions of the measured value change in time. Dynamic characteristics are: operator sensitivity, complex sensitivity, transient response, amplitude-frequency and phase-frequency characteristics (AFC and PFC), etc. A metrological characteristic is a characteristic of one of the properties of a measuring instrument that affects the measurement result and its error. For each type of measuring instruments, their metrological characteristics are established. The metrological characteristics established by regulatory and technical documents are called normalized metrological characteristics, and those determined experimentally are called actual metrological characteristics.

Consider the main metrological characteristics of SI. The measurement range is the range of values ​​within which the permissible error limits of the measuring instrument are normalized. The values ​​of the quantity that limit the measurement range from below and above (left and right) are called the lower measurement limit or the upper measurement limit, respectively. The lower limit of measurement (conversion) is never really equal to zero, since it is usually limited by the threshold of sensitivity, interference or measurement errors. The measurement range should not be confused with the range of indications of a measuring instrument. The measured, converted quantity characterizes the purpose of the IP for measuring (converting) a particular physical quantity. For each IP, a natural input value is set, which is best perceived by it against the background of noise, and a natural output value, which is determined in a similar way.

For example, the natural input quantity of a RTD is temperature, and the natural output quantity is resistance. The calibration characteristic of a measuring instrument is the dependence between the values ​​of the quantities at the input and output of the measuring instrument, obtained experimentally.

The graded characteristic can be expressed as a formula, graph or table.

For IP, the nominal static calibration characteristic YH = fH(X) is normalized. It is assigned to a measuring instrument based on an analysis of the totality of such instruments.

The sensitivity of a measuring instrument is a property of a measuring instrument, determined by the ratio of the change in the output signal of this instrument to the change in the measured value that causes it.

Calculation of the accuracy class of the measuring instrument.

Absolute error

Measurement accuracy is usually estimated not by absolute, but by relative error - expressed as a percentage of the absolute error to the actual value of the measured value:

To assess the accuracy of electrical measuring instruments, the reduced error is used, which is determined by the following expression

where is the nominal value of the instrument scale, i.e. the maximum value of the scale at the selected measurement limit of the device. The given error determines the accuracy class of the instrument.

The numbers indicating the accuracy class of the device r 0 indicate the largest allowable reduced error in percent (r 0 ? g pr. max). Those. during normal operation, the maximum value of the reduced error should not exceed the accuracy class.

Measured quantities cannot be determined with absolute certainty. Measuring tools and systems always have some tolerance and interference, which is expressed in terms of the degree of inaccuracy. In addition, it is necessary to take into account the features of specific devices.

The following terms are often used in relation to measurement inaccuracy:

• Error- error between true and measured value
• Accuracy— random spread of measured values ​​around their mean
• Permission— the smallest recognizable value of the measured value

Often these terms are confused. Therefore, here I would like to consider the above concepts in detail.

Measurement inaccuracy

Measurement inaccuracies can be divided into systematic and random measurement errors. Systematic errors are caused by gain deviations and zeroing of the measuring equipment. Random errors are caused by noise and/or currents.

Often the concepts of error and accuracy are considered as synonyms. However, these terms have completely different meanings. The error indicates how close the measured value is to its actual value, i.e. the deviation between the measured value and the actual value. Accuracy refers to the random spread of measured values.

When we take a certain number of measurements until the voltage stabilizes or some other parameter, then some variation will be observed in the measured values. This is caused by thermal noise in the measuring circuit of the measuring equipment and the measuring setup. The chart below shows these changes.

Definitions of uncertainties. On the left is a series of measurements. On the right are the values ​​in the form of a histogram.

bar chart

The measured values ​​can be displayed as a bar graph, as shown on the right in the figure. The bar graph shows how often the measured value is observed. The highest point on the histogram is the most frequently observed measured value, in the case of a symmetrical distribution it is equal to the mean value (shown as a blue line on both graphs). The black line represents the true value of the parameter. The difference between the average of the measured value and the true value is the error. The width of the histogram shows the spread of the individual measurements. This variation in measurements is called accuracy.

Use the right terms

Accuracy and accuracy thus have different meanings. Therefore, it is possible that the measurement is very accurate, but has an error. Or vice versa, with a small error, but not exact. In general, a measurement is considered reliable if it is accurate and has a small margin of error.

Error

The error is an indicator of the correctness of the measurement. Due to the fact that in one measurement the accuracy affects the error, the average of a series of measurements is taken into account.

The error of a measuring instrument is usually given by two values: the error of indication and the error on the entire scale. These two characteristics together determine the total measurement error. These measurement errors are given as a percentage or in ppm (parts per million, parts per million) relative to the current national standard. 1% corresponds to 10000 ppm.

The accuracy is given for the specified temperature ranges and for a certain period of time after calibration. Please note that in different ranges, various errors are possible.

Indication error

The indication of percentage deviation without further specification also applies to the indication. Voltage divider tolerances, amplification accuracy, and absolute readout and digitization tolerances are the causes of this error.

Inaccuracy of indications in 5% for a value of 70 V

A voltmeter that reads 70.00V and has a specification of "±5% of reading" will have an error of ±3.5V (5% of 70V). The actual voltage will lie between 66.5 and 73.5 volts.

Full Scale Accuracy

This type of error is due to bias errors and linearity errors in the amplifiers. For devices that digitize signals, there is a non-linearity of the conversion and ADC errors. This characteristic applies to the entire measuring range used.

The voltmeter may have a "3% of scale" characteristic. If 100V (full scale) is selected during measurement, the error is 3% of 100V = 3V regardless of the measured voltage. If the reading is 70 V in this range, then the actual voltage lies between 67 and 73 volts.

Accuracy 3% of span on 100V range

It is clear from the figure above that this type of tolerance is independent of readings. At 0 V, the actual voltage lies between -3 and 3 volts.

Scale error in numbers

Often for digital multimeters, the scale error is given in digits instead of a percentage value.

For a DMM with a 3½ digit display (range -1999 to 1999), the specification may say "+ 2 digits". This means that the indication error is 2 units. For example: if the range is 20 volts (± 19.99), then the scale error is ±0.02 V. The display shows 10.00 and the actual value will be between 9.98 and 10.02 volts.

Measurement uncertainty calculation

The indication and scale tolerance specifications together define the instrument's total measurement error. The following calculations use the same values ​​as in the examples above:

Accuracy: ±5% of reading (3% of span)

Range: 100V

Indication: 70 V

The total measurement error is calculated as follows:

In this case, the total error is ±6.5V. The true value lies between 63.5 and 76.5 volts. The figure below shows this graphically.

Total imprecision for 5% and 3% of span reading inaccuracies for 100V range and 70V reading

Percent error is the ratio of the error to the reading. For our case:

Numbers

DMMs may have a specification of "± 2.0% reading, + 4 digits". This means that 4 digits must be added to the 2% reading error. As an example, consider the 3½ digit digital indicator again. It reads 5.00V for the selected 20V range. 2% of reading would mean an error of 0.1V. Add to that the numerical error (=0.04V). The total error is therefore 0.14 V. The true value should be between 4.86 and 5.14 volts.

Total error

Often, only the error of the measuring instrument is taken into account. But also, in addition, the errors of measuring instruments should be taken into account, if they are used. Here are some examples:

Increasing the error when using a probe 1:10

If a probe 1:10 is used in the measurement process, then it is necessary to take into account not only the measuring error of the device. The error is also affected by the input impedance of the device being used and the resistance of the probe, which together make up the voltage divider.

The figure above is schematically shown with a 1:1 probe connected to it. If we consider this probe to be ideal (no connection resistance), then the applied voltage is transferred directly to the input of the oscilloscope. The measurement error is now determined only by the allowable deviations of the attenuator, amplifier and circuits involved in further signal processing and is set by the device manufacturer. (The error is also affected by the resistance of the connection, which forms the internal resistance. It is included in the specified tolerances).

The figure below shows the same oscilloscope, but now the 1:10 probe is connected to the input. This probe has an internal connection resistance and, together with the oscilloscope's input resistance, forms a voltage divider. The tolerance of the resistors in the voltage divider is the cause of its own error.

1:10 probe connected to oscilloscope introduces additional error

The oscilloscope's input impedance tolerance can be found in its data sheet. The tolerance of the probe connection resistance is not always given. However, system accuracy is claimed by the manufacturer of a specific oscilloscope probe for a particular type of oscilloscope. If the probe is used with a different type of oscilloscope than the recommended one, then the measurement error becomes undefined. This should always be avoided.

Let's assume that the oscilloscope has a tolerance of 1.5% and a 1:10 probe is used with an error in the system of 2.5%. These two characteristics can be multiplied to obtain the total error of the instrument reading:

Here is the total error of the measuring system, is the error of the reading of the instrument, is the error of the probe connected to the oscilloscope of a suitable type.

Shunt Resistor Measurements

Often, when measuring currents, an external shunt resistor is used. The shunt has some tolerance that affects the measurement.

The specified shunt resistor tolerance affects the reading error. To find the total error, the allowable deviation of the shunt and the error in the readings of the measuring device are multiplied:

In this example, the total reading error is 3.53%.

The shunt resistance is temperature dependent. The resistance value is determined for a given temperature. The temperature dependence is often expressed in .

For example, let's calculate the resistance value for the ambient temperature. The shunt has the characteristics: Ohm(respectively and ) and the temperature dependence .

The current flowing through the shunt causes energy to be dissipated in the shunt, which leads to an increase in temperature and, consequently, to a change in the resistance value. The change in resistance value when current flows depends on several factors. To make a very accurate measurement, it is necessary to calibrate the shunt for resistance drift and the environmental conditions under which measurements are made.

Accuracy

Term accuracy is used to express the randomness of the measurement error. The random nature of the deviations of the measured values ​​in most cases has a thermal nature. Due to the random nature of this noise, it is not possible to obtain an absolute error. Accuracy is only given by the probability that the quantity being measured lies within certain limits.

Gaussian distribution

Thermal noise is Gaussian, or, as they say, normal distribution. It is described by the following expression:

Here, is the mean value, shows the variance, and corresponds to the noise signal. The function gives a probability distribution curve as shown in the figure below, where is the mean and the effective noise amplitude is .

and

The table shows the chances of getting values ​​within the given limits.

As you can see, the probability that the measured value lies in the ± range is equal to .

Accuracy Improvement

Accuracy can be improved by oversampling (changing the sampling rate) or filtering. The individual measurements are averaged, so the noise is significantly reduced. The spread of the measured values ​​is also reduced. When using resampling or filtering, be aware that this can lead to a decrease in throughput.

Permission

Permission, or, as they say, resolution of the measuring system is the smallest recognizable measurable quantity. The definition of instrument resolution does not refer to measurement accuracy.

Digital measuring systems

The digital system converts the analog signal to a digital equivalent using an A/D converter. The difference between the two values, i.e. the resolution, is always one bit. Or, in the case of a digital multimeter, it's a single digit.

It is also possible to express resolution in units other than bits. As an example, consider having an 8-bit ADC. Vertical sensitivity set to 100 mV/div and the number of divisions is 8, the full range is thus 800 mV. 8 bits are represented 2 8 =256 different meanings. The resolution in volts is then 800 mV / 256 = 3125 mV.

Analog measuring systems

In the case of an analog instrument, where the measured value is displayed mechanically, as in a pointer instrument, it is difficult to obtain an exact number for resolution. First, the resolution is limited by mechanical hysteresis caused by the friction of the hand mechanism. On the other hand, the resolution is determined by the observer making his own subjective assessment.

As is known, when measuring (testing, controlling, analyzing) a physical quantity, the result must be expressed with an accuracy corresponding to the task and established requirements.

Measurement result accuracy is a qualitative indicator, which, when processing the results of observations (single observed values), must be expressed through its quantitative characteristics. At the same time, the observed value is according to GOST R 50779.10-2000 (ISO 3534.1-93) “Statistical methods. Probability and bases of statistics. Terms and definitions” is the characteristic value obtained as a result of a single observation in multiple measurements.

Existing regulations currently use a number of accuracy indicators. Our analysis of normative and legislative documents showed that the Federal Law “On Ensuring the Uniformity of Measurements” does not contain a definition of the fundamental metrological concept “indicators of measurement accuracy”.

In the recently used (RMG 29-99) and new (RMG 29-2013) terminological documents, the concept of "measurement accuracy indicators" and its definition are also not regulated.

Among the relevant documents (interstate - GOST, national - GOST R, as well as methodological instructions and recommendations - MI, R, RD), we also did not find a standard regulating the indicators of measurement accuracy and the form of their expression.

However, in the note to the concept of “measurement result” given in RMG 29-2013, it is indicated that “... accuracy indicators include, for example, the standard deviation, confidence limits of the error, standard measurement uncertainty, total standard and extended uncertainty”.

GOST R ISO 5725-1-2002 defines accuracy as the degree of closeness of a measurement result to an accepted reference value. The normative document reflects the concept of "accepted reference value" used in international metrological practice instead of the concept of "true value of a physical quantity" characteristic of domestic metrology until 2003 (before the adoption of MS ISO 5725 in our country).

The document explains as a note (with reference to the international standard) "... in relation to multiple measurements," the term "accuracy", when it refers to a series of measurement results (tests), includes a combination of random components and a total systematic error (ISO 3534- 1), which does not contradict the approach to expressing accuracy in terms of the error components of the measurement result. In addition to the general concept of a qualitative characteristic of accuracy, an explanation is given of which parameters can be taken as quantitative characteristics of multiple measurements (tests).

However, until 1986, in our country, accuracy indicators were regulated by GOST 8.011-72 “GSI. Indicators of measurement accuracy and forms of expression of measurement results. Currently, GOST 8.011-72 has been replaced by MI 1317 (the document is relevant in the 2004 version).

In metrological practice, the accuracy of measurements is described by a number of indicators shown in Figure 1.3, and some of them are expressed in the concept of error, and the other part in the concept of uncertainty.

The new version of the International Dictionary of Terms and Definitions - VIM 3 (2010) emphasizes that “the concept of “measurement accuracy” is not a quantity and it cannot be assigned a numerical value of a quantity. It is considered that a measurement is more accurate if it has a smaller measurement error. In addition, VIM 3 notes that a complete characterization of the accuracy of measurements can be obtained by evaluating both indicators of accuracy - correctness and precision. The term "measurement accuracy" should not be used to refer to the correctness of measurements, and the term measurement precision should not be used to refer to "measurement accuracy", although the latter has a connection with these two concepts.

Figure 1.3 - Indicators of the accuracy of the results, traditionally used in regulatory documents

Of all the accuracy indicators presented and traditionally used in metrological practice, we have singled out only those that give a complete picture of the accuracy indicators of measurement results. The results of the analysis are summarized in tables 1.1 and 1.2.

As "indicators of measurement accuracy", as follows from the diagram (Figure 1.4), characteristics can also be used,

regulated by GOST R 8.563-2009:

Characteristics of measurement error according to MI 1317-2004;

characteristics of uncertainty according to RMG 43-2001 (the use of MD on the territory of the Russian Federation has been discontinued since 01.10.2012);

Accuracy indicators according to GOST R ISO 5725-2002.

Table 1.1 - Analysis of the possibility of applying the characteristics of the error in as indicators of the accuracy of the measurement result_

Feature or d, mathematical expression G in the concept of error or uncertainty		Comment
1 Measurement uncertainty		Expression (1) is theoretical, since the true value of the measured quantity always remains unknown, therefore equation (2) is used in practice. As a model of measurement error, a model of a random variable (or a random process) is taken. Therefore, metrologists do not consider the possibility of using expression (2) to develop ideas about the indicators of measurement accuracy.
2 Borders, in error measurements located with given probability		The limits of measurement error for a given probability give full reason to judge the possible degree of closeness of the measurement result to the actual value of the measured quantity.
3 Mean square deviation of the error		Knowledge of Od allows (under certain assumptions about the form of the error probability density distribution function) to estimate the range of values ​​in which X l can be located.
4 Average quadratic deviation random component errors measurements		Knowing only the standard deviation of the random component of the measurement error Odel in the general case does not allow one to judge the possible degree of closeness of the measurement results to the actual value of the measured value Х l, since in addition to the random component of the measurement error there may be a systematic component.

Continuation of table 1.1

5 Convergence results measurements	Estimated by convergence measures	By itself, the convergence of measurements does not give the slightest idea of ​​the limits in which the measurement error may lie.
6 Reproducibility of results	Assessed by measures of reproducibility	Like the convergence of measurements, reproducibility also does not give an idea of ​​the limits in which the measurement error can lie.
7 Average quadratic deviation systematic component errors measurements		By themselves, the characteristics of the systematic component of the measurement error (no matter how satisfactory they may seem) do not allow us to judge the boundaries in which the total measurement error can lie (at a given probability). The reasons for this are not taking into account the role of the random component of the measurement error.
8 Borders, in which are not excluded systematic component errors measurements located with given probability
9 Measurement precision	Characterizes the degree of closeness between independent results and measurements obtained under certain accepted conditions.	Knowing only the standard deviation of precision does not allow us to judge the degree of possible closeness of the measurement results to the actual value of the measured value X l.

Regulated by the national standard GOST R ISO 5725-2002, harmonized with international requirements, the measurement accuracy indicators are shown in Figure 1.5.

Figure 1.4 - Measurement accuracy indicators of the methodology regulated by GOST R 8.563-2009

Figure 1.5 - Indicators of measurement accuracy, regulated in GOST R ISO 5725-1-2002

Table 1.2 - Analysis of the possibility of applying characteristics

uncertainties as indicators of the accuracy of a measurement result_

Index

Characteristic or mathematical expression in the concept of error or uncertainty