4. Measurement uncertainties
4.1. The concept of measurement error
Every measurement process, regardless of the conditions in which it is carried out, is associated with errors that distort the idea of the actual value of the measured quantity.
Various factors may serve as sources of error in the measurements, the main ones being the imperfection of the design of measuring instruments or the schematic diagram of the measurement method, inaccuracy in the manufacture of measuring instruments, non-observance of external conditions in measurements, subjective errors, etc.
The imperfection of measuring instruments is, for example, the non-observance of the Abbe principle in linear measurements, according to which during the measurement process the measurement object must be located in series with the measure of comparison, i.e., so that the measure and the measurement line are a continuation of each other./p>
To the group of errors caused by the imperfection of the design of measuring instruments, one can attribute measurement errors caused by the measuring force in contact measurements.
4.2. Classification of measurement errors
The error of measuring instruments is the deviation of its reading (output signal) from the measured value (input signal) acting on its input.
The errors that occur during the measurement can be divided into systematic and random. In addition, rough (very large) errors may appear in the measurement process, and misses can also be made.
To systematic errors include the component of the measurement error, which remains constant or regularly changes with repeated measurements of the same value. As a rule, systematic errors can be in most cases studied before the measurement starts, and the measurement result can be refined by introducing corrections if their numerical values are determined or by using such measurement methods that make it possible to exclude the influence of systematic errors without their determination .
To the random errors of measurement include the components of the measurement error, which vary randomly with repeated measurements of the same value.
Unlike systematic errors, random errors can not be eliminated in advance. However, the measurement result can be refined by performing repeated measurements, that is, to find the value of the measurand closer to the true one than the result of one measurement. These errors are a consequence, for example, of changes in the external conditions of random measurements, changes in the readings of the measuring device, rounding errors when taking the count, etc.
Flaws and gross errors are called measurement errors, which significantly exceed the systematic or random errors expected under given measurement conditions. If the measurement results are used in calculations, then before that, it is necessary to eliminate measurements containing gross errors. The main reasons for these errors are: the errors of the experimenter; sudden and unexpected change in measurement conditions; malfunction of the device, etc. To determine gross errors used methods of mathematical statistics.
4.3. Systematic errors
4.3.1. General information on systematic errors
The systematic errors in repeated measurements remain constant or vary according to a certain law. These errors can in some cases be determined experimentally, and consequently the result of the measurement can be refined by introducing an amendment.
There are a number of ways to exclude systematic errors, which can be conditionally divided into four main groups:
- elimination of sources of errors prior to measurement;
- elimination of errors in the process of measurement by means of substitution, compensation of errors in sign, opposition, symmetrical observations;
- making known corrections to the result of the measurement (elimination of errors by calculation);
- estimation of the boundaries of systematic errors, if they can not be excluded.
By the nature of manifestation, systematic errors are divided into permanent, progressive and periodic.
Constant systematic errors - errors that remain important throughout the measurement time. For example, if a scale is used to measure a certain value and there is an error in the calibration, then this error is transferred to all measurement results. This refers to the error of the end measures of length, weights, etc.
Progressive errors - errors that increase or decrease during measurement. Such errors include, for example, the errors resulting from the wear of the contacting parts of the measuring instruments, the gradual voltage drop of the current source feeding the measuring circuit, etc.
Periodic errors - errors whose values are a periodic function of time or a function of moving the meter pointer. Such errors are found in the dial gauge (instruments with a dial and an arrow). For example, if the axis of the indicator's arrow is mixed with respect to the center of the scale by some amount, then the error of Ato varies according to the sinusoidal law Ato = e sin to, where e is the eccentricity (mixing of the center of the scale); to - the angle of rotation of the arrow during the measurement, measured from the straight line passing through the center of the scale and the axis of rotation of the arrow.
Systemic errors can also vary according to a complex law due to the combined effect of several systematic errors. For example, such an error is the error of a measure of length that arises when the temperature deviates, at which measurements are made from the normal temperature. The magnitude of this error is determined by the formula
where A /, is the error of the measure of length, which arises when the temperature changes by DL ° C;/n is the length of the measure at normal temperature; Ar =/& quot; -/n - deviation of temperature from normal;/n is the normal temperature;/and - temperature when applying a measure of length; a and & iexcl; 5 are constants determined experimentally.
In the group of systematic errors can be attributed: instrumental errors; errors due to improper installation of the measuring device; errors resulting from external influences; errors in the method of measurement (theoretical errors); subjective errors.
Instrumental errors are called errors, the cause of which lies in the properties of the measuring instruments used. For example, the balance of the balance can not be ideally equilateral. The cause of instrumental errors is also the friction in the articulations of moving parts of devices.
Measuring means having a scale have errors inherent in the inaccuracy of the marked scale marks (calibration errors). Instrumental errors can appear due to wear (the size of the end gauge of the length decreases). The amount of wear depends on the intensity of use.
The correctness of the indications of a number of measuring instruments can also depend on the position of their moving parts with respect to the fixed ones. Such means include, for example, equilibria, scales, the construction of which includes a pendulum or other suspended mobile parts (galvanometers). The deviation of such a means from the correct position can lead to an error in the result. To reduce the measurement error in such tools, devices are used to set them in the correct position (levels, plumb lines, etc.). Ambient temperature, magnetic and electric fields, atmospheric pressure, air humidity refer to external conditions, leading to errors due to their change. If the values of individual factors exceed the established limits, then this may cause additional errors.
If there is no theoretically proved dependence between the measured phenomenon or the property and the principle of the measuring instrument action, this can cause the errors of the measurement method (theoretical errors).
The errors in the measurement method result from simplifications or assumptions, the use of empirical formulas and dependencies. An example of such measurements is the measurement of the hardness of metals by various methods (Rockwell, Brinell, Vickers, etc.). In each of these methods, hardness is measured in its conventional units, and the translation of the results from one scale to another is performed approximately.
Individual properties of a person, which are due to the characteristics of his body or ingrained wrong skills, lead to subjective systematic errors. For example, the speed of response to a signal is different for different persons (for a sound signal, the reaction rate of a person varies within the range 0.082-0.195 s, and the light signal is 0.15-0.225 s).
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