Any measurement procedure, regardless of the conditions in which it is carried out, is associated with errors. They are deviations that distort the idea of the real value of the quantity.
Sources of error
Deviations occur for a variety of reasons. The main ones include:
- Imperfect designs of measuring instruments or inaccuracy of their manufacture.
- Failure to comply with the rules during the procedure.
- Human factor.
- Imperfect methods, etc.
Deviation classification
During the measurement process, systematic and random errors may occur.
Systematic deviations are classified on various grounds. In particular, depending on the nature of the manifestation, they are divided into periodic, constant and progressive errors.
Gross errors or errors may also appear. They arise due to:
- Mistakes of the expert.
- Sudden changes in measurement conditions.
- Equipment malfunctions, etc.
Systematic errors
These deviations can usually be studied prior to measurement. Such indicators remain constant or change naturally during repeated measurements of the same value. The result of the study can be adjusted by amending, if the numerical value of the deviation is known, or by using such measuring tools that can eliminate the influence of these errors without determining their value.
For repeated measurements, certain laws apply, in accordance with which the values of systematic errors change. These deviations can sometimes be determined experimentally. Accordingly, the result can be clarified by correction.
Nature of manifestation
As mentioned above, three groups of systematic errors are distinguished by this feature. It:
- Constant deviations. These include such errors that, throughout the entire measurement process, retain their value. For example, if a specialist uses a scale of an instrument whose calibration has an error to determine an indicator, its value is transferred to all experimental results.
- Progressive abnormalities. Such errors decrease or increase during measurements. These include, for example, deviations resulting from wear of the contacting elements of the measuring means, a gradual decrease in the voltage of the current source from which the measuring circuit is powered, etc.
- Periodic errors . Their values are determined by the periodic function of time or by the function of moving the pointer on the device used for measurement. They arise in indicators with a dial and arrows.
Deviation rates can vary due to the simultaneous influence of several systematic errors. This is manifested, for example, when measuring temperature.
Other species
Systematic deviations also include:
- Theoretical errors . They are also called measurement method errors.
- Instrumental errors .
- Deviations due to improper positioning of the measuring device.
- Personal errors .
- Deviations due to the influence of external factors.
Instrumental errors
These include deviations due to the properties of the measuring instruments used. For example, equal-arm scales cannot be perfectly equal-arm.
Deviations also arise due to friction of the joints of the movable elements of the measuring devices. They may occur due to wear and tear on the equipment. The wear rate, respectively, will depend on the intensity of operation of the device.
Result error
The accuracy of the readings of some measuring instruments depends on the position of their moving elements relative to stationary. It is, in particular, about such devices as equal-arm scales, means, the construction of which is a pendulum or other moving suspended parts. When the device deviates from the correct position , the reference point shifts and an error in the result occurs. To prevent its occurrence during the installation of devices, special devices are used: levels, plumb, etc.
The influence of external factors
Temperature, humidity, air pressure are external conditions that entail the appearance of errors when changing their values. If the indicators of certain factors go beyond the specified boundaries, then additional deviations may occur.
Measurement method errors
They can occur when there is no theoretically proven relationship between the measured property or phenomenon and the operating principle of the measuring device.
The error of the method is caused by assumptions or simplifications when applying empirical dependencies and formulas. Such a situation arises, for example, when measuring the hardness of metals in different ways: using the Brinell, Rockwell, Vickers, etc. methods . Each of them has its own arbitrary units. Translation of results is carried out approximately.
Subjective deviations
Personal errors are determined by the individual properties of a person. They, in turn, are associated with the characteristics of the body, ingrained skills (often incorrect). For example, all people have different reaction rates to a signal: it varies in the range of 0.082-0.195 s for sound, and 0.15-0.225 s for light.
Error Exclusion
Systematic deviations entail bias in the measurement results. The greatest danger in these situations is deviations that remain undetected and the presence of which experts do not even suspect. Such errors became the cause of incorrect scientific conclusions, the establishment of false laws of physics, imperfect designs of measuring instruments, marriage in production.
Systematic errors must be identified and eliminated or taken into account when measuring. Methods of exclusion and accounting deviations are divided into several groups:
- Elimination of sources of deviations before the start of the measurement procedure (prevention).
- Elimination of errors during the process (experimental methods).
- Amendment of measurement results. In this case, errors are eliminated by the calculation method.
- Estimation of the limits of systematic errors, if their exclusion is impossible.
Elimination of Sources
Preventive measures before starting the measurement are considered the most rational way to eliminate errors. In this case, the specialist is partially or completely freed from the need to identify and eliminate deviations during the measurement.
The most effective preventive measures include:
- Regulation or repair of measuring instruments. The need for these activities is determined by verification.
- Correction of the installation of the device. To prevent the shift of the reference point , skews and other negative phenomena, plumb bows and other devices are used.
To eliminate errors arising from the influence of external factors, you can remove their direct source or protect the measuring device from exposure.
The elimination of errors during experiments usually involves re-measurement. In this regard, the methods described above are more appropriate to apply when working with stable phenomena, indicators, etc.
Amending Results
This method of eliminating systematic errors involves correcting the measurement result by calculation.
The most common version of the amendment is considered the algebraic summation of the result and the amendment itself (taking into account the sign). Its numerical value is equal to systematic deviation, and the sign is the opposite. In this way, additive deviation is eliminated.
In some cases, a systematic error can be eliminated by multiplying the indicator obtained as a result of the measurement by a correction factor. Its value approaches unity (more or less than it). It is advisable to use the correction factor if necessary to exclude the multiplicative error.
Estimation of deviation limits
It is produced when it is impossible to rule out systematic errors in practice. This phenomenon occurs if the deviations are insufficiently studied or studied, but cannot be used to adjust the result. The latter is characteristic of integrating measuring instruments (counters).
Random errors
When re-measuring a constant physical parameter under the same conditions, the results often often differ slightly. Moreover, the deviations between the values are not systematic, do not obey any laws. Such errors are usually called random.
Deviations occur with the simultaneous impact on the process (object, measuring tool, specialist, etc.) of a number of factors. Each source may slightly affect the result, but their combined effect will lead to a significant deviation from the actual indicator of the measured object.
Sources of exposure manifest themselves differently in a given time period. At the same time, they act separately from each other, without any logical connection. This leads to differences in sign and size of discrepancies in the measurement results. They change without any connection with both previous and subsequent values. Accordingly, it is impossible to take them into account in any way.
In the framework of probability theory, mathematical methods are used to study the properties of random phenomena in their large aggregates. During the development of measuring equipment and metrology, it was found that they are fully consistent with the task of studying random deviations. In many cases, the results obtained with their help are consistent with data obtained experimentally.
In probability theory, an event is considered accidental, the occurrence of which is unambiguously impossible to predict. In other words, in a certain set of conditions, this event may or may not occur. When applying this definition to the field of measurement, we can say that when performing repeated experiments with a certain physical parameter under the same conditions, each of the probable insignificant sources of random changes in the results can either appear or not appear. Consequently, deviations become unpredictable both in magnitude and in sign.
Given the above, we can give the following definition of random errors: these are deviations that vary from one dimension to another, cannot be directly accounted for in connection with a chaotic change, due to the simultaneous influence of several factors isolated from each other on the result.
The presence of random errors, unlike systematic ones, is quite easily detected during repeated measurement.