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A Complete Guide to Measurement Error

Measurement is essential in all kinds of physical experiments and technology development processes, and as long as the measurement result, measurement error is inevitable. The error affects measurement accuracy, so the technical staff concerned must learn and master the theory of error, have a comprehensive and systematic understanding of the characteristics, nature, and classification of error, and finally find a reasonable and scientific way to eliminate it.


What is the Definition of Truth Value and Measurement Error?

The truth value, also known as the theoretical value, is an objective, real value that reflects the characteristics of something under certain conditions of time and space. In measurement, there is a certain deviation, more or less, between the measured result and the truth value, and this deviation is the measurement error.

The truth value is an ideal concept and, in the strictest sense, cannot be obtained by actual measurement and therefore the error cannot be obtained accurately. In the actual error assessment process, the conventional truth value is often used as the truth value, which may itself be inaccurate and therefore only an estimate of the error can be obtained.

length measure

For example, a standard metre is defined as the distance travelled by light in 1/299792458 seconds in a vacuum. Because of the invariance of the speed of light, one standard metre is the conventional truth value, but in practice we do not measure it with the speed of light, but with the help of a scale. Then the reading of the scale is the measured value and its deviation from one standard metre is the error of a particular measurement.

Why is there a measurement error?

Measurement is based on certain theories or methods, using certain instruments, in a certain environment and carried out by specific people. The influence of factors such as approximations in experimental theory, difficulties in methodological refinement, limitations in the sensitivity and resolving power of experimental instruments, and instability in the surrounding environment. All these undesirable observation conditions are the root cause of the error.

Specifically, measurement errors arise from the following four main sources.

1 Measurement error of instrument

Instruments in the process of processing and assembly, can not ensure that the structure of the instrument can meet a variety of geometric relationships, such instruments will inevitably bring errors to the measurement. Such as the zero point or specifications of the instrument are not accurate.

2 Measurement error environmental impact

Mainly refers to the observation environment in the temperature, air pressure, air humidity and clarity, wind and atmospheric refraction and other factors of constant change, resulting in measurement results with errors.

Mainly refers to the temperature, air pressure, air humidity and clarity, wind and atmospheric refraction and other factors of constant change in the observation environment, which results in measurement error.

3 Measurement error of test method

This is due to the approximation of the theoretical formulae on which the measurement is based itself, or the failure of the test conditions to meet the requirements set out in the theoretical formulae, or the imperfection of the test method itself. For example, the thermal test does not take into account the heat loss caused by heat dissipation, the voltammetric method of measuring resistance does not take into account the influence of the internal resistance of the electric meter on the test results, etc.

4 Measurement error of human

Due to the limitations of the observer’s sensory discrimination and the different levels of technical proficiency, which can lead to deviations during instrument alignment, levelling and aiming, it varies from person to person and is related to the observer’s mental state at the time.

Types of Errors in Measurement

Measurement errors are divided into three main categories: systematic errors, random errors and gross errors.

1 Systematic error

Systematic error is also called regular error, it is in certain measurement conditions, the test results always show a similar pattern when the same object is measured several times over.

Systematic error

The characteristics of the systematic error: in the same measurement conditions, repeated measurement results are always large or small, multiple measurements for the average can not eliminate the systematic error. We should identify the main causes of systematic error according to the specific test conditions and the characteristics of systematic error, and take appropriate measures to reduce its impact.

There are many reasons for systematic errors, including instrument errors, theoretical errors, operational errors, etc. Some of these systematic errors are constant, such as the inaccuracy of the instrument’s zero point, and some are cumulative, for example, when measured with a steel scale that has been subjected to thermal expansion, the reading is small.

2 Random error

Random error, also known as chance error, even in the ideal situation of completely eliminating systematic error, repeatedly measuring the same measurement object many times, will still be due to a variety of accidental, unpredictable uncertainty interference and measurement error, called random error.

random error

The size of random error, the plus or minus of the random error are not fixed, but multiple measurements will find that the absolute value of the same positive and negative random error appears roughly equal probability, so they can often cancel each other out, from the random error distribution law can be seen, increase the number of measurements, and according to the statistical theory of the measurement results can be processed to reduce the random error.

Random error factors are very complex, such as the electromagnetic field of the micro-variation, parts of the friction, clearance, thermal fluctuations, air disturbances, air pressure and humidity changes, the physiological changes in the sensory organs of the measurement personnel, and their combined impact can become a factor in the generation of random error.

measurement error
T: truth value, X: measuring value

3 Gross error

Under certain conditions, the measurement result deviates significantly from the truth value, i.e. the error that clearly distorts the measurement result. The main causes of gross errors are as follows.

Objective reasons: sudden changes in voltage, mechanical shock, external vibration, electromagnetic (electrostatic) interference, instrument failure, etc. caused by the test instrument’s measurement value abnormal or the relative movement of the measured object’s position, thus generating a gross error.
Subjective causes: use of defective gauges; negligence and carelessness in operation; errors in reading, recording, calculation, etc. In addition, perverse and sudden changes in environmental conditions are factors that produce these errors.

Gross error is not offsetting, it is present in all scientific experiments and cannot be completely eliminated, but only attenuated to some extent. It is an outlier and seriously distorts the reality, so it should be removed when processing the data, otherwise it will have a serious impact on the standard deviation and mean deviation.

How to reduce errors in measurement?

As coarse errors distort the actual situation, they should be eliminated when processing the data, while random errors, which are the result of countless unknown factors influencing the measurement, conform to a normal distribution and can be reduced by increasing the number of measurements and processing the results according to statistical theory.

The main discussion here is how to reduce systematic error.

1 Correction in the measurement results

For known fixed-value systematic errors, the measurement results can be corrected with the correction value; for variable-value systematic errors, try to find out the variation pattern of the errors and correct the measurement results with the correction formula or correction curve; for unknown systematic errors, they are treated as random errors.

2 Eliminate the root causes of systematic errors

Before measuring, check the instrument carefully, adjust and install it correctly, prevent external interference, choose a good observation position to eliminate parallax, choose a time when the environmental conditions are more stable for reading, etc.

3 Real-time feedback correction

Due to the application of automated measurement technology and computers, real-time feedback correction can be used to eliminate complex changes in a systematic error. During the measurement process, the sensor will be used to convert these changes in error into some form of a physical quantity (generally electricity), in a timely manner in accordance with its functional relationship, through the computer to calculate the value of the error affecting the measurement results, and to make real-time automatic correction of the measurement results.

There are also methods that are specifically tailored to different situations, such as alternative method, substitution method, compensation method, symmetric measurement, combined measurement, etc.

Since errors exist in all measurements, it is essential to discuss measurement errors and to understand their laws, nature, sources and magnitude. Analyzing measurement errors is important for people to improve their experiments, to increase the precision and accuracy of measurements and even new discoveries.

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