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The difference in measurement uncertainty & measurement error


Measurement uncertainty and error are basic propositions studied in metrology, and also one of the important concepts often used by metrology testers. It is directly related to the reliability of the measurement results and the accuracy and consistency of the value transmission. However, many people easily confuse or misuse the two due to unclear concepts. This article combines the experience of studying "Evaluation and Expression of Measurement Uncertainty" to focus on the differences between the two. The first thing to be clear is the conceptual difference between measurement uncertainty and error.


Measurement uncertainty characterizes the evaluation of the range of values in which the true value of the measured value lies. It gives the interval in which the true value may fall according to a certain confidence probability. It can be the standard deviation or multiples thereof, or the half-width of the interval indicating the confidence level. It is not a specific true error, it just quantitatively expresses the part of the error range that cannot be corrected in the form of parameters. It is derived from the imperfect correction of accidental effects and systematic effects, and is a dispersion parameter used to characterize the measured values that are reasonably assigned. Uncertainty is divided into two types of evaluation components, A and B, according to the method of obtaining them. Type A assessment component is the uncertainty assessment made through the statistical analysis of observation series, and type B assessment component is estimated based on experience or other information, and it is assumed that there is an uncertainty component represented by an approximate "standard deviation".


In most cases, error refers to measurement error, and its traditional definition is the difference between the measurement result and the true value of the measured value. Usually can be divided into two categories: systematic errors and accidental errors. The error exists objectively, and it should be a definite value, but since the true value is not known in most cases, the true error cannot be known accurately. We just seek the best approximation of the truth value under certain conditions, and call it the conventional truth value.


Through the understanding of the concept, we can see that there are mainly the following differences between measurement uncertainty and measurement error:


1. Differences in assessment purposes:


Uncertainty of measurement is intended to indicate the scatter of the measured value;


The purpose of measurement error is to indicate the degree to which the measurement results deviate from the true value.


2. The difference between the evaluation results:


Measurement uncertainty is an unsigned parameter expressed by standard deviation or multiples of standard deviation or the half-width of confidence interval. It is evaluated by people based on information such as experiments, data, and experience. It can be quantitatively determined by two types of evaluation methods, A and B. ;


The measurement error is a value with a positive or negative sign. Its value is the measurement result minus the measured true value. Since the true value is unknown, it cannot be obtained accurately. When the conventional true value is used instead of the true value, only the estimated value can be obtained.


3. The difference of influencing factors:


Measurement uncertainty is obtained by people through analysis and evaluation, so it is related to people's understanding of the measurand, influencing quantity and measurement process;


Measurement errors exist objectively, are not affected by external factors, and do not change with people's understanding;


Therefore, when performing uncertainty analysis, various influencing factors should be fully considered, and the evaluation of uncertainty should be verified. Otherwise, due to insufficient analysis and estimation, the estimated uncertainty may be large when the measurement result is very close to the true value (that is, the error is small), or the uncertainty given may be very small when the measurement error is actually large.


4. Differences by nature:


It is generally unnecessary to distinguish the properties of measurement uncertainty and uncertainty components. If they need to be distinguished, they should be expressed as: "uncertainty components introduced by random effects" and "uncertainty components introduced by system effects";


Measurement errors can be divided into random errors and systematic errors according to their properties. By definition, both random errors and systematic errors are ideal concepts in the case of infinitely many measurements.


5. The difference between the correction of the measurement results:


The term "uncertainty" itself implies an estimable value. It does not refer to a specific and exact error value. Although it can be estimated, it cannot be used to correct the value. The uncertainty introduced by imperfect corrections can only be considered in the uncertainty of the corrected measurement results.


If the estimated value of the system error is known, the measurement result can be corrected to obtain the corrected measurement result.


After a magnitude is corrected, it may be closer to the true value, but its uncertainty not only does not decrease, but sometimes it becomes larger. This is mainly because we cannot know exactly how much the true value is, but can only estimate the degree to which the measurement results are close to or away from the true value.


Although measurement uncertainty and error have the above differences, they are still closely related. The concept of uncertainty is the application and expansion of error theory, and error analysis is still the theoretical basis for the evaluation of measurement uncertainty, especially when estimating B-type components, error analysis is inseparable. For example, the characteristics of measuring instruments can be described in terms of maximum allowable error, indication error, etc. The limit value of the allowable error of the measuring instrument specified in the technical specifications and regulations is called the "maximum allowable error" or "allowable error limit". It is the allowable range of the indication error specified by the manufacturer for a certain type of instrument, not the actual error of a certain instrument. The maximum allowable error of a measuring instrument can be found in the instrument manual, and it is expressed with a plus or minus sign when expressed as a numerical value, usually expressed in absolute error, relative error, reference error or a combination thereof. For example ±0.1PV, ±1%, etc. The maximum allowable error of the measuring instrument is not the measurement uncertainty, but it can be used as the basis for the evaluation of the measurement uncertainty. The uncertainty introduced by the measuring instrument in the measurement result can be evaluated according to the maximum allowable error of the instrument according to the B-type evaluation method. Another example is the difference between the indication value of the measuring instrument and the agreed true value of the corresponding input, which is the indication error of the measuring instrument. For physical measuring tools, the indicated value is its nominal value. Usually, the value provided or reproduced by a higher-level measurement standard is used as the agreed true value (often called calibration value or standard value). In the verification work, when the expanded uncertainty of the standard value given by the measurement standard is 1/3 to 1/10 of the maximum allowable error of the tested instrument, and the indication error of the tested instrument is within the specified maximum allowable error , it can be judged as qualified.

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