"Precision" is a non-standard term with uncertain meaning

"Precision" is a non-standard term with uncertain meaning

In some publicity materials of the weighing instrument industry, you will see the term “high precision ×× scale” from time to time, but “precision”

It is not a standard term, and it is often used to express different meanings. Therefore, its meaning is ambiguous and cannot be passed on.

Pass a clear meaning and should avoid continuing to use it improperly.

Why is "precision" an irregular term with ambiguous meaning? because:

First of all, "precision" is just a popular term that once appeared, but it has never been a formal definition of metrology. Secondly, there are two English words corresponding to Chinese "precision": one is precision and the other is accuracy;

In metrology terms, the former refers to "precision" and the latter refers to "accuracy". In addition, there are some occasions where "precision" is used to refer to the "division value". For example, some weighing instrument manufacturers describe the specifications of the so-called "high-precision platform scales" in their product sales materials: "range 60kg, 75kg, 100kg/accuracy 1g, 2g, 5g, 10g, scale size 30cm ×40cm; measuring range 150kg, 200kg, 300kg/accuracy 1g, 2g, 5g, 10g, 20g, 50g, weighing platform size 40cm×50cm. "In fact, the grades of these products of the same series are the same.

According to JJF1181-2007 "Weighing Apparatus Measurement Terms and Definitions" 6.2.2, the definition of scale interval (d, scale interval) means: "The difference between two adjacent (digitally indicated) indications expressed in mass units or (Analog indication) The difference between the values corresponding to the scale marks." Therefore, the "precision" referred to here is only the size of the indicator display division specified during the design and manufacture of the weighing instrument. Related terms similar to this include:

6.2.3 Verification scale value (e) verification scale interval The value expressed in mass units for the classification or verification of weighing instruments. 6.2.5 Number of verification scale interval (n) The ratio of the maximum scale (Max) to the verification scale value (e), that is, n=Max/e.

7.7 Discrimination The ability of a discrimination weighing instrument to respond to small changes in load.

7.9 Resolution The resolution indicating device can effectively distinguish the ability of the weighing value of close neighbors.

It can be seen that the "precision" here is not as good as "discrimination" or "verification division value", "verification division number", etc., which can objectively reflect the measurement performance of the weighing instrument.

As for the two meanings of "precision" and "accuracy" that are used to evaluate the main measurement performance, they are not the same. When evaluating and analyzing the error of measuring instrument (error of measuring instrument), in addition to the careless error caused by accidental negligence, the remaining error generally includes the systematic error of the measuring instrument ( There are two major parts: systematic error and random error in detection. They come from different sources, and to eliminate or reduce them, different targeted measures need to be taken. In other words: Em=Es+Er Formula 1: Em is the measurement error, Es is the system error, and Er is the random error. The measurement error refers to the reference between the value given by the measuring instrument (system) and the corresponding input value The difference in value. Repeating multiple measurements on the same object can increase the credibility of the results. If the results of n measurements are:

x i = x 1, x 2, x 3, ……, x n; the reference value (conventional true value) of the input quantity of the measured object is T, then:

Em i = x i -T Equation 2 System error is also called measurable error or regular error. Its characteristic is: when the same value is repeatedly measured under actual measurement conditions, the measurement error component remains basically constant (that is, the absolute value and sign remain unchanged), or changes in a foreseeable manner (the absolute value and sign Changes have a certain pattern). Among them, the former is also called constant error, and the latter is also called

Variable value error. The degree of system error (E S) is trueness, and the arithmetic average of multiple measurements (or

The mathematical expectation is measured by the difference between μ and the agreed true value T, that is, bias.

Random error is also called undetermined error. Its characteristic is that when the same quantity is repeatedly measured under actual measurement conditions, the absolute value and sign of the measurement error component change in an unpredictable manner. From the point of view of probability theory and mathematical statistics, it is the part of the error that randomly changes around the arithmetic mean (mathematical expectation) of the measurement results under the measurement conditions. The regularity of its appearance is very complicated, and only statistics can be used. The method finds out the numerical relationship between the size of the error and the number of occurrences, that is, finds out the probability distribution law of the error. The classic error theory believes that the probability distribution of random errors is a normal distribution, and on this premise, a statistical analysis method for random errors has been established. When the number of measurements continues to increase, the arithmetic mean of this error tends to zero. Reflecting the degree of random error is precision (precision), which refers to the independent test results under specified test conditions.

The degree of agreement between the results can be measured by deviation. The precision of a single measurement can be expressed by the difference between each single measurement result and the average value of multiple measurement results on the same object under repeated conditions, namely:

Er = x i-μ Equation 4 For a finite number of samples, it is usually expressed by the standard deviation σ (standard deviation) of a large number of test results, namely:

It can be seen that precision depends on the distribution of random errors, and is only related to the expected value, not the true value. As for accuracy (accuracy) refers to the degree of agreement between the test result and the true value. Accuracy is usually measured by error, which is composed of a random error component (bias) and a systematic error component (offset). Therefore, when we compare the accuracy of two sets of data, we should compare their accuracy and precision at the same time. Comparison of three terms used to reflect the magnitude of different types of errors

Error category Measurement error Em System error Es Random error Er The term reflecting the degree Accuracy (trueness) Definition of precision*

5.5 The degree of agreement between the measurement result and the measured true value

  Under repeated conditions, the difference between the average value of an infinite number of measurements of the same measured value and the true value of the measured value is the difference between the average value of the same measured value of an infinite number of measurements under repeated conditions The difference evaluation method and the corresponding value name The difference between the indicated value and the true value The difference between the expected value and the true value The standard deviation of a large number of indicated values Indication error (error) Offset (bias) Deviation (deviation) The number of the previous standard is defined as "JJF 1181- The numbers of the corresponding clauses in the 2007 Weighing Apparatus Measurement Terms and Definitions are described below with archery as a metaphor to further illustrate the difference between correctness, precision and accuracy:

If A, B, C, and D shoot 20 arrows each, set the bullseye (10 rings) as the true value, and use the relevant formulas of probability statistics

The formula calculates the mathematical expectation and standard deviation of each person’s performance, and the results are as follows:

The total scores of A, B, C and C are 170 rings and an average of 8.5 rings. Compared with the "true value" bullseye, the bias of the scores of the three is 8.5-10=-1.5, which means that the system error or accuracy of the three is Are equal. But their precision and accuracy are not exactly the same. The lowest score of A is 6 rings, the lowest of B is 7 rings, and the lowest of C is 8 rings, that is, the maximum errors of the three are not equal. The standard deviations of the three persons of A, B and C decrease successively, indicating that the random errors of the three are not equal, that is, the precision of A is the worst, second is the second, and C is the highest (although A hits 10 rings 6 times, and B hits 3 times , And C is 0 times).

Looking at the different expectations of B and D, it is obvious that the correctness and accuracy will not be the same; but their standard deviations are both 1, which means that the random error or precision of the two is equal. Accuracy was once called "precision", some people referred to it as "precision", but it is just a popular term, and there is no strict equivalent relationship; but on many occasions, people will regard "precision" as "precision". Abbreviation for "degree". Therefore, the English translation corresponding to "high precision" also has two types, high precision and high accuracy, which makes the meaning of "precision" uncertain. In order to avoid confusion, the term "precision" has been discontinued and changed to "accuracy", and "precision" should no longer be understood as its abbreviation.

The accuracy of the measuring instrument can reflect the degree of deviation of the measured value of the measured object from the actual value (the agreed true value). The measurement error includes both the deviation (random error) and the offset (system error); and the precision It only reflects random errors, and does not include systematic errors. Therefore, the meaning of "precision" in "high-precision XX scale" is often ambiguous. Therefore, does the term "precision" referred to by others mean "precision" or "accuracy", or even just It is "display division value", we must figure it out so as not to misunderstand. It is also necessary to be wary of individual unscrupulous merchants deliberately misusing non-standard language to mislead and deceive customers. At the same time, we should no longer blindly follow the trend, so as not to make people's "precision" a non-deterministic meaning, so as not to make people unable to determine the true meaning of the expression.