How to minimize measurement errors?

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What do product measurement knowledge and methods have to do with digital quality?

We believe that.

1, a thing if you can measure it and can express it with numbers, you have a deep understanding of it; but if you don’t know how to measure it and can’t express it with numbers, then your knowledge may be barren and unsatisfactory.

2、We know quality by ‘gauge’ and ‘moment’, there is a measurement to have data, there is data to have calculation, there is a calculation to have analysis, there is analysis to have optimization, and there is optimization to have assurance.

3、Measurement is to perceive quality, digitalization is to solve “know what is right” on the basis of “know what is right”, good at using mathematics to solve problems, in order to avoid “seems to be right, but in fact is wrong “.

If you agree with the above logic, let’s learn the basics of the digital quality business layer.

I. Measurement accuracy

Measurement accuracy is one of the most important parameters of the instrument index, most of the instrument accuracy is basically one percent, one thousandth, the part can reach one ten-thousandth, the higher the accuracy, on behalf of the measurement error is smaller, then the error is how to define it?

Second, the terminology of the measurement error

True value: the true value of the measured itself, is an ideal concept, generally difficult to know.

Designated true value: the state to establish a variety of physical standards as far as possible to maintain the same, in the form of a decree, designating the value of the quantity it embodies as the designated value of the unit of measurement, also called the agreed true value.

Actual value: the state through a series of physical measurement standards at all levels forms a value transfer network, the national benchmark embodied in the unit of measurement at each level of comparison, to the daily work of instruments or gauges. In each level of comparison, the value embodied in the standard at the previous level is the accurate value.

Nominal value: The value calibrated on the measuring instrument.
Due to the lack of manufacturing and measurement accuracy and environmental and other factors, the nominal value is not necessarily equal to its true or actual value, so also marked by the error range or accuracy level.
For the nominal value of 100HZ, the working error ≤ ± 3% ± 1HZ
The actual value of 100±100×3%±1HZ

Indicated value: the measured value indicated by the measuring instrument. The indicated value may differ from the reading of the measuring instrument.

Third, the measurement error classification

Measurement error according to its nature and characteristics, can be divided into three categories: systematic error, accidental error (random error), and omission error.

Systematic error

In certain measurement conditions, the measured value contains a fixed or by a certain rule of error, known as the system error.

Systematic error is usually generated by the error of the measuring apparatus, measuring instruments and meters themselves. In addition, due to the imperfection of the measurement method and the testers test habits generated by the error is also known as systematic error.

The size of the systematic error can measure the degree of deviation of the test data from the true value, that is, the accuracy of the measurement. The smaller the systematic error, the more accurate the measurement results.

Elimination or reduction of systematic error

  1. eliminating the factors causing the systematic error is the most basic method to reduce systematic error.

— select instruments and equipment with high accuracy levels to eliminate the basic error of the instrument.
— make the instrumentation work under the specified conditions to eliminate the additional errors of the instrumentation; — make the instrumentation work under the specified conditions to eliminate the additional errors of the instrumentation
–selecting reasonable measurement methods and designing correct measurement steps to eliminate method errors and theoretical errors
–improve the measurement quality of measurement personnel and improve the measurement conditions in order to eliminate personnel errors.

  1. elimination by using corrective methods

Automatically or manually add the measurement readings or results to the corrected values during the data processing of measurement to eliminate or attenuate the systematic errors from the measurement readings or results.

  1. Elimination by using special measurement methods

Substitution method: First connect the measured Ax to the measuring device, adjust the measuring device in a certain state, and then replace Ax with the same kind of standard quantity AN as the measured one, adjust the standard quantity AN, so that the measuring device restores the original state, so Ax = AN.

Difference method: Measure the difference between the measured Ax and the standard quantity AN, that is, a=Ax-AN, and use Ax=AN-a to find out the measured.

Positive and negative error compensation method: Under different measurement conditions, the measured measurement twice, so that the error of one measurement result is positive, the error of the other measurement result is negative, take the average of the two measurement results as the measurement result of the method.

Symmetric observation method: In the measurement process, the practical design of the measurement steps to obtain symmetric data, with the corresponding data processing procedures, in order to obtain the measurement results independent of the amount of influence.

Chance error

caused by the sum of many complex factors of small changes, the law of change is unknown, but has all the characteristics of a random variable, under certain conditions obeys the statistical law, so after many measurements, the sum of which can be described by the statistical law. For example the micro-variation of electromagnetic field, the ups, and downs of temperature, air perturbation, micro-vibration of the earth, irregular and small changes in the senses of the measuring personnel, etc. These changes are beyond people’s control and are irregular, which leads to the fact that the measurement results cannot be identical, and if they are identical, it can only mean that the instrument is not sensitive enough.

Although the chance error is not able to be eliminated by people, the chance error is in line with the normal distribution. That is, the probability of occurrence of small measurement errors is large, and the probability of occurrence of relatively large errors is small. The probability of occurrence of positive and negative errors of equal size is also equal.

The law of distribution of chance errors of normal distribution.

symmetry absolute value of equal positive error and a negative error occurs an equal number of times
The single-peaked absolute value of the small error than the absolute value of the error appears more times
Bounded In certain measurement conditions, the absolute value of the random error will not exceed a certain limit
offsetting As the number of measurements increases, the arithmetic mean of the random error tends to zero

Spurious error

Under certain conditions, the measurement results significantly deviate from the actual value of the error corresponding to the measurement value containing the spurious error is a suspicious value or abnormal value, can not participate in the data processing of the measured value and should be rejected.

It arises for two main reasons.
One is caused by the experimenter itself.
The second is caused by the measurement conditions.

Qualitative judgment omission error: measurement conditions, measurement equipment, measurement steps to analyze, check whether there are errors or factors that cause omission error, you can also check the measurement data with other people using other methods or measured by different instruments to find the omission error.

Quantitative judgment of the error of negligence: based on the statistical principles and relevant expertise to establish the criteria for negligence, the abnormal values or bad values to reject.

Comparison of the three types of errors

The difference between these three kinds of errors can be taken as an example of target shooting. The bullet impact point in Figure 3-a is uniformly in the bull’s eye, which indicates that there is no systematic error, but the distribution is scattered indicating a large chance error. The point of impact in Figure 3-b is off the center of the bullseye, which indicates that the systematic error is larger. The impact point in Figure 3-c is dense in the bull’s eye, which means there is only chance error and no systematic error.

Fourth, the measurement error of the representation method and the calibration of the accuracy of the instrument

1、Absolute error

The difference between the measured value X and its true value A is called the absolute error of X. Absolute error is expressed in △x, that is, △x = X – A.

Because from the measurement point of view, the true value is an ideal concept, it is impossible to really get. Therefore, A is usually replaced by the exact measurement value x0.

2、Relative error

The absolute error can only indicate the degree of approximation of a certain measurement value. However, with two different sizes of measurements, when have the same absolute error, the degree of accuracy and different. For example the measurement of the distance from Beijing to Guangzhou, the error of 1 meter, which is not a large error, but if the measurement of the distance from Tiananmen Square to the Great Hall of the People, the error of 1 meter, which is then a relatively large error. In order to measure the accuracy of the measured value in a more customary way, the concept of relative error is introduced.

The ratio of the absolute error to the true value of the measured is called the relative error of the measured value. That is

3、Instrument error and accuracy

Absolute error and relative error are the result of the representation and measurement from the error to reflect the error of a measured value, but can not be used to evaluate the accuracy of the measurement instrument.

When the instrument works under the specified normal conditions, the ratio of the absolute error picture of the indicated value to its range picture is called the introduction error of the instrument, expressed in pictures, that is, pictures, because the reference error to the range picture for comparison, so also known as the reference error. The maximum quoted error that occurs in the whole range of the measuring instrument is called the tolerance error of the instrument, that is, the tolerance error for the picture. The error marked in the technical specifications of the instrument is referred to as the tolerance error.

For the pointer instrument, set the absolute value of the permissible error for the picture, the picture in the formula – the accuracy level of the instrument, which indicates the size of the absolute value of the permissible error of the instrument, which is what we usually call the accuracy.

Five, the system error elimination method

Eliminate the error introduced by measuring instruments and meters

In the measurement process, according to the requirements of the accuracy of the measurement choose different accuracy levels of instruments, and meters.

Eliminate the error caused by the measurement method or theoretical analysis ;

Not fully considered before the measurement, but in the measurement of the role of the error caused by some factors involved, often due to inadequate theoretical analysis or when caused by the use of an approximate formula. These situations should be avoided.

Elimination of errors caused by the measurement personnel

The errors caused by the physiological characteristics of the experimenter’s reaction speed and inherent habits are human errors. For example, when recording a signal, the observer has the tendency to overshoot or lag, and the tendency varies from person to person, which inevitably leads to errors, so these factors must be taken into account when measuring.

VI. Eliminate the impact of errors through data analysis and observation

In summary, completely accurate and error-free measurement in the actual test does not exist. Whether it is the systematic error of the instrument, accidental error, or negligence error, it can not be completely avoided. But we can use scientific methods to minimize the error as much as possible so that the measurement data is closer to the true value, the most perfect and effective method tool is through the data for long-term analysis and observation, to avoid the impact of errors.

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