Correlation analysis method in accuracy evaluation

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Correlation analysis method in accuracy evaluation of testing equipment

Abstract: the evaluation of testing equipment, especially the accuracy evaluation of multi parameter comprehensive measuring machine (instrument), has always been a thorny problem, but it is also of great concern to enterprises and urgently needs to be solved. This paper analyzes several existing methods, and then puts forward that the correlation analysis in mathematical statistics is used as the basis for objective evaluation of accuracy, and then through data processing and correction, compensation methods, the accuracy of the measured quantity equipment can be truly reproduced

key words: accuracy evaluation correlation coefficient correction compensation

1 evaluation of testing equipment

special equipment located at the production site, which is directly used to monitor the process quality of parts and components and the operation of technological process, is often called testing equipment. They play an important role in the quality assurance system of modern enterprises characterized by mass production. Therefore, the importance of correct and reasonable evaluation, that is, the acceptance of new equipment before it is put into use and the regular calibration of equipment in use, is self-evident

although this kind of special detection equipment, especially the multi parameter comprehensive measurement equipment, is used in different occasions, and its working principle and type structure are also very different, there are many commonalities in the operation mode: the measurement object is basically fixed, but the shape is complex, there are many tested parameters, the use frequency is very high, most of them adopt the comparative measurement principle, and the working environment is poor. On this basis, since the early 1990s, a variety of evaluation standards and guiding technical documents have emerged abroad, which have played an important role in unifying and standardizing the acceptance and evaluation of testing equipment, and have also had a profound impact on the vast industrial sectors including China's automobile industry

although the expressions of various documents are different, the evaluation indicators of testing equipment mainly include the following two items: repeatability and accuracy. Repeatability represents the consistency between the results of continuous multiple measurements on the same measured object under the same conditions, which profoundly reflects the ability of the equipment itself to adapt to the detection work. Using this index, we will have a thorough understanding of the random error of the measurement results. For repeatability, the evaluation methods and index values adopted by various standards are not very different, and the competent department of the enterprise is also easier to grasp and operate, but the situation is completely different for accuracy

accuracy refers to the degree to which the measured test result is consistent with its true value. According to the interpretation of the terms in the ISO and national standards "evaluation and expression of measurement uncertainty" issued three years ago, it is a qualitative rather than quantitative indicator. In order to avoid misunderstanding, the following is the traditional name of accuracy, which is not contrary to accaracy in many foreign guiding standards. Undoubtedly, accuracy is the comprehensive reflection of systematic error and random error in the measurement results. Like repeatability, it is also an important index to evaluate a testing equipment (instrument)

2 analysis of accuracy evaluation method of testing equipment

whether traditional error analysis or a priori probability score estimated based on experience or other information is used, this function is also the first time to use the standard deviation of BMW cloth to express the measurement uncertainty (class B evaluation), which is essentially a static method. In order to have a quantitative basic estimation of the accuracy level of the testing equipment, especially the general measuring (testing) instruments, the application of this method is necessary and effective. However, as a user of a testing equipment, he will always require a more direct way to objectively evaluate the accuracy of this equipment, rather than being satisfied and limited to item by item analysis and synthesis. In fact, the dynamic evaluation method of "comparison + processing" adopted by various guiding technical documents in foreign countries in recent ten years follows this idea. Simply put, this method is based on the data processing results of two groups of corresponding measured values of the same batch of workpieces on the special inspection (instrument) equipment and another inspection instrument with higher accuracy, and then compare with the corresponding regulations, and then make an evaluation

those special measuring instruments with single measurement and simple structure, such as electronic (pneumatic) caliper, can be directly compared with the measuring instrument in the measuring room or even the gauge block as the standard. At this time, the accuracy AC can be expressed as:

where XG and XO are the indication values of the gauge and the standard respectively, and there are also the average values obtained after repeated measurements. However, the main body of today's testing is comprehensive measurement. As mentioned earlier, the tested objects of this kind of equipment are often complex in shape and have many parameters. The instruments used for comparison are generally coordinate measuring machines (CMM). Although CMM has strong versatility and high accuracy, in view of the great difference between its working principle and measurement method and the compared detection equipment, it is obviously not comprehensive to compare and evaluate only a certain parameter of a workpiece according to the method of formula (1), because the influence of various different attribute factors is often great

looking at some existing evaluation standards (guiding technical documents), they all adopt the method of comparative measurement with a certain number of samples, but the data processing and evaluation regulations are different. The specific method of sampling is to collect a number of samples n in a period of time according to the process characteristics of the tested parts (products), then measure a group of data Yi (i=1~n) on the special detection equipment, and then measure another group of data Xi on the CMM. For more rigorous consideration, some standards also stipulate that Yi and Xi need to be measured several times. The following are two representative evaluation types. The two groups of measured values of several samples are simply processed Yi Xi:, it is required that all the differences (Yi XI) are within the range of [a1, a2]. This evaluation criterion can also be expressed as

ac=max{y-x} (2)

although this evaluation method seems too simple, it is often used because it is easy to operate and understand. One example is the testing equipment on the car butt welding production line. In order to confirm the accuracy of measuring the total or upper key points of welding, this method is adopted. Sample collection stipulates that at least 20 workpieces should be extracted from 14 days of continuous production, and they should be tested on two kinds of measuring equipment, and the difference of all measured values should be within [- 0.2mm, 0.2mm]. The measurement of splices is especially large-scale two plate injection molding machine, and the point tolerance monopolized by a few European and Japanese brands is ± 1mm, so the accuracy requirement is: AC ≤ 20% t

The general expression of the accuracy evaluation criterion is

ac=es+ks (3)

in equation (3), ES is the system error, s is the experimental standard deviation, and the coefficient K is the confidence factor, which is determined by the level of confidence probability p, ac=es+ks. If P is 95%, k=2

when calculating es and s in different guiding technical documents, comparative measurement is adopted, and several repeated measurements are often carried out on special detection equipment, but the data processing mode is different. But generally speaking, the whole process of this kind of evaluation is cumbersome, which restricts their application to a certain extent

taking a relatively simple evaluation standard as an example, this paper introduces the calculation method of ES. Select n workpieces for continuous measurement on the special detection equipment, and the average value of the ith workpiece after M repeated measurements is:

after these n workpieces are measured by instruments with higher accuracy (such as CMM), a group of measurement values x1, X2, xn are obtained, from which the system error ESI of the detection equipment measuring the ith workpiece is obtained:

and ES is given by the following formula

u95lab in the above formula is called "measurement uncertainty", It is determined according to the specific situation. When the measured parameter is a geometric quantity, u95lab can be taken as 0.5um. The calculation of the experimental standard deviation s is somewhat similar and will not be repeated here. According to the final accuracy AC value, the evaluation standard is clearly specified

ac ≤ 20% · t (RA ≤ 0.8um)

ac ≤ 30% · t (0.8um ≤ RA ≤ 6.3um)

ra is the measured surface roughness of the workpiece

3 application of regression analysis theory in accuracy evaluation

systematic error is caused by factors that deviate from the measurement conditions or are introduced due to measurement methods, which has a very important impact on the detection results. Unlike random errors, systematic errors have certain regularity, but how to reveal them and improve the accuracy of some measuring equipment is not easy. It is possible to do this only by using correct, reasonable and operable analysis and processing methods

of course, it should be pointed out that if, according to the typical method introduced in the previous section, after a series of tests and data processing, the accuracy AC has reached the index specified in the corresponding evaluation standard, there is no need to explore the internal law of system error. The repeatability test that has been carried out before is qualified, which indicates that the stability of the equipment meets the requirements

however, this thorny situation does exist. The repeatability of the detection equipment fully meets the evaluation index, but after comparison with CMM and subsequent data processing, the accuracy AC is out of tolerance, or even seriously out of tolerance. We believe that we should treat it seriously at this time

strictly speaking, systematic error can be divided into fixed value systematic error and variable value systematic error. The influence of the former on each measured value follows a certain law in both size and direction. By confirming the existence of system error and finding its changing law, it is possible to adopt the processing method of "setting correction - compensation" to effectively eliminate the fixed value system error

we apply the regression analysis theory to study the relationship between the two groups of data generated after comparative measurement, in order to find the change law of the measurement error of the evaluated testing equipment. Finally, the following two purposes are achieved:

(1) by evaluating the linear correlation of the two groups of measured values, to confirm whether there is consistency and comparability between the detection equipment and the CMM and other instruments with higher accuracy. If there is a weak correlation or even no correlation between them after calculation and judgment, the original conclusion of unqualified accuracy is valid

(2) if the evaluation results show that there is a strong correlation between the two groups of measured values, then after the corresponding data processing and finding out the correction amount, compensation measures should be taken to eliminate the fixed value system error in the measurement results of the detection equipment. After the correction/compensation steps are completed, the accuracy evaluation is carried out to verify whether AC has reached the specified index

correlation refers to the relationship between two or more random variables, and the correlation coefficient is a measure of the closeness of this relationship. Then purified syngas is made into methanol, which is defined as the ratio of the covariance of two random variables to the product of their standard deviation, expressed in Q

in actual work, it is impossible to measure infinite times, so the correlation coefficient in the ideal situation cannot be obtained. The estimation can only be obtained from the data obtained from limited measurements, expressed in R (x, y)

today, the values of n samples measured by coordinate measuring machines and detection equipment are recorded as {x1, X2, X3,..., xn} and {y1, Y2, Y3,... Y4}, and I is the sample number, so the respective arithmetic mean values X and y are obtained, And the experimental standard deviations s (x) and S (y). Then the estimated value R (x, y) of the correlation coefficient can be calculated according to formula (4). It should be noted that we replace the N Xi values obtained from n measurements of a random variable x with the N Xi values obtained from each measurement of n samples on the CMM

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