This part of GB/T6379 describes alternative methods to the basic method for determining the standard deviation of repeatability and reproducibility of standard measurement methods, which is a supplement to GB/T6379.2, and also provides a robust method for analyzing precision test results. GB/T 6379.5-2006 Accuracy (Trueness and Precision) of Measurement Methods and Results Part 5: Alternative Methods for Determining the Precision of Standard Measurement Methods GB/T6379.5-2006 Standard Download Decompression Password: www.bzxz.net
This part of GB/T6379 describes alternative methods to the basic method for determining the standard deviation of repeatability and reproducibility of standard measurement methods, which is a supplement to GB/T6379.2, and also provides a robust method for analyzing precision test results.

1CS 03. 120. 30
National Standard of the People's Republic of China
GB/T6379.5—2006/ISO5725-5:1998 Partially replaces GB/T6379—1986
GB/T11792—1989
Accuracy (trueness and precision) of measurement methods and results—Part 5:alternative methods for the determination of the precisionof a standard measurement method(ISO 5725-5.1998.IDT)
Released on November 13, 2006
Digital anti-counterfeiting
General Administration of Quality Supervision, Inspection and Quarantine of the People's Republic of China Standardization Administration of China
Implementation on April 1, 2007
Normative references
Split-level design
4.1 Application of split-level design
Split-level design arrangement
Organization of split-level experiment
Statistical model
Split-level design Statistical analysis of test data
Checking for data consistency and outliers
Reporting the results of the level test·
4.8 Example 1: Level test - Determination of protein quality 5 Non-uniform material design·
Application of non-uniform material design
Arrangement of non-uniform material design
Organization of non-uniform material test
Statistical model of non-uniform material test
Statistical analysis of test data of non-uniform material Checking for data consistency and outliers
Reporting the results of non-uniform material test Results of the test:
Example 2: Test of non-uniform materials
General formula for design calculation of non-uniform materialsExample 3: →Application of general formula
6 Robust methods for data analysis
Application of robust methods for data analysis
Robust analysis: Algorithm A
Robust analysis: Algorithm S
Formula: Robust analysis of specific levels of uniform level designExample 4: Robust analysis of specific levels of uniform level designFormula: Robust analysis of specific levels of split level designExample 5: Robust analysis of specific levels of split level design 6.8 Formula: Robust analysis of specific levels in tests on non-uniform materials 6.9
Example 6: Robust analysis of specific levels in tests on non-uniform materials
Appendix A (Normative Appendix)
Symbols and abbreviations used in GB/T 6379
Appendix B (Informative Appendix)
Appendix C (Informative Appendix)
Appendix D (Informative Appendix)
Derivation of coefficients used in Algorithm A and Algorithm S Derivation of formulas used in robust analysis
TaiZhe Literature
GB/T 6379.5-2006/ISO 5725-5:199810
GB/T6379.5—2006/ISO5725-5:1998GB/T6379 Accuracy of measurement methods and results (correctness and precision) is divided into the following parts, its structure and corresponding international standards are:
Part 1: General principles and definitions (IS05725-1:1994, IDT): Part 2: Basic methods for determining the repeatability and reproducibility of standard measurement methods (ISO5725-2:1994, ID T): Part 3: Intermediate measures of precision of standard measurement methods (ISO5725-3: 1994 IDT): Part 4: Basic methods for determining the trueness of standard measurement methods (1S05725-4: 1994, IDT): Part 5: Alternative methods for determining the precision of standard measurement methods (1SO5725-5: 1998. IDT): Part 6: Practical application of accuracy values ​​(1SO5725-6: 1994. IDT) This part is the 5th part of GB/T6379.
This part of GB/T6379 is equivalent to the international standard ISO5725-5: 1998% Accuracy of measurement methods and results (trueness and precision) Part 5: Alternative methods for determining the precision of standard measurement methods and the technical amendment 1SO5725-5: 1998/Cor.1: 2005 issued by IS0 on June 1, 2005. The following amendments and corrections have been made to the borrowing errors of 1SO5725-5:1998 and 1SO5725-5:1998/Cor1:2005:
Correct the "unit difference" in the first row of Table 6 of Example 1 in 4.8 to "unit average":
D=［(/g）+1/g)/（F-]
in formula (18) in 5.3.3 to:
D=（-1)+(/g)+1/(g)/x(g-):
Correct the "sample sum of squares" in 5.9 e) to "laboratory average "Square and" Correct the formula (75) in 6.6 \s, = s2\ to \3 = 2": Correct the value of "1N when = 1.5 in B.1 to the value of \1/sequence when = 1.5: Correct the \\ on the summation sign in formula 25) and formula (26) in 5.4.2 of Technical Modification 1S05725-5/Cor.1: 2005 to \p\\;
Change the (pm-)X=p--X+(mm
in the derived formula (C.4 process in Appendix C to:
(puu)X(p--u)×a+-u)×1. 5
Part 1 to Part 6 of GB/T6379 replace GB/T6379-1986 and GB/T11792-1989 as a whole. The standard expands the original concept of precision and adds the concept of correctness, which is collectively referred to as accuracy. In addition to the repeatability condition and reproducibility condition, the intermediate precision condition is added.
Appendix A of this part is a normative appendix; Appendix B, Appendix C and Appendix D are informative appendices. This part was proposed and coordinated by the National Technical Committee for Standardization of Statistical Methods. Drafting units of this part: Institute of Mathematics and Systems Science, Chinese Academy of Sciences, Guangdong Exit-Entry Inspection and Quarantine Bureau, China National Institute of Standardization. The main drafters of this part: Feng Zhuyong, Ding Wenxing, Jiang Jian, Yu Zhener, Li Chengming, Xiao Hui, Chen Yuzhong. This part was first issued in 2006.
GB/T6379.5--2006/IS05725-5:1998 cited
0.1This part of GB/T6379 uses two terms, "trueness" and "precision" to refer to the accuracy of a measurement method. Trueness refers to the degree of agreement between the (arithmetic) mean of a large number of test results and the true value or accepted reference value: while precision refers to the degree of agreement between test results.
0.2General considerations for the above quantities are given in GB/T6379.1 and are not repeated in this part of GB/T6379. GB/T6379.1 should be read in conjunction with all other parts of GB/T6379 (including this part) because GB/T6379.1 gives basic definitions and general provisions
0.3GB/T6379.2 Standard measures for estimating precision using inter-laboratory trials, namely the repeatability standard deviation and the reproducibility standard deviation This gives a basic method for estimating precision using homogeneous level designs. This part of GB/T 6379 describes alternative methods to the basic method.
Using the basic method creates the risk that the operator's measurement results on one sample will affect the subsequent measurement results on another sample of the same material, thereby biasing the estimates of the repeatability standard deviation and the reproducibility standard deviation. When this risk is serious, it is better to use the split level design described in this part of GB/T 6379 because it reduces this risk. b) The basic method requires the preparation of a large number of identical samples of the test material for testing, which may not be possible for non-homogeneous materials, so the use of the basic method will increase the estimate of the reproducibility standard deviation due to the variation between samples. This part of GB/T 6379 eliminates the variation between samples when calculating the estimate of the reproducibility variance because it can obtain information about the variation between samples that cannot be obtained by the basic method. ) The basic method requires that the data be tested and outliers be removed when calculating the repeatability standard deviation and reproducibility standard deviation. The removal of outliers sometimes has a great impact on the estimation of the repeatability standard deviation and reproducibility standard deviation. In practice, when detecting outliers, the data analyst may have to make judgments on which data should be excluded. This part of GB/T6379 describes some robust methods for data analysis. These methods do not require the inspection and removal of outliers and can directly calculate the repeatability standard deviation and reproducibility standard deviation. In this way, the calculation results are no longer affected by the judgment of the data analyst. 1 Scope
GB/T6379.5—2006/IS05725-5:1998 Accuracy (Trueness and Precision) of Measurement Methods and Results Part 5: Alternative Methods for Determining the Precision of Standard Measurement Methods
This part of GB/T6379:
Specifies in detail the alternative methods to the basic method for determining the repeatability standard deviation and reproducibility standard deviation of standard measurement methods, namely split level design and non-uniform material design:
Specifies the robust method for analyzing the set of precision tests, which does not require the detection and elimination of outliers in the data during the calculation process. In particular, the use of one of the methods is described in detail. This part of GB/T 6379 is a supplement to GB/T 6379.2. It provides some alternative design methods that are more valuable than the basic method given in GB/T 6379.2 in some cases. It also provides a robust analysis method for estimating the standard deviation of repeatability and reproducibility, which relies less on the judgment of the data analyst than the basic method described in GB/T 6379.2. 2 Normative references
The clauses in the following documents become clauses of this part through reference in this part of GB/T 6379. For any dated referenced document, all subsequent amendments (excluding errata) or revised versions are not applicable to this part. However, parties to an agreement based on this part are encouraged to study whether the latest versions of these documents can be used. For any undated referenced document, the latest version applies to this part.
GB/T3358.1-1993 Statistical terminology Part 1: General statistical terms GB/T3358.3-1993 Statistical terminology Part 3: Experimental design terms GB/T6379.1-2004
Accuracy (trueness and precision) of measurement methods and results Part 1: General principles and definitions (ISO 5725-1:1994-IDT)
GB/T6379.2-2004 Accuracy (trueness and precision) of measurement methods and results Part 2: Basic methods for determining the repeatability and reproducibility of standard measurement methods (ISO5725-2:1994.IDT) ISO3534-1:1993 Statistics - Vocabulary and symbols - Part 1: Probability and general statistical terms 3 Definitions
GB/T3358.1. The definitions given in GB/T3358.3 and GB/T6379.1 are still applicable in this part of GB/T6379. The symbols used in GB/T6379 are given in Appendix A. 4 Split level design
4.1 Application of split level design
4.1.1 The uniform level design described in GB/T6379.2 requires two or more identical samples of the test material to be tested at each test level for each laboratory participating in the test. There is a risk in adopting this design that when the operator measures one sample, the measurement result may affect the measurement result of subsequent samples of the same material. Once this happens, the precision test results will be distorted: the repeatability standard deviation, the estimated value will decrease: and the estimated value of the standard deviation between laboratories will increase. In the split level design, for each test level, two samples of two similar materials are provided to each participating laboratory, and the operators are told that the two samples are different but not how big the difference is. Thus, split-level designs provide a method of determining the repeatability and reproducibility standard deviations of standard measurement methods that can reduce the aforementioned risks. 4.1.2 The data obtained at one level of a split-level experiment can be used to plot a graph in which the data of two different but similar materials are plotted as the horizontal and vertical axes, respectively. Figure 1 is an example of such a graph: Such a graph can help identify those laboratories with the greatest bias relative to other laboratories. Such identification is useful when it is possible to investigate the cause of the greatest laboratory bias and take corrective action. 4.1.3 The repeatability and reproducibility standard deviations of measurement methods usually depend on the level of the material. For example, when the measurement result is the ratio of an element obtained by chemical analysis, the repeatability and reproducibility standard deviations often increase with the increase of the ratio of the element. For split-level experiments, two materials at the same level of the experiment are very similar and can be considered to have the same repeatability and reproducibility standard deviations. For split-level designs, it is acceptable to obtain almost identical measurements for two materials at the same level of the test. It is more meaningful to arrange two materials that are quite different. In many chemical analysis methods, the presence of the component of interest can affect the precision, so for split-level tests, it may be difficult to prepare two products that are similar enough for split-level tests. Sometimes, when the material is extracted from two natural or manufactured products, it may be difficult to prepare two products that are similar enough for split-level tests. It should be remembered that the purpose of selecting materials that are different from the split level design is to provide the operator with a possible solution. 4.2 Split level design 4.2.1 Split level design As shown in Table 1, in a laboratory, two samples are measured at the same level in each test, a and b. In each level, a represents the sample of one material, while b represents the sample of another similar material. 4.2.2 The data for the split levels are expressed as: Subscript 1 represents -1.2, subscript represents the outlet, 12..9, subscript represents the sample (a or b). 4.3 Split level tests 4.3.1 When planning a split level test, the guidance given in 6.8 of GB/T 6379.1-2004 and Chapter 6 of GB/T 6379.1-2004 should be followed (the formula contains a quantity usually expressed as . These formulas are used to determine the number of laboratories to be included in the test. The split level will be determined by the method specified in Note 24 of GB/T 6379.1-2004 for evaluating the repeatability standard deviation for repeatability and reproducibility. ||Uncertainty of the estimated value of the standard deviation, calculate the following quantity: S
v2(p-1)
1+262-11+1
8Y(p-1)
where ya/a.
If the repetition times in equations (9) and (10) in GB/T6379.1-2004 are -2. Then it can be seen that equations (9) and (10) in GB/T6379.1-2004 are the same as equations (1) and (2) above, except that P-1 is sometimes used here instead of force in GB/T6379.1-2004. This is a small difference, so Table 1, Figure B.1 and B.2 in GB/T6379.1-2004 are used.2 can be used to assess the uncertainty of the estimate of the standard deviation of repeatability and reproducibility for split-level tests. To assess the uncertainty of the estimate of the bias of the measurement method for split-level tests, calculate the quantity A defined in GB/T 6379.1-2004, where # = 2, (or use Table 2 of GB/T 6379.1-2004), and use this quantity as described in GB/T 6379.1. 2
GB/T 6379.5-2006/ISO 5725-5.1998 To assess the uncertainty of the estimate of laboratory bias for split-level tests, calculate the quantity A* defined in Equation 16 of GB/T 6379.1-2004, where # = 2. Because the number of replicates in the split-level test is 2, it is not possible to reduce the uncertainty of the estimate of laboratory bias by increasing the number of replicates. (If this uncertainty must be reduced, a uniform level design should be used instead of a split-level design). 4.3.2 Details on the organization of split-level tests should follow the guidance in Chapters 5 and 6 of GB/T 6379.2-2004. In GB/T 6379.2, the number of repetitions n is the number of split-level designs, i.e. 2. Samples a and samples α should be randomly assigned to the test participants according to some randomization process. In split-level tests, the statistician must be able to distinguish which results are material α and which are material stress in the reported data for each test level. Therefore, the samples are marked, but it is important not to disclose this information to the test participants. Table 1
Recommended format for data organization of split-level test designs CHINA
Laboratory
4.4 Statistical model
Requirements for use This model is derived from equation (1) in Chapter 5 of CB/T 3791-2004. To estimate the accuracy (trueness and density) of the measurement 4.4. 1GB/T 6379
method, assume that for a given test material, each measurement result is the sum of a component: m
where:
the mean value of a given level is 0 (expected), -1.…, aB, — the laboratory component of the bias of a given laboratory 1. Given
under repeatability conditions. p:j-1.*q!
(3)
under a repeatability condition, the random error of the test result obtained by the laboratory at the level is, day-1.…, open. 4.4.2 For split-level tests, the above model becomes yu-meB+et
. The only difference from equation (3) in 4.4.1 is that for the level. The subscripts on the a in equation (4) indicate that the overall mean depends on material a or 6<6=1 or 2).
B has no subscript, indicating that for one level, it is assumed that the corresponding laboratory bias does not depend on material a or 6. This is an important reason for requiring the two materials to be similar.
4.4.3 The unit mean and unit difference are defined as: y+u/2
Da-Yu-Van
4.4.4 The total mean of the level test is defined as: 15)
(6)
GB/T 6379.5—2006/1SO 5725-5:1998m=(ma+mg)/2
4.5 Statistical analysis of split level test data 4.5.1 Place the data in the table shown in Table 1. Each combination of each laboratory and each level in the table constitutes a "unit", which contains two data and V.
Calculate the unit difference D and place them in the table shown in Table 2. The analysis method requires that each difference be calculated in the same way as 0-1, and the sign of the difference be retained.
Calculate the unit mean and place them in the table shown in Table 3. 4.5.2 If a cell in Table 1 does not have two test results (e.g. due to sample damage or data being excluded after outlier testing as described below), then the corresponding cells in Tables 2 and 3 should be left blank. 4.5.3 For each test level j, calculate the mean value D, and standard deviation n of the difference values ​​D, in the column , of Table 2: D, -ED,Ip
sp-2(DD/C-)bzxZ.net
Here, it means the sum of the products of laboratories 1-1,2. If there are blank cells in Table 2, P is the number of cells with data in the first column of Table 2, and the sum is performed for all non-blank cells. 4.5.4 For each test level, calculate the average y and standard deviation of the average value in the first column of Table 3: y=2yutp
Here, it means the sum of laboratories 11, 2. (8
If there are blank cells in Table 3, P is the number of cells with data in the first column of Table 3, and the sum is performed for all non-blank cells. 4.5.5 Using Tables 2 and 3 and the statistics calculated in 4.5.3 and 4.5.4, use the method described in 4.6 to test the data for consistency and outliers. If any data is rejected, the statistics should be recalculated. 4.5.6 Calculate the repeatability standard deviation and reproducibility standard deviation according to the following formula 5 period one year old||tt| |(12)
%=number+product/2
4.5.7 Check whether $ and 8# depend on the mean value. If so, use the method described in 7.5 of GB/T6379.22004 to determine the covariance coefficient.
Table 2 Recommended format for the list of unit differences in split-level design
Laboratory
Laboratory
GB/T6379.5—2006/1SO5725-5:1998Table 3 Recommended format for the list of unit means in split-level design
4.6 Check for data consistency and outliers4.6.1 Use the statistics described in 7.3.1 of GB/T6379.2—2004 to test the consistency of the data. Check the consistency of unit differences The statistic is: h-(D.-DD/sp
The post-statistic of the consistency of the mean value of the test set of units is: ay/s
In order to reveal inconsistent laboratories, the laboratories are grouped and these statistics are plotted in horizontal order, as shown in Figures 2 and 3. The interpretation of these graphs has been fully discussed in 7.3.1 of GB/T6379.2-2004. If one laboratory has poor repeatability than other laboratories, many statistics with large unit differences will appear in the graph. If the measurement results of a laboratory are generally consistent, then most of the non-statistics obtained based on the unit mean values ​​are in one direction of the graph. If either of the above two situations occurs, the laboratory should be required to investigate and feedback their findings to the organizer of the test. 4.6.2 Use The Grubbs test described in 7.3.4 of GB/T6379.2-2004 is used to test the data for outliers and outliers. To test for outliers and outliers in the unit difference, each column of Table 2 is subjected to the Grubbs test. To test for outliers and outliers in the unit mean, each column of Table 3 is subjected to the Grubbs test. The interpretation of these tests is fully discussed in 7.3.2 of GB/T6379.2--2004. These tests are used to identify data that are very inconsistent with other data reported in the test. If these data are included in the calculation of the repeatability and reproducibility standard deviation, these statistics will be significantly affected. Generally, data judged as outliers should be eliminated from the calculation; data judged as outliers should be retained unless there is a good reason for doing so. If the test shows that the values ​​in one of Tables 2 and 3 are excluded in the calculation of the repeatability and reproducibility standard deviation, the corresponding values ​​in the other table should also be excluded in the calculation. 4.7 Reporting the results of split-level experiments
4.7.1 7.7 of GB/T6379.2-2004 recommends the following: Report the results of the statistical analysis to the leadership team: The leadership team makes the decision:
Prepare a comprehensive report.
4.7.2 7.1 of GB/T6379.1-2004 recommends the format for publishing the standard deviation of repeatability and reproducibility of the method 4.8 Example 1: Split-level experiment - Determination of protein 4.8.1 Table 4 is the experimental data for the determination of the total amount of protein in the diet by oxidation. There are 9 experimental spaces participating in the experiment, and the experiment has 14 levels. Each level uses two diets with similar protein content. 4.8.2 Tables 5 and 6 are the unit means and differences calculated using the data of the 14th level of the experiment according to the method in 4.5.1. Using the difference in Table 5 and formula (8) and formula (9) in 4.5.3, we can get: 5
GB/T6379.5—2006/ISO5725-5:1998D=8.34%
s/=0.4361%
Applying formula (10) and formula (11) in 4.5.4 to the unit average in Table 6, we can get: V14=85.46%
8=0.4534%
So using formula (12) and formula (13) in 4.5.6, the repeatability and reproducibility standard deviation is: S-0.31%
Table 7 gives the calculation results for other levels
4.8.3 Figure 1 shows the Youdenplot of the results of sample a in each laboratory against the results of sample b for level 14 in Table 4. The point of laboratory 5 is located at the bottom corner of the graph while the point of laboratory 1 is located at the bottom corner, which indicates that the data from laboratory 5 have a consistent negative bias for samples a and b, while the data from laboratory 1 have a consistent positive bias for the two samples. This type of pattern can be seen when plotting data from a graded level design like Figure 1. The figure shows that the results from Laboratory 4 are abnormal because the straight lines of equality are farther apart. The points from the other experiments are in the middle of the dot plot. Figure 1 provides an example that should be investigated to explain the abnormal bias for this laboratory. Note that the diagram explains level 14. See Figures 2 and 3. In Figure 3, the small negative bias of Experiment 8 and 9 is smaller. The clock interaction may be caused by the fact that Figure 2 does not reveal this. 4.8.5 Table 8 gives the results of 4.8.6. After checking the original analysis, we continued the analysis. We hope that the statistics calculated by the method described in GB/T 6379.2 laboratory instrument are shown in Table 6 and Table 6. The dot plots of the statistics at all levels show that the data may have a negative bias. The figures for all levels are almost all dominated by the statistics of the Booth statistics, which indicates that their data are not very interesting. The figures also show that the values ​​of the Booth statistics for the laboratories are all negatively biased (positive bias is higher than that for laboratory 5), and there is a positive laboratory bias. The differences between the laboratories and the levels vary with the level, which is a clue that the evidence is suspicious. Before starting to analyze the suspicious data of the experiment, the statistical expert should immediately remove all the data from the laboratory. If the repeatability and reproducibility are not calculated, the standard deviation should be calculated. Since these problems have been included in the possible differences between the total mean and the standard deviation of the reproducibility, the determination of the total amount of dietary fortification should be expressed as a percentage. 13, 54
Laboratory
Laboratory
Laboratory
Example 1: Water
Table 4 (continued)
Unit difference
Unit difference
Energy basis
-1,215
GB/T 6379.52006/1S0 5725-5:19989
87:Edit 8
Table 6 Example 1: Unit average of level 1
Laboratory
Unit average
Statistics
GB/T6379.5—2006/1SO5725-5:1998 Example 1: Average, average difference and standard deviation calculated based on all 14 levels of data in Table 4 Table 7
Number of laboratories
Total average
One minimum value||t t||minimum values
average difference
Table 8 Example 1: Grubbs statistic
Grubbs statistic of the difference
two minimum values
0,7571
standard deviation
same maximum value
0.1418(6:8)
0:2943
Grubbs statistic of the unit mean
another minimum value
two maximum values
0.1291 (649)
one maximum value
1, 535
2. 296*45)
2.224-(4)
maximum values
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