This standard specifies the method for checking the acceptability of test results obtained under repeatability and (or) reproducibility conditions when the repeatability standard deviation and (or) reproducibility standard deviation of a given test method is given, and specifies the method for expressing multiple test results as one final test result. This standard applies to the same test method, and the test results obtained repeatedly under repeatability and (or) reproducibility conditions for the same specimen when the repeatability standard deviation and (or) reproducibility standard deviation of the test method is given. This standard assumes that the error of the test result follows a normal distribution. This standard uses a probability level of approximately 95% in the calculation. GB/T 11792-1989 Precision of test methods Checking the acceptability of test results obtained under repeatability or reproducibility conditions and determining the final test results GB/T11792-1989 standard download decompression password: www.bzxz.net
This standard specifies the method for checking the acceptability of test results obtained under repeatability and (or) reproducibility conditions when the repeatability standard deviation and (or) reproducibility standard deviation of the test method are given, and specifies the method for expressing multiple test results as one final test result. This standard applies to the same test method, and the test results obtained repeatedly under repeatability and (or) reproducibility conditions for the same specimen when the repeatability standard deviation and (or) reproducibility standard deviation of the test method are given. This standard assumes that the error of the test result follows a normal distribution. This standard uses a probability level of approximately 95% in the calculation.

National Standard of the People's Republic of China
Precision of test method
Check the acceptabillty of testrcsults obtainicd under repeatabillty or reproducibilityconditions and to determine final test results1 Subject content and scope of application
GB/T11792--89
This standard specifies the method for checking the acceptability of test results obtained under repeatabillty or reproducibilityconditions when the repeatability standard deviation and/or reproducibility standard deviation of a test method are given, and specifies the method for expressing multiple test results as a final test result. This standard is applicable to the test results obtained under repeatability and/or reproducibility conditions for opposite specimens for the same test method and when the repeatability standard deviation and/or reproducibility standard deviation of the test method are known. This standard assumes that the errors of the test results follow a normal distribution. This standard uses a probability level of approximately 95% in the calculations. 2 Referenced standards
GB3358 Statistical terms and derivatives
GB6379 Test method precision Determine the repeatability and reproducibility of standard test methods through laboratory tests 3 Terms and special symbols
This standard uses the terms in GB 3358 and GB 6379 Repeatability terms
Tests performed independently of each other in a short time interval on the same material in the same laboratory by the same operator using the same equipment using the same test method.
Reproducibility terms
Tests performed independently of each other in a short time interval on the same material in different laboratories by different operators using different equipment using the same test method. Repeatability limit
-a value ", under repeatability conditions, the absolute value of the difference between two test results does not exceed this number with a probability of 95%, reproducibility limit
a value F, under reproducibility conditions, the absolute value of the difference between two test results does not exceed this number with a probability of 95%, repeatability critical range
a value, under simple and complex conditions, the range of several test results does not exceed this number with a probability of 95%, reproducibility critical difference
a value, under reproducibility conditions, the absolute value of the difference between two test results or the final result (such as mean, median, etc.) calculated from two groups of test results does not exceed this number with a probability of 95%, median
Approved by the State Administration of Technical Supervision on November 22, 1989 and implemented on July 1, 1990
GB/ 11792—89
If the values ​​are arranged in ascending order of their algebraic values ​​and are numbered from n to n, when n is an odd number, the median of the measured values ​​is the nth value; when n is an even number, the median is between the nth value and the nth+1th value, and the arithmetic average of these two values ​​is taken.
Standard deviation
Cfo(n)
Xmux+Xmin
Standard deviation of repeatability
Standard deviation of reproducibility
Repeatability limit
Reproducibility limit
Initial test efficiency
Repeatability critical range for sample size n
Reproducibility critical range coefficient for sample size non-reproducible critical difference
Random variable, extreme value of the test result
Test result
Final test result used as an estimate of the value of the measured characteristic 4 Methods for checking the acceptability of test results obtained under repeatability conditions and determination of the final test results 4.1 Single test result
In various tests The situation of only one test result is rare. When a test result is obtained, it is impossible to directly perform a statistical test of acceptability with the given repeatability standard deviation. A second test result should be obtained when there is any doubt about the accuracy of the test result. 4.2 Two initial test results
Two test results should be taken under repeatability conditions: the absolute confidence interval of the difference between the two results is compared with the repeatability limit \4.2.1 Case with low testing cost
If the absolute value of the difference between the two test results is not less than the value, the two results can be accepted, and the final test result is equal to the average of the two results. If the absolute value of the difference between the two results is greater than the value, two more tests must be performed. If the difference of the four results (Tmx-Xmn) is equal to or less than 1 The critical range, Bgs(4), is taken as the average of the four results as the final test result. The expression of the critical range, ss(4) is:
E, (n) -(n)G,
The f(a) value in the above formula is shown in the table.
Table 1 Critical range coefficient f(n)
: The critical range coefficient is the normalized fraction of (Xmz Xr)/car, m and Xr are the maximum and minimum values ​​of the normal distribution with standard deviation r in the population and sample size. GB/T 11792—89
If the range of the four results is less than the critical range of repeatability, then take the digit of the result as the final test result. The above process can be represented by Figure 1.
2 initial test results
IX,-X.αr
Take 2 more test results
In the middle of the 4 results
4.2.2 If the test cost is relatively lowWww.bzxZ.net
I=the half mean of the 2 results
-the average of the 4 results
If the absolute value of the difference between the two test results is less than the value, the two results are acceptable. The final test result is equal to the average of the two results. If the absolute value of the difference is greater than the "value", another test result should be taken. If the range of the three results is equal to or less than the critical range C,H95(3), the optimal test result μ is equal to the average of the three results. If the range of the three results is greater than the critical range C,%(3), the situation in which the fourth test result may be obtained is determined by one of the following two situations: The laboratory should take the median as the final test result: This process can be represented by Figure? GB/T1179289
2 initial test results
Take another test result
Xmina,C,R.,(3)
When the fourth test result is possible at the median of -3 results
: b
The average of the two wrong results
=the average of the 3 results
The laboratory should take the fourth test result. If the range of the four results is equal to or less than the critical range R(4), the average of the four results is taken as the final test result. If the range is greater than R(4), the median of the four results is taken as the final test result. This process can be represented by Figure 3.
2 initial test results
Take another test result
Xmin.C,R(3)
Take another test result
Xmin,G.Ru(4)
=median of 4 results
=average of 2 results
is the average of 43 results
is the average of 4 results
4.2.3 Reporting the final test results
When reporting the final test results, the following should be stated:
number of tests;
whether the mean or median is taken.
4.3 "More than two initial results
GB/I ​​11792-89
In actual work, the initial result is often greater than 2. Under repeatability conditions, the method for determining the final result is the same when >2 and =2.
The test result has a unique range of X-X. Compared with the critical range CR% (), if the range is equal to CR (), the average of the results is taken as the final test result.
If the range is greater than CR (), the final test result is determined according to one of the following three situations. 4.3.1 Test cost is lower Case
Look at the initial test result
The range of several results
Take another test result
The range of 2 results
CrR..(2n)
In = the median of 2n results
4.3.2 Case of high test cost
Except the initial test result
The range of several results
GCR(n)
is the median of one result
4. 3. 35 Test cost is low - or 3,The test cost is higher in the case of = average value of several results
u=average value of 2n results
half mean of each result
G8/T 11792-89
no initial test results
range of several results
≤C.,R..(n)
then take m\ results
n+range of the first results
/4 = 0. 016 6A2 A unit uses GB812087 high purity n-heptane and isooctane purity determination method (capillary chromatography) to determine the concentration of n-heptane. It is known that when the concentration of n-heptane is greater than 99.5%, the repeatability limit is r=0.010. Two data of the same sample have been measured: X: 99.538 yuan x: —99. 552%.
Solution: [X1-X2=0.014%>0.010%
Two more results are measured: X, -99.555%, X-99.545% [YX: 1 --0. 017%
Critical range C, R(4)=f(4)×
Due to 0. 017%0. 013%
Therefore, the median of one result is taken as the final test result", = (99.552% + 99.545%) / 2 = 99.548% A3 A unit uses GB4945-85% petroleum products and lubricants neutralization value determination method (color indicator method) 3 to test a certain oil product. It is known that this method is effective when the neutralization value is 0.01-0.1, = 0.03. The 6 data of the same sample have been measured as 0.019, 0.022, 0.022, 0.025, 0.063. 0.060. Find the final test result. Solution: Range 0.063-0.019-0.044
Critical range c, Rs(6)-(6)×2.03-
Since the range is greater than the critical range, the two results are 0. 029, 0. 029. The difference of these 8 results is still 0.044. GB/T17792-89
0.03-0.046
But the critical range is, g:(8)=f(8)×
Since the range is smaller than the critical range, the average value is taken as the final test result: 4=(0.019+0.022+0.022+0.025+0.063+0.060+0.029+0.029)/8- 0.033 6
A4 A certain unit uses the antimony-phosphorus-molybdenum blue photometric method in GB223.3-81 "Determination of the content of iron and steel and alloys" to determine the phosphorus content in steel. It is known that this method has a = 0.0030 and R = 0.0045 when the phosphorus content is 0.055. There are two laboratories that have measured the same sample and obtained the following results: Laboratory 1 measured the results as 0.0622, 0.0622, 0.0614; Laboratory 2 measured the results as 0.0495, 0.0538. Try to compare the differences in laboratory results and find the final test results.
Solution, Laboratory 1
was different 0. 062 2 —0. 061 1- 0. 000 80. 003 0
The critical range C, R3) = f(3)×
The range is less than the critical range, so the mean is \0. 003 5
# -- (0. 062 2 + 0. 062 2 + 0. 061 4)/3 - 0. 06) 9 Experimental blank 2
Range 0.05380.0495-0.0013
Because 0.0043>0.0030, two more results are 0.0532, 0.05320.030
Critical extreme 0, D (4) - F (4)\=3.6×
Because the range is greater than the critical range, the median is taken as the final result 2=(0.0532+0.0532)/2=0.0532
The difference between the final results of laboratory 2—=0.00873The critical difference is r, Ra: =
1(c(n)*
The difference between the results of laboratory 2 and the critical difference
=0.003 75
After finding the cause, it was found that there was a problem in the operation of the second laboratory. It should be handled according to Article 5.2 of this standard. Additional notes:
This standard is proposed by the National Technical Committee for the Application of Statistical Methods. This standard is under the jurisdiction of the China Institute of Standardization and Information Classification and Coding. This standard was drafted by the Working Group of the Application Subcommittee of the National Technical Committee for the Application of Statistical Methods. The main drafters of this standard are Liu Guangyi, Xiang Kefeng and Yu Zhenfan.
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