Re-inspection and re-test procedures for assessment of declared quality levels
Some standard content:
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National Standard of the People's Republic of China
GB/T16306-2008
Replaces GB/T16306-1996
Re-inspection and re-test procedures for assessment of declared quality levels2008-08-06 Issued
General Administration of Quality Supervision, Inspection and Quarantine of the People's Republic of China Digital Anti-Counterfeiting
Standardization Administration of China
2009-01-01 Implementation
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GB/T16306—2008
Normative Reference Documents
3 Terms, Definitions and Symbols
3.1 Terms and Definitions
3.2 Symbols
4 Re-test Procedure and Implementation of Sample Products
Test Method for Acceptability of Test Results Obtained under Repeatability Conditions and Determination of Final Reported Results Test for Acceptability of Test Results Obtained under Reproducibility Conditions Determination of method and final reported result4.3
4.4 Application example
5 Re-inspection of the verification population
5.1 Re-inspection procedure for the verification population
5.2 Implementation of re-inspection sampling
Appendix A (informative appendix) Comprehensive OC curve for quality verification sampling inspectionStandard download station
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GB/T16306-2008
This standard specifies the method for re-inspection of the verification population and re-inspection of sample products when assessing product quality. This standard replaces GB/T16306-1996 "Product quality supervision review procedure and sampling plan". The main technical differences between this standard and GB/T16306-1996 are as follows: the supervision population is changed to the verification population;
The supervision quality level (e~) is changed to the claimed quality level (DQL, DQL); the non-pass judgment value is changed to the limit value;
The requirements for normality test are added;
The discussion on comparing the actual quality level with the claimed quality level is added; When the sample products are re-tested, the content about the standard deviation of the intermediate precision is added; When the samples specified in this standard cannot be obtained for re-testing, the results of the first random inspection are used as the final results; The sampling plan table is added.
Appendix A of this standard is an informative appendix.
This standard is proposed by the China National Institute of Standardization. This standard is developed by the National Technical Committee for the Application of Statistical Methods. The drafting units of this standard are: Wuxi Product Quality Supervision and Inspection Institute, China National Institute of Standardization, Guangdong Provincial Administration for Industry and Commerce, PLA Ordnance Engineering College, Institute of Mathematics and Systems Science, Chinese Academy of Sciences. The main drafters of this standard are: Chen Huaying, Yu Zhenfan, Chen Yehuai, Wu Jianguo, Ding Wenxing, Chen Min, Zhang Yuzhu, Feng Tuyong. This standard was first published in 1996, and this revision is the first revision. Standard Download Site
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GB/T16306—2008
GB/T16306 specifies the methods for re-inspection of the verification population and re-testing of sample products when evaluating product quality. This standard contains two parts: re-inspection of the verification population and re-inspection of the test object. For the sampling inspection of the population, my country has promulgated three sampling standards for quality verification, which are GB/T2828.4 "Sampling Inspection Procedure for Attributes Part 4: Assessment Procedure for Claimed Quality Level", GB/T2828.I1 Sampling Inspection Procedure for Attributes Part 11: Assessment Procedure for Claimed Quality Level of Small Population", and GB/T6378.4 "Sampling Inspection Procedure for Quantity Measurement Part 4: Assessment Procedure for Claimed Quality Level of Mean".
The purpose of quality inspection and quality acceptance is different, and the sampling plans used are also different. The system of acceptance sampling procedures specified in quality acceptance is applicable to bilateral agreements between two related parties (such as suppliers and users). Acceptance sampling procedures are only used as practical rules for delivering products after inspecting a sample of the inspection batch. Therefore, these procedures do not explicitly involve any form of claimed quality level. In acceptance sampling, it is believed that there is no clear boundary between the quality levels of acceptable batches and unacceptable batches. The design of the transfer rules and sampling plans in the counting adjustment type and the measurement adjustment type is to encourage the supplier to produce products with a process average quality level that is better than the selected AQL.
GB/T2828.4, GB/T2828.11 and GB/T6378.4 are all for evaluating whether the quality level of the verification population does not meet its claimed quality level. Due to the randomness of sampling, any assessment based on sampling will have inherent uncertainty in the judgment results. These standards design some rules so that when the actual quality level of the verification population actually meets the claimed quality level, the risk of judging the verification population as unqualified is controlled at 5%. If you also hope that when the actual quality level of the verification population does not meet the claimed quality level, the risk of judging the verification as passed is also very small, you must have a larger sample size. In order to minimize the sample size, it is allowed that when the actual quality level does not actually meet the claimed quality level, the risk of judging the verification as passed is slightly higher. Since its sampling plan "has a 5% probability of judging the inspection population as unqualified when the actual quality level of the inspection population actually meets the claimed quality level", in order to reduce this risk, re-inspection is required. The re-inspection part in this standard is designed for this purpose.
For the re-inspection of the inspection object, this standard specifies the method of reporting the final result in multiple inspections. Only when the relevant inspection standards have specified the repeatability limit, reproducibility limit and standard deviation under the conditions of intermediate precision, can the method of this standard be used to determine the final reported result in multiple inspections. In GB/T6379.2 "Accuracy (Trueness and Precision) of Measurement Methods and Results Part 2: Basic Methods for Determining Repeatability and Reproducibility of Standard Measurement Methods" and GB/T6379.3 "Accuracy (Trueness and Precision) of Measurement Methods and Results Part 3: Intermediate Measures of Precision of Standard Measurement Methods" which has been submitted for approval, the method of obtaining the repeatability limit, reproducibility limit and standard deviation under the conditions of intermediate precision has been specified.
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1 Scope
Assessment Procedure for Re-inspection and Re-testing of Claimed Quality Level This standard specifies the assessment procedure for re-inspection and re-testing of claimed quality level of product quality. GB/T16306—2008
The re-inspection in this standard is only applicable to the verification population composed of discrete individuals, not to bulk materials. The re-testing in this standard is applicable to the situation where the error of the test results of the sample products obeys or approximately obeys the normal distribution. When the quality level of the verification population is expressed as the percentage of non-conforming products, the verification population size N should be greater than 250 and the ratio of the population size to the sample size should be greater than 10, that is, N/n>10. When the verification population size does not exceed 250, or the ratio of the population size to the sample size is not greater than 10, the sampling plan retrieved by this standard is approximate and should be used with caution. The sampling plan can also be determined according to the method specified in GB/T13264. 2 Normative references
The clauses in the following documents become clauses of this standard through reference in this standard. For any dated referenced document, all subsequent amendments (excluding errata) or revisions are not applicable to this standard. However, parties to an agreement based on this standard 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 standard GB/T2828.1-2003 Sampling procedures for inspection by attributes Part 1: Sampling plans for batch inspection based on acceptance quality limit (AQL) (ISO2859-1: 1999, IDT)
GB/T4882 Statistical processing and interpretation of data Normality test (GB/T4882-2001, idtISO5479: 1997) GB/T19000 —2000 Quality Management System Fundamentals and Vocabulary (idtISO9000:2000) GB/T15482 Product Quality Supervision Small Population Count Single Sampling Inspection Procedure and Sampling Table GB/T6379.1
Accuracy (Trueness and Precision) of Measurement Methods and Results (GB/T6379.1—2004, ISO5725-1:1994, IDT) Part 1 General Principles and Definitions
GB/T6379.2 Accuracy (trueness and precision) of measurement methods and results Part 2: Basic methods for determining the repeatability and reproducibility of standard measurement methods (GB/T6379.2—2004 ISO5725-2:1994, IDT) GB/T8054 Procedures and tables for single sampling inspection of metrological standards GB/T10111 Generation of random numbers and their application in product quality sampling inspection GB/T13264 Procedures and sampling tables for small batch sampling inspection of percentage of non-conforming products ISO3534-1:2006 Statistical vocabulary and symbols Part 1: General statistical terms and terms used in probability ISO3534-2:2006
Statistical vocabulary and Symbols Part 2: Applied statistics ISO5725-3:1994
Intermediate measuresbZxz.net
Accuracy (trueness and precision) of measurement methods and results Part 3: Precision of standard measurement methods ISO5725-6:1994
Accuracy (trueness and precision) of measurement methods and results Part 6: Practical application of accuracy values 3 Terms, definitions and symbols
The terms, definitions and symbols determined in GB/T2828.1-2003, ISO3534-1:2006, ISO3534-2:2006 and GB/T19000--2000 and the following terms, definitions and symbols apply to this standard. 3.1 Terms and definitions
Re-test
Further test of sample products under repeatability, reproducibility or intermediate precision conditions. Standard download station
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GB/T16306—2008
Re-inspection
Re-sample from the original inspection population for inspection to determine whether the inspection population is unqualified. 3.1.3
Observed value
The characteristic value determined as a result of an observation. [ISO3534-2:2006,3.2.8]
test result
testresult
the value of a characteristic determined by a specified test method [ISO 3534-2.2006,3.4
repeatableconditions
repeatableconditions
test conditions performed independently by the same operator using the same equipment in the same laboratory
intermediateprecision
measurement
test conditions performed independently by the same operator in the same laboratory Repeatability limit is a value under reproducibility conditions between two measurements. Note: Repeatability limit is expressed in terms of reproducibility conditions.
For the same test method, when the same conditions
equipment is "not calibrated"
for the same object in a short period of time, the probability that the absolute difference of the results is less than or equal to this number is 95%.
For different operators using different equipment to perform the same test method on the same object independently, the probability that the absolute difference of the results is less than or equal to this number is 95%. Note: The symbol R represents reproducibility limit
Repeatability critical difference repeatabilitycriticaldifference A numerical value. Under repeatability conditions, the absolute value of the difference between two test results or the final result (such as the mean, median, etc.) calculated from two groups of test results does not exceed this number with a certain probability. 3.1.11
Repeatability critical range
repeatabilitycriticaldifference A numerical value. Under repeatability conditions, the range of m test results or the final value (such as the mean, median, etc.) calculated from m groups of test results does not exceed this number with a certain probability. 3.1.12
Reproducibility critical difference producibilitycriticaldifference 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%. Standard download station
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Audit population audit population
The entirety of the unit products being audited. 3.1.14
GB/T16306—2008
Audit population quality level of audit population Quality indicators in the audit population (based on unqualified The maximum number of nonconforming items allowed in the sample of the verification population based on the claimed quality level. Note: For the case where the number of nonconforming products per hundred units is used as the quality indicator, the limiting number of nonconformities should be used. 3.1.16
Limiting value limiting value
The minimum value allowed for the quality statistic based on the claimed quality level. 3.2 Symbol
. Standard deviation
Repeatability standard deviation
Sample repeatability standard deviation
Reproducibility standard deviation
Repeatability limit
RReproducibility limit
Intermediate precision standard deviation
CR. (m) Repeatability critical range for sample size m f(m) Repeatability critical range coefficient for sample size m CD.95 Reproducibility critical difference (probability is 0.95) X., X, Test result
XXm Extreme value of random variable test result
N Total number of unit products included in the verification population, that is, the verification population DQL Claimed quality level
Claimed quality level expressed as a percentage of defective products (or the number of defective products per hundred units) Claimed quality level expressed as a population mean DQL
L Limit number of defective products| |tt||nSample size
（n, L）Counting re-inspection sampling plan
QR quality ratio
LQR limit quality ratio
LQL limit quality level
NInspection population size
DNumber of defective products in the inspection population
dNumber of defective products in the sample
PActual quality level of the inspection population
PQuality level with risk of missed judgment
P（p）When the actual quality level of the inspection population is equal to the force, the probability of judging the inspection population as passed according to the sampling plan. 3
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GB/T16306—2008
Probability of first type error (risk of misjudgment)
βProbability of second type error (risk of missed judgment) 4Re-inspection procedures and implementation of sample products
For non-destructive testing, when there is an objection to the result of the first test, the test conditions at that time must be found out first. If the test conditions at that time were wrong, the first test results shall be discarded and the test shall be repeated. If the test conditions at that time were correct, the test under repeatability conditions, reproducibility conditions or intermediate precision conditions may be carried out if necessary. For destructive testing, re-testing of backup sample products is allowed only when there is reliable evidence that the first test was wrong. Otherwise, it should be handled according to the re-inspection situation.
4.1 Test methods for acceptability of test results obtained under repeatability conditions and determination of final reported results If there is doubt about the accuracy of the first test result and it is possible to obtain a second or more test results under repeatability conditions, the final results may be reported in accordance with the following provisions
4.1.1 Final reported results
For various products
4.1.1.2 Final reported
Quality characteristics should be in accordance with GB/T6379.2 Determine the repeatability limit r. Determination method
When the absolute value of two test results
is not greater than
,
the result is the arithmetic mean of the two results. If the difference between the two
is equal to or less than
, if the three results are extremely
, it is expressed.
For the critical range ORO in the temporary ticket
, start from two nests
Saevay
a result
, that is, the absolute value of the difference between the
results is extremely
CR.C3
, then the final report is the final report result
, where xe, is the second smallest test result in the ranking. Both results are acceptable, and the final report value should be
, and
test results should be hired again.
The result μ is equal to 3
The average value of the results;
The median of the results.
This process can be shown in Figure 1
The final reporting result
The final reporting result
Figure 1 The final reporting method of the test results obtained under repeatability conditions (Case A) When additional testing is difficult, m (m>2) results can also be tested simultaneously. When the range of the m results is not greater than the critical range, the average value of the m results is used as the final result. When the range of the m results is greater than the critical range, the median of the m results is used as the final result.
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Starting from m results
The range of m results
≤CRas(m)
The median of all m results is the final reported result
The arithmetic mean
of all m results is the final reported result
GB/T16306—2008
Figure 2 Method for final reporting of test results obtained under repeatability conditions (Case B) The general expression of the critical range CRa.95 (3) is: CRa.gs(m)=f(m)o,=f(m)r/2.77 The value of f(m) in the above formula is shown in Table 1.
Explanation of the final results
When reporting the final results, the following should be stated:
a) the number of tests;
whether the average or median is taken,
the critical range coefficient (m)
4.2 Test method for acceptability of test results obtained under reproducibility conditions and determination of the final reported results f(m)
This method is applied to situations where two laboratories participate in the test and their test results or the average values of the results are different. In this case, the given reproducibility standard deviation should be used for statistical testing, just like repeatability. In all cases, it should be ensured that there are enough test sample products to obtain the test results, including the storage of a part of the spare sample products for use when retesting is necessary. The number of spare sample products depends on the test method and the test. Due to the complexity of the test, spare sample products should be properly preserved to prevent damage and deterioration.
4.2.1 Statistical test for consistency of test results of two laboratories 4.2.1.1 Test of one test result obtained by each laboratory When each laboratory obtains only one test result, the absolute value of the difference between the two results is tested using the reproducibility limit. If the absolute value of the difference is less than or equal to R, the two results are consistent, and their average is taken as the final reported result. If the absolute value of the difference between the two results is greater than R, efforts should be made to find out whether the cause of the difference is due to a malfunction in the test equipment, low precision of the test method, and/or differences in the test sample products: After negating the above reasons, each laboratory should conduct the test under repeatability conditions in accordance with the provisions of 4.1.
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GB/T16306—2008
4.2.1.2 Inspection of more than one test result obtained by each laboratory 4.2.1.2.1 Assuming that each laboratory has obtained the final reported results according to the prescribed steps in 4.1, it is sufficient to consider the acceptability of the two final results. Use the absolute value of the difference between the two results and the critical difference CD. Compare to check whether the results of the two laboratories are consistent. The inspection method is as follows:
Both results are average values (the number of repetitions is mim respectively), and the critical difference CDu.gs is expressed as a)
b) One of the two results is the average value and the other is the median (the number of repetitions is mi, mz respectively), and the critical difference CD. 95 is expressed as:
( C(mz))
C(m) is the ratio of the median standard deviation to the mean standard deviation, and its value is shown in Table 2. When both results are medians (the number of repetitions is m and mz respectively), the critical difference CDo.5 is expressed as: CDo.95
The value of C(m,))(i=1,2...) in the formula is shown in Table 2. Number of test nests m
(C(m)(Cmz))2
Table 2 C(m) value
Number of test results m
-（2）
（3）
4.2.1.2.2If the absolute value of the difference is less than the critical difference, the final results reported by the two laboratories are acceptable, and the weighted average of the two results i=（m+mzz）/（m+m2） is taken as the final reported result. If the absolute value of the difference between the two results is greater than the critical difference, the steps specified in 4.2.2 shall be adopted.
4.2.2 Solutions to the inconsistency of the results reported by the two laboratories The reasons for the inconsistency of the results reported by the two laboratories may come from systematic errors, inconsistent sample products or errors in the determination and (or) o, process (see GB/T6379.2 and ISO5725-3). Each laboratory should use another sample product for testing to determine whether the systematic error exists and the degree of deviation. If possible, calibrated reference materials should be used. If this is not possible, standard samples (preferably with known values) should be tested. Its advantage is that the systematic error of a laboratory or two laboratories can be found. If the systematic error cannot be found by this method, the two laboratories should refer to the results of a third laboratory to reach an agreement. When the difference comes from inconsistent sample products, the two laboratories should jointly make samples or entrust a third party to make samples. 4.3 Test methods for the acceptability of test results obtained under intermediate precision conditions and determination of the final reported results If there is doubt about the accuracy of the first test result, obtain a second or more test results under intermediate precision conditions. The determination of the final reported results can be obtained in the same way as 4.1, only the repeatability standard deviation needs to be replaced by the intermediate precision standard deviation. 6
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4.4 Application Examples
GB/T16306—2008
Example 1: Determine the phosphorus content in steel by the antimony phosphorus molybdenum blue photometric method in GB/T223.3. The data of the sample product measured for the first time in a certain laboratory was 0.0170, and there was an objection to this test result. After verification, no error in the test conditions was found. With the consent of the responsible department, the second test result of the same sample product under repeatability conditions was 0.0178. Since (0.0170+0.0178)/2=0.0174, the repeatability limit r=0.0017 when the theoretical phosphorus content is 0.0174 is found from the relevant standards. Find the final reported result under repeatability conditions. Solution: Range X,-X2|=10.0170-0.0178/=0.0008 because |X, -XTo rank the second smallest test result, both results are acceptable, and the final reported value should be hired again
test results.
The result μ is equal to the average value of 3
results;
The median of the results.
This process can be shown in Figure 1
is the final reported result
is the final reported result
Figure 1 The method of reporting the final result of the test results obtained under repeatability conditions (Case A) When additional testing is difficult, m (m>2) results can also be tested simultaneously. When the range of the m results is not greater than the critical range, the average value of the m results is used as the final result. When the range of the m results is greater than the critical range, the median of the m results is used as the final result.
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Starting from m results
The range of m results
≤CRas(m)
The median of all m results is the final reported result
The arithmetic mean
of all m results is the final reported result
GB/T16306—2008
Figure 2 Method for final reporting of test results obtained under repeatability conditions (Case B) The general expression of the critical range CRa.95 (3) is: CRa.gs(m)=f(m)o,=f(m)r/2.77 The value of f(m) in the above formula is shown in Table 1.
Explanation of the final results
When reporting the final results, the following should be stated:
a) the number of tests;
whether the average or median is taken,
the critical range coefficient (m)
4.2 Test method for acceptability of test results obtained under reproducibility conditions and determination of the final reported results f(m)
This method is applied to situations where two laboratories participate in the test and their test results or the average values of the results are different. In this case, the given reproducibility standard deviation should be used for statistical testing, just like repeatability. In all cases, it should be ensured that there are enough test sample products to obtain the test results, including the storage of a part of the spare sample products for use when retesting is necessary. The number of spare sample products depends on the test method and the test. Due to the complexity of the test, spare sample products should be properly preserved to prevent damage and deterioration.
4.2.1 Statistical test for consistency of test results of two laboratories 4.2.1.1 Test of one test result obtained by each laboratory When each laboratory obtains only one test result, the absolute value of the difference between the two results is tested using the reproducibility limit. If the absolute value of the difference is less than or equal to R, the two results are consistent, and their average is taken as the final reported result. If the absolute value of the difference between the two results is greater than R, efforts should be made to find out whether the cause of the difference is due to a malfunction in the test equipment, low precision of the test method, and/or differences in the test sample products: After negating the above reasons, each laboratory should conduct the test under repeatability conditions in accordance with the provisions of 4.1.
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GB/T16306—2008
4.2.1.2 Inspection of more than one test result obtained by each laboratory 4.2.1.2.1 Assuming that each laboratory has obtained the final reported results according to the prescribed steps in 4.1, it is sufficient to consider the acceptability of the two final results. Use the absolute value of the difference between the two results and the critical difference CD. Compare to check whether the results of the two laboratories are consistent. The inspection method is as follows:
Both results are average values (the number of repetitions is mim respectively), and the critical difference CDu.gs is expressed as a)
b) One of the two results is the average value and the other is the median (the number of repetitions is mi, mz respectively), and the critical difference CD. 95 is expressed as:
( C(mz))
C(m) is the ratio of the median standard deviation to the mean standard deviation, and its value is shown in Table 2. When both results are medians (the number of repetitions is m and mz respectively), the critical difference CDo.5 is expressed as: CDo.95
The value of C(m,))(i=1,2...) in the formula is shown in Table 2. Number of test nests m
(C(m)(Cmz))2
Table 2 C(m) value
Number of test results m
-（2）
（3）
4.2.1.2.2If the absolute value of the difference is less than the critical difference, the final results reported by the two laboratories are acceptable, and the weighted average of the two results i=（m+mzz）/（m+m2） is taken as the final reported result. If the absolute value of the difference between the two results is greater than the critical difference, the steps specified in 4.2.2 shall be adopted.
4.2.2 Solutions to the inconsistency of the results reported by the two laboratories The reasons for the inconsistency of the results reported by the two laboratories may come from systematic errors, inconsistent sample products or errors in the determination and (or) o, process (see GB/T6379.2 and ISO5725-3). Each laboratory should use another sample product for testing to determine whether the systematic error exists and the degree of deviation. If possible, calibrated reference materials should be used. If this is not possible, standard samples (preferably with known values) should be tested. Its advantage is that the systematic error of a laboratory or two laboratories can be found. If the systematic error cannot be found by this method, the two laboratories should refer to the results of a third laboratory to reach an agreement. When the difference comes from inconsistent sample products, the two laboratories should jointly make samples or entrust a third party to make samples. 4.3 Test methods for the acceptability of test results obtained under intermediate precision conditions and determination of the final reported results If there is doubt about the accuracy of the first test result, obtain a second or more test results under intermediate precision conditions. The determination of the final reported results can be obtained in the same way as 4.1, only the repeatability standard deviation needs to be replaced by the intermediate precision standard deviation. 6
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4.4 Application Examples
GB/T16306—2008
Example 1: Determine the phosphorus content in steel by the antimony phosphorus molybdenum blue photometric method in GB/T223.3. The data of the sample product measured for the first time in a certain laboratory was 0.0170, and there was an objection to this test result. After verification, no error in the test conditions was found. With the consent of the responsible department, the second test result of the same sample product under repeatability conditions was 0.0178. Since (0.0170+0.0178)/2=0.0174, the repeatability limit r=0.0017 when the theoretical phosphorus content is 0.0174 is found from the relevant standards. Find the final reported result under repeatability conditions. Solution: Range X,-X2|=10.0170-0.0178/=0.0008 because |X, -XTo rank the second smallest test result, both results are acceptable, and the final reported value should be hired again
test results.
The result μ is equal to the average value of 3
results;
The median of the results.
This process can be shown in Figure 1
is the final reported result
is the final reported result
Figure 1 The method of reporting the final result of the test results obtained under repeatability conditions (Case A) When additional testing is difficult, m (m>2) results can also be tested simultaneously. When the range of the m results is not greater than the critical range, the average value of the m results is used as the final result. When the range of the m results is greater than the critical range, the median of the m results is used as the final result.
Standard download site
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Starting from m results
The range of m results
≤CRas(m)
The median of all m results is the final reported result
The arithmetic mean
of all m results is the final reported result
GB/T16306—2008
Figure 2 Method for final reporting of test results obtained under repeatability conditions (Case B) The general expression of the critical range CRa.95 (3) is: CRa.gs(m)=f(m)o,=f(m)r/2.77 The value of f(m) in the above formula is shown in Table 1.
Explanation of the final results
When reporting the final results, the following should be stated:
a) the number of tests;
whether the average or median is taken,
the critical range coefficient (m)
4.2 Test method for acceptability of test results obtained under reproducibility conditions and determination of the final reported results f(m)
This method is applied to situations where two laboratories participate in the test and their test results or the average values of the results are different. In this case, the given reproducibility standard deviation should be used for statistical testing, just like repeatability. In all cases, it should be ensured that there are enough test sample products to obtain the test results, including the storage of a part of the spare sample products for use when retesting is necessary. The number of spare sample products depends on the test method and the test. Due to the complexity of the test, spare sample products should be properly preserved to prevent damage and deterioration.
4.2.1 Statistical test for consistency of test results of two laboratories 4.2.1.1 Test of one test result obtained by each laboratory When each laboratory obtains only one test result, the absolute value of the difference between the two results is tested using the reproducibility limit. If the absolute value of the difference is less than or equal to R, the two results are consistent, and their average is taken as the final reported result. If the absolute value of the difference between the two results is greater than R, efforts should be made to find out whether the cause of the difference is due to a malfunction in the test equipment, low precision of the test method, and/or differences in the test sample products: After negating the above reasons, each laboratory should conduct the test under repeatability conditions in accordance with the provisions of 4.1.
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GB/T16306—2008
4.2.1.2 Inspection of more than one test result obtained by each laboratory 4.2.1.2.1 Assuming that each laboratory has obtained the final reported results according to the prescribed steps in 4.1, it is sufficient to consider the acceptability of the two final results. Use the absolute value of the difference between the two results and the critical difference CD. Compare to check whether the results of the two laboratories are consistent. The inspection method is as follows:
Both results are average values (the number of repetitions is mim respectively), and the critical difference CDu.gs is expressed as a)
b) One of the two results is the average value and the other is the median (the number of repetitions is mi, mz respectively), and the critical difference CD. 95 is expressed as:
( C(mz))
C(m) is the ratio of the median standard deviation to the mean standard deviation, and its value is shown in Table 2. When both results are medians (the number of repetitions is m and mz respectively), the critical difference CDo.5 is expressed as: CDo.95
The value of C(m,))(i=1,2...) in the formula is shown in Table 2. Number of test nests m
(C(m)(Cmz))2
Table 2 C(m) value
Number of test results m
-（2）
（3）
4.2.1.2.2If the absolute value of the difference is less than the critical difference, the final results reported by the two laboratories are acceptable, and the weighted average of the two results i=（m+mzz）/（m+m2） is taken as the final reported result. If the absolute value of the difference between the two results is greater than the critical difference, the steps specified in 4.2.2 shall be adopted.
4.2.2 Solutions to the inconsistency of the results reported by the two laboratories The reasons for the inconsistency of the results reported by the two laboratories may come from systematic errors, inconsistent sample products or errors in the determination and (or) o, process (see GB/T6379.2 and ISO5725-3). Each laboratory should use another sample product for testing to determine whether the systematic error exists and the degree of deviation. If possible, calibrated reference materials should be used. If this is not possible, standard samples (preferably with known values) should be tested. Its advantage is that the systematic error of a laboratory or two laboratories can be found. If the systematic error cannot be found by this method, the two laboratories should refer to the results of a third laboratory to reach an agreement. When the difference comes from inconsistent sample products, the two laboratories should jointly make samples or entrust a third party to make samples. 4.3 Test methods for the acceptability of test results obtained under intermediate precision conditions and determination of the final reported results If there is doubt about the accuracy of the first test result, obtain a second or more test results under intermediate precision conditions. The determination of the final reported results can be obtained in the same way as 4.1, only the repeatability standard deviation needs to be replaced by the intermediate precision standard deviation. 6
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4.4 Application Examples
GB/T16306—2008
Example 1: Determine the phosphorus content in steel by the antimony phosphorus molybdenum blue photometric method in GB/T223.3. The data of the sample product measured for the first time in a certain laboratory was 0.0170, and there was an objection to this test result. After verification, no error in the test conditions was found. With the consent of the responsible department, the second test result of the same sample product under repeatability conditions was 0.0178. Since (0.0170+0.0178)/2=0.0174, the repeatability limit r=0.0017 when the theoretical phosphorus content is 0.0174 is found from the relevant standards. Find the final reported result under repeatability conditions. Solution: Range X,-X2|=10.0170-0.0178/=0.0008 because |X, -X1. Test of two laboratories each obtaining one test result When each laboratory obtains only one test result, the absolute value of the difference between the two results is tested using the reproducibility limit. If the absolute value of the difference is less than or equal to R, the two results are consistent, and the average value is taken as the final reported result. If the absolute value of the difference between the two results is greater than R, efforts should be made to find out whether the cause of the difference is due to a malfunction of the test equipment, low precision of the test method, and/or differences in the test sample products: After the above reasons are denied, each laboratory should conduct the test under repeatability conditions as specified in 4.1.
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4.2.1.2 Test of each laboratory obtaining more than one test result 4.2.1.2.1 Assuming that each laboratory has obtained the final reported result according to the steps specified in 4.1, it is sufficient to consider the acceptability of the two final results. Use the absolute value of the difference between the two results and the critical difference CD. Compare to test whether the results of the two laboratories are consistent. The test method is as follows:
When both results are mean values (repetition times are mim), the critical difference CDu.gs is expressed as a)
b) When one of the two results is mean value and the other is median value (repetition times are mi, mz), the critical difference CD.95 is expressed as:
(C(mz))
C(m) is the ratio of the median standard deviation to the mean standard deviation, and its value is shown in Table 2. When both results are medians (repetition times are m, mz), the critical difference CDo.5 is expressed as: CDo.95
In the formula, the value of C(m,) (i=1,2...) is shown in Table 2. Test nesting times m
(C(m)(Cmz))2
Table 2 C(m) value
Test results times m
-(2)
(3)
4.2.1.2.2 If the absolute value of the difference is less than the critical difference, the final results reported by the two laboratories are acceptable, and the weighted average of the two results i=(m+mzz)/(m+m2) is taken as the final reported result. If the absolute value of the difference between the two results is greater than the critical difference, the steps specified in 4.2.2 shall be adopted.
4.2.2 Solutions to inconsistent results reported by the two laboratories The reasons for the inconsistent results reported by the two laboratories may be due to systematic errors, inconsistent sample products or errors in the determination and (or) o, process (see GB/T6379.2 and ISO5725-3). Each laboratory shall use another sample product for testing to determine the existence of systematic errors and the degree of deviation. Where possible, calibrated reference materials should be used. If this is not possible, standard samples (preferably with known values) should be tested. The advantage is that the systematic error of one or both laboratories can be found. If this method cannot find the systematic error, the two laboratories should reach an agreement with reference to the results of a third laboratory. When the difference comes from the inconsistency of the sample products, the two laboratories should jointly make the samples or entrust a third party to make the samples. 4.3 Test methods for the acceptability of test results obtained under intermediate precision conditions and determination of the final reported results If there is any doubt about the accuracy of the first test result, obtain a second or more test results under intermediate precision conditions. The determination of the final reported results can be obtained in the same way as in 4.1, only the intermediate precision standard deviation needs to be used instead of the repeatability standard deviation. 6
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4.4 Application Examples
GB/T16306—2008
Example 1: Determination of phosphorus content in steel by the antimony phospho-molybdenum blue photometric method in GB/T223.3. The first test result of a sample product in a laboratory was 0.0170. There was an objection to the test result. After verification, no error was found in the test conditions. With the consent of the responsible department, the second test result of the same sample product under repeatability conditions was 0.0178. Since (0.0170+0.0178)/2=0.0174, the repeatability limit r=0.0017 when the theoretical phosphorus content is 0.0174 is found from the relevant standards. Find the final reported result under repeatability conditions. Solution: Range X,-X2|=10.0170-0.0178/=0.0008 Because |X, one X1. Test of two laboratories each obtaining one test result When each laboratory obtains only one test result, the absolute value of the difference between the two results is tested using the reproducibility limit. If the absolute value of the difference is less than or equal to R, the two results are consistent, and the average value is taken as the final reported result. If the absolute value of the difference between the two results is greater than R, efforts should be made to find out whether the cause of the difference is due to a malfunction of the test equipment, low precision of the test method, and/or differences in the test sample products: After the above reasons are denied, each laboratory should conduct the test under repeatability conditions as specified in 4.1.
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GB/T16306—2008
4.2.1.2 Test of each laboratory obtaining more than one test result 4.2.1.2.1 Assuming that each laboratory has obtained the final reported result according to the steps specified in 4.1, it is sufficient to consider the acceptability of the two final results. Use the absolute value of the difference between the two results and the critical difference CD. Compare to test whether the results of the two laboratories are consistent. The test method is as follows:
When both results are mean values (repetition times are mim), the critical difference CDu.gs is expressed as a)
b) When one of the two results is mean value and the other is median value (repetition times are mi, mz), the critical difference CD.95 is expressed as:
(C(mz))
C(m) is the ratio of the median standard deviation to the mean standard deviation, and its value is shown in Table 2. When both results are medians (repetition times are m, mz), the critical difference CDo.5 is expressed as: CDo.95
In the formula, the value of C(m,) (i=1,2...) is shown in Table 2. Test nesting times m
(C(m)(Cmz))2
Table 2 C(m) value
Test results times m
-(2)
(3)
4.2.1.2.2 If the absolute value of the difference is less than the critical difference, the final results reported by the two laboratories are acceptable, and the weighted average of the two results i=(m+mzz)/(m+m2) is taken as the final reported result. If the absolute value of the difference between the two results is greater than the critical difference, the steps specified in 4.2.2 shall be adopted.
4.2.2 Solutions to inconsistent results reported by the two laboratories The reasons for the inconsistent results reported by the two laboratories may be due to systematic errors, inconsistent sample products or errors in the determination and (or) o, process (see GB/T6379.2 and ISO5725-3). Each laboratory shall use another sample product for testing to determine the existence of systematic errors and the degree of deviation. Where possible, calibrated reference materials should be used. If this is not possible, standard samples (preferably with known values) should be tested. The advantage is that the systematic error of one or both laboratories can be found. If this method cannot find the systematic error, the two laboratories should reach an agreement with reference to the results of a third laboratory. When the difference comes from the inconsistency of the sample products, the two laboratories should jointly make the samples or entrust a third party to make the samples. 4.3 Test methods for the acceptability of test results obtained under intermediate precision conditions and determination of the final reported results If there is any doubt about the accuracy of the first test result, obtain a second or more test results under intermediate precision conditions. The determination of the final reported results can be obtained in the same way as in 4.1, only the intermediate precision standard deviation needs to be used instead of the repeatability standard deviation. 6
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4.4 Application Examples
GB/T16306—2008
Example 1: Determination of phosphorus content in steel by the antimony phospho-molybdenum blue photometric method in GB/T223.3. The first test result of a sample product in a laboratory was 0.0170. There was an objection to the test result. After verification, no error was found in the test conditions. With the consent of the responsible department, the second test result of the same sample product under repeatability conditions was 0.0178. Since (0.0170+0.0178)/2=0.0174, the repeatability limit r=0.0017 when the theoretical phosphorus content is 0.0174 is found from the relevant standards. Find the final reported result under repeatability conditions. Solution: Range X,-X2|=10.0170-0.0178/=0.0008 Because |X, one Xr, and it is necessary to test again, and the third data is 0.0164, so Xm=0.0179, Xmm=0.0161, /Xmx-Xmm/=0.0179-0.0161=0.0018. Since (0.0179+0.0161+0.0164)/3=0.0168. According to the relevant standards, when the theoretical phosphorus content is 0.0168, the repeatability standard deviation S,=0.00057, the critical range CR. .95(3)=F(3)S,=3.31×0.00057=0.0019. Since 1Xmx一Xmn|CRo.9s (3), so the final reported result is the median of these three data: μ = 0.0161. Example 4: If the data of the sample product measured for the first time in Example 1 is 0.0179, and there is an objection to this test result, after verification, it is found that the test conditions are not wrong. Because the time interval is very long and the first tester cannot conduct the second test, the responsible department agrees to conduct a second test on the same sample product under the intermediate precision conditions (the intermediate precision conditions here are changed in time and the tester). The result of the second test under the intermediate precision conditions is 0.0152. Since (0.0179 + 0.0152)/2 = 0.01655, the intermediate precision standard deviation when the theoretical phosphorus content is 0.01655 is si(To) = 0.00129 from the relevant standards. Find the final reported result under the intermediate precision conditions.
Solution: Range 1X-X2|=10.0179-0.0152|=0.0027 Because X, -X, <0.00129×2.8 (0.00129×2.8=0.0036), 1X, -Xz/<2.8sTo), so the final result is:
μ=（0.0179+0.0152)/2=0.01655, rounded to 0.0165Example 5: If the data of the sample product measured for the first time in Example 1 is 0.0179, and there is an objection to this test result, after verification, it is found that the test conditions are not incorrect. Due to the long time interval and the inability of the first tester to conduct the second test, the responsible department agrees to conduct a second test on the same sample product under intermediate precision conditions (the intermediate precision conditions here are that the time and the tester are changed). The result of the second test under the intermediate precision condition is 0.0136. Since (00179+0.0136)/2=0.01575, the intermediate precision standard deviation when the theoretical phosphorus content is 0.01575 is s(TO=0.00128 from the relevant standards. Find the final reported result under the intermediate precision condition.
Solution: Range/X, -Xz/=|0.0179-0.0136|=0.0043 Because | X, -X1>0.00128×2.8 (0.00128×2.8=0.0036), and it is necessary to test again in the second laboratory, and the third data is 0.0154, so Xmx=0.0179, Xmim-0.0136, 1Xmx-Xmm/=0.0179-0.0136=0.00437
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GB/T16306—2008
Since (0.0179+0.0136+0.0154)/3=0.01563, the intermediate precision standard deviation when the theoretical phosphorus content is 0.01563 is obtained from the relevant standards as SCTO)=0.00127, then the critical range CRa.%(3)=(3)5kTo)=3.31×0.00127=0.00420 Xmm/>CRe.ss（3）, so the final result is the median value of the three data: μ=0.0154
Example 6: Determine the phosphorus content in steel by the antimony phosphorus molybdenum blue photometric method in GB/T223.3: The first laboratory measured a result of 0.0580, and there was an objection to this result. After verification, no error in the test conditions was found. With the consent of the responsible department, the same object was tested again by the second laboratory, and the test result was 0.0532. Since (0.0580 + 0.0532)/2=0.0556, the reproducibility limit R=0.0035 when the theoretical phosphorus content is 0.0556 is found from the relevant standards. Since 0.0580-0.0532=0.0048, this value is greater than R, and the two laboratories were checked separately, and no error in the test conditions was found. With the consent of the responsible department, the two laboratories were retested separately. The result measured by the first laboratory is 00559,/X,-X2/=|0.0580-0.0559/=0.0021. Since (0.0580+0.0559)/2=0.05695, the repeatability limit r=0.0020 when the theoretical phosphorus content is 0.05695 is found from the relevant standards. At this time, the range is greater than the repeatability limit, so it is necessary to test more times, and the data is 0.0558. The calculated range |Xm-Xmm=0.0580-0.0558=0.0 022, since (0.0580+0.0559+0.0558)/3=0.05657, the repeatability standard deviation S=0.000694 when the theoretical phosphorus content is 0.05657 can be obtained from the relevant standards, and the critical range CRo.$5(3)=F(3)S,=3.31×0.000694=0.0023. At this time, the range is less than the critical range, so the average value is taken as (0.0580+0.0559+0.0558)/3=0.0566. The result measured by the second laboratory is 0.0565. Since 1X,-X21=10.0565-0.0532=0.0033, and (0.0532+0.0565)/2=0.05485, the repeatability limit when the theoretical phosphorus content is 0.05485 is obtained from the relevant standards = 0.0019. Since this range is greater than the repeatability limit, it is necessary to test it once more, and the data is 0.0538. Therefore, there is a range of 1Xmx-Xmm/=0.0565-0.0532=0.0033. Since (0.0532+0.0565+0.0538)/3=0.0545, the repeatability standard deviation S,=0.000692 and the critical range CR are obtained from the relevant standards when the theoretical phosphorus content is 0.0545. 95（3）=F(3)S,-3.31X0.000692=0.00229, the range is greater than the critical range, so the median is taken as 0.0538. Try to compare the difference between the results of the two laboratories and find the final reported results. Solution: The difference between the final results of the two laboratories -|=0.0566-0.0538=0.0028 Since (0.0566+0.0538)/2=0.0552, the reproducibility limit R=0.00345~0.0035 is obtained from the relevant standards when the theoretical phosphorus content is 0.0552; in the first laboratory, the theoretical phosphorus content is 0.0566 from the relevant standards. The repeatability limit is = 0.00197. In the second laboratory, the repeatability limit r = 0.00194 when the theoretical phosphorus content is 0.0545 is found from the relevant standards. The smaller one r = min (, rz) = 0.00194 is taken. The critical difference of reproducibility is:
Rr(1-2m)-
1_(C(m2））
-（.16018）
=/0.0035′0.001 94[1-2×3
Due to | one
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