Directives for the work of reference materials (3) General principles and statistic methods for certificatoin of reference materials
Some standard content:
National Standard of the People's Republic of China
Directives for the work of reference materials (3)
General principles and statistical methods for the determination of reference materials GB/T15000.3—94
This standard adopts the International Organization for Standardization Guide 351985 (E) "General principles and statistical methods for the determination of reference materials" Subject content and scope of application
This standard specifies the general principles and statistical methods for the determination of reference samples. This standard is applicable to the determination of standard samples with qualified uniformity of chemical composition, physicochemical properties and engineering properties. The determination of other characteristics can be adopted by reference.
2 Reference standards
GB/T4882 Statistical processing and interpretation of data Absoluteness test GB/T1883 Statistical processing and interpretation of data Judgment and processing of abnormal values in positive samples GI/T8170 Rules for numerical rounding
GB/T15000.2 Guidelines for standard sample work (2) Common terms and definitions of standard samples 3 General principles for value determination
3.7 General concepts
Value determination of standard samples is a procedure for determining one or more measured values of a material using a technically accurate method, and this procedure ultimately produces a standard sample certificate or document.
3.2 Value determination method
Value determination of standard samples is generally carried out by determination method. There are many ways to use determination method to determine value. The main ones are as follows: a. Determination in one laboratory using an authoritative determination method (or absolute determination method or definition method): b. Determination in one laboratory using two or more accurate and reliable methods: c. Determination in multiple laboratories using one or more accurate and reliable methods in collaboration. The above methods can be used alone or in combination. The specific method to be used should be selected by the standard sample development unit based on the type of standard sample, its final use requirements, the technical level of the participants in the collaborative experiment, and the accuracy of the measurement method used.
3.3 Standard value and its uncertainty
Errors are inevitable in any measurement. Therefore, the standard value of a performance is not the true value of the performance. It only represents the most recent estimate of the true value. The deviation of the standard value should not exceed the stated measurement uncertainty. The uncertainty of a standard value indicates the quality of the standard value. The uncertainty is usually composed of the following components, some of which are based on data, while others are not guaranteed by data: confidence limits on the error limits of the mean value determination based on data and statistical calculations, statistical tolerance limits for material inhomogeneities based on data and statistical calculations, deviations caused by variations between laboratories and (or) operators and between determination methods, and the resultant value (absolute value sum or square root of the sum of squares) of the estimated limits of known possible sources of systematic error based on experience and judgment (in other words, no data or insufficient data for statistical calculations). Uncertainty can be expressed in many different ways, depending on how the standard sample is prepared, the personnel responsible for the work, and the expected use rate of the standard sample, but no matter what expression method is used, the content it describes should be unambiguous, meaningful, and contain all the information suitable for the user.
3.4 Reference value
Sometimes, after the material is measured, some small standard sample performance values with standard value level may be obtained. However, this is still of reference value to the user and should be explained. If the reliability of the value is worse, it can be published as an information value, but it must be clearly explained. 4 Laboratory test determination
4.1 Determination by weighted reduction method
Authoritative determination method is a test method with a strict theoretical basis and high precision level. It determines the performance, either directly based on the basic measurement unit, or indirectly linked to the basic unit based on the accurate mathematical equation established through physical or chemical theory, with negligible systematic errors. The laboratory that uses authoritative method for determination should be an authoritative laboratory for the work or a recognized high-level laboratory. The use of authoritative method for determination generally requires two or more people with skilled operating skills and test experience to operate independently, and it is best to use different experimental equipment.
4.2 Confidence interval of mean value
4.2.1 Concept
When the inhomogeneity of the material is so small as to be negligible compared with the analytical error, for the fixed value performance of the standard sample, all its units are considered to have the same value, so the value of each unit is consistent with the average value of all units. Therefore, it is necessary to determine the uncertainty of the mean value. In this case, the measurement error is the main source of uncertainty, and the most commonly used method to express this uncertainty is the confidence interval of the mean value.
4.2.2 Statistical calculation
Assume that the data obtained by n independent measurements of the measured performance are: I,+I+++++-++I.
Then the confidence interval of the mean value of the performance has the following form: X± tec n
Where: —
(x, -x)
ta-1 represents the significance level α in the t distribution table and the degree of freedom -1! The value is called the confidence coefficient of the distribution. See Table A for the t value table. 4.2.3 Transformation of data
GB/T 15000.3-94
In some cases, in order to meet the assumption of normal distribution error, it is necessary to transform the data (for example, take the logarithm), then find the mean and standard deviation of the transformed distribution, and finally transform the above mean and standard deviation into the value of the original distribution to obtain the confidence interval. In addition, if the transformation still cannot meet the requirements of normal distribution, a strong or non-parametric statistical process can be used to obtain the validity confidence interval of the measured performance value.
4.3 Statistical tolerance interval
4.3.1 Concept
When the inhomogeneity of the material is not negligible compared with the analytical error, there is a slight change between units for the fixed value performance of the standard sample, but this variability does not affect the intended use of the material. In this case, the statistical tolerance interval can be used to describe the variation range of the material between units.
4.3.2 Statistical calculation
Assume I112, I2. are independent data obtained from n identical units, then the statistical tolerance interval has the following form x±xs
(X:-X)3
K is a parameter related to the number of samples n, the confidence probability P. and the allowable probability, and is called the bilateral tolerance factor of the normal distribution. The value of K is shown in Appendix B.
4.3.3 Transformation of numbers
When the data needs to be transformed to meet the assumption of normal distribution error, refer to Article 4.2.3. 5 Collaborative test determination by multiple laboratories
5.1 General concept
Multiple laboratories collaborate to determine the value of standard samples, that is, the participating laboratories constitute a population, a measurement system, and each laboratory is required to have the same test technology level in determining the performance value of the standard sample. The results provided have qualified accuracy, and naturally the differences between the independent results are statistically significant. When multiple laboratories are used to collaboratively determine the value, "the average value of each laboratory is generally used as an unbiased estimate of the performance, and the total average value of the experimental blanks is used as the best estimate of the performance. However, in the case of very irregular distribution, a stronger statistic can be used, such as the median, harmonic mean, etc.
In actual work, the number of laboratories that can participate in collaborative determination is limited. Therefore, in most cases, the random design model cannot be fully implemented.
5.2 General procedures
The general procedure for multiple laboratories to collaborate in the determination of standard samples is shown in Figure 1: Laboratory plan
Calculation of consistent value range
Uncertainty
Determination of value
Standard group product verification
And release
GB/T 15000.3-94
More concentrated experiment
Kron's improvement
Standard sample undetermined value
Figure 1 Collaborative value determination procedure for multiple laboratories
Each stage of the procedure has different judgment criteria, and only when they are met can the next stage be carried out. 5.3 Laboratory collaboration plan
The laboratory collaboration plan must have clear objectives, effective design and efficient organization. The plan should include time arrangements, the number of participating laboratories, the number of sample units, the number of repeated measurements for each unit, the measurement method and how to report the results. 5.3.1 Time arrangements
The organizer of the plan must specify the time for distributing samples and moving out the results. 5.3.2 Number of participating laboratories
The number of participating laboratories will vary with the complexity of the measurement process. The more complex the process, the greater the expected variation between laboratories. In order to obtain consistent values with a predetermined accuracy, the number of participating experiments needs to be increased. However, the more complex the process, the fewer laboratories are capable of completing the process.
In general, the number of participating laboratories is preferably 8-10. When conditions do not allow, it can be appropriately reduced. The number of laboratories can be supplemented according to the actual needs of each industry, but the number of independent measurement results reported by the measurement method shall not be less than 8 groups. 5.3.3 Number of samples and number of measurements
Each participating laboratory shall measure one sample. The number of independent measurements shall not be less than 4 times.5.3.4 Determination method
The performance determination shall preferably adopt the corresponding national standard and industry standard analysis method. If there is no corresponding national standard or industry standard analysis method, the corresponding method that has been confirmed to be reliable can be selected.5.3.5 Reporting results
When each participating laboratory reports the results, it shall report a single independent result instead of the average value of the results. The number of significant digits of the reported results shall also comply with the provisions of the plan. In addition, the determination method used shall be reported. If a non-standard method is used, it is best to report the key points of the method and references in more detail.5.4 Preliminary processing of results
The results provided by each participating laboratory shall be processed according to the following procedures:5.4.1 Summarizing results
For ease of processing and future reference, all data provided by each laboratory shall be summarized in a table classified by performance. The table shall include the experimental CB/T 15000.3—94
Laboratory name and determination method or their code, independent results, average value and other items. When a participating laboratory provides two or more groups of data according to different determination methods, each group should be treated independently, that is, the other group can be regarded as the result from another laboratory. For the convenience of subsequent data processing, the number of individual results reported by each method should be the same.
5.4.2 Before statistical estimation, it is necessary to technically review whether there are any results that do not meet the requirements. If there are any results that do not meet the requirements, the relevant laboratories should be notified to find out the reasons, conduct a re-examination, and re-report the results. If it is still an out-of-bounds value, it should be eliminated. After eliminating the out-of-bounds values, the number of remaining result groups must be consistent with the minimum number of laboratories required by the original plan. 5.4.3 Check the normality of the result distribution. If the result distribution is monotonous, it can be judged whether it obeys the normal distribution by visually observing the histogram, or by using the normality test method specified in (GH/I4882), or by previous experience with the relevant measurement attributes. In some cases, the results must be converted into a form that obeys the normal distribution, such as logarithmic, square root or exponential form. If the transformation still does not meet the normal distribution requirements, a strong or non-parametric statistical procedure can be used. If the results are relatively scattered and even distributed in a multi-peaked shape, carefully check the measurement methods, test equipment and operating procedures used by each laboratory, find out the reasons and make improvements, and re-measure. 5.4.4 Check and deal with statistical outliers. The deviation of a result is compared with the deviation of other results in the group, or the deviation of a group is compared with the deviation of other groups, whether in terms of precision or accuracy. If the accuracy exceeds the statistical fluctuation tolerance of the given frequency distribution, then this single result or this group of results should be suspected to be a statistical outlier. The judgment and treatment of statistical outliers shall be carried out in accordance with GB/T1883. 5.5 Statistical calculations
Let X, be the result reported by laboratory i
P is the number of data groups
n is the number of data reported in each group
Total average
Total average The standard deviation of the mean (X) is:
P(P-1)
The confidence interval of the total mean (x) is ±-a(P1)S where -a(P-1) is the 1-/2 quantile of the t distribution of the degree of freedom (P-1) 5.6 Representation of the result of fixed value
5.6.1 The standard value is rounded off according to GB/TB170. The standard deviation is rounded off according to the principle of only rounding up and not rounding down, and its digits are aligned with the standard value digits, generally retaining 1 to 2 significant figures, GB/T15000.3-94
5.6.2 The result of the determination is composed of the standard value and uncertainty, which can be expressed in one of the following ways. 5.6.2.1 Expressed by the standard value and confidence interval; 2 Expressed by the standard value and statistical tolerance interval: 5. 6. 2. 2
3 The average value of the test data of each laboratory and each test method is regarded as a single test value. The result of the determination is expressed by the standard value and the standard deviation of the single test value, and the number of test data groups involved in the determination is given. 1
Number of measurements
GB/T 15000.3—94
Appendix A
1Value table
Table Alt(u)Numerical value
Appendix B
K value table
Table B1K. Value
Pe= 0. 99
P,= 0. 95
Measurement number
P,= 0. 95
GB/T 15000.3—94
Continued Table B1
P,= 0. 99
Pe= 0. 99
P,=0, 90
Additional remarks:
This standard is proposed by the State Administration of Technical Supervision. GB/T15000.3—94
This standard is under the jurisdiction of the National Technical Committee for Standards. This standard was drafted by the Secretariat of the National Technical Committee for Standards. This standard is interpreted by the Secretariat of the National Technical Committee for Standards. The main drafter of this standard is Zhang Guangwei, member of the National Technical Committee for Standards.2. Before statistical estimation, it is necessary to technically review whether there are any results that do not meet the requirements. If there are any results that do not meet the requirements, the relevant laboratories should be notified to find out the reasons, conduct re-examination, and re-report the results. If it is still an outlier, it should be eliminated. After eliminating the outliers, the number of remaining result groups must be consistent with the minimum number of laboratories required by the original plan. 5.4.3 Check the normality of the result distribution. If the result distribution is monotonous, it can be judged whether it obeys the normal distribution by visually observing the histogram, or by using the normality test method specified in (GH/I4882), or by previous experience with the relevant measurement attributes. In some cases, the results must be converted into a form that obeys the normal distribution, such as logarithmic, square root or exponential form. If the transformation still does not meet the normal distribution requirements, a strong or non-parametric statistical procedure can be used. If the results are relatively scattered and even distributed in a multi-peaked shape, carefully check the measurement methods, test equipment and operating procedures used by each laboratory, find out the reasons and make improvements, and re-measure. 5.4.4 Check and deal with statistical outliers. The deviation of a result is compared with the deviation of other results in the group, or the deviation of a group is compared with the deviation of other groups, whether in terms of precision or accuracy. If the accuracy exceeds the statistical fluctuation tolerance of the given frequency distribution, then this single result or this group of results should be suspected to be a statistical outlier. The judgment and treatment of statistical outliers shall be carried out in accordance with GB/T1883. 5.5 Statistical calculations
Let X, be the result reported by laboratory i
P is the number of data groups
n is the number of data reported in each group
Total average
Total average The standard deviation of the mean (X) is:
P(P-1)
The confidence interval of the total mean (x) is ±-a(P1)S where -a(P-1) is the 1-/2 quantile of the t distribution of the degree of freedom (P-1) 5.6 Representation of the result of fixed value
5.6.1 The standard value is rounded off according to GB/TB170. The standard deviation is rounded off according to the principle of only rounding up and not rounding down, and its digits are aligned with the standard value digits, generally retaining 1 to 2 significant figures, GB/T15000.3-94
5.6.2 The result of the determination is composed of the standard value and uncertainty, which can be expressed in one of the following ways. 5.6.2.1 Expressed by the standard value and confidence interval; 2 Expressed by the standard value and statistical tolerance interval: 5. 6. 2. 2
3 The average value of the test data of each laboratory and each test method is regarded as a single test value. The result of the determination is expressed by the standard value and the standard deviation of the single test value, and the number of test data groups involved in the determination is given. 1wwW.bzxz.Net
Number of measurements
GB/T 15000.3—94
Appendix A
1Value table
Table Alt(u)Numerical value
Appendix B
K value table
Table B1K. Value
Pe= 0. 99
P,= 0. 95
Measurement number
P,= 0. 95
GB/T 15000.3—94
Continued Table B1
P,= 0. 99
Pe= 0. 99
P,=0, 90
Additional remarks:
This standard is proposed by the State Administration of Technical Supervision. GB/T15000.3—94
This standard is under the jurisdiction of the National Technical Committee for Standards. This standard was drafted by the Secretariat of the National Technical Committee for Standards. This standard is interpreted by the Secretariat of the National Technical Committee for Standards. The main drafter of this standard is Zhang Guangwei, member of the National Technical Committee for Standards.2. Before statistical estimation, it is necessary to technically review whether there are any results that do not meet the requirements. If there are any results that do not meet the requirements, the relevant laboratories should be notified to find out the reasons, conduct re-examination, and re-report the results. If it is still an outlier, it should be eliminated. After eliminating the outliers, the number of remaining result groups must be consistent with the minimum number of laboratories required by the original plan. 5.4.3 Check the normality of the result distribution. If the result distribution is monotonous, it can be judged whether it obeys the normal distribution by visually observing the histogram, or by using the normality test method specified in (GH/I4882), or by previous experience with the relevant measurement attributes. In some cases, the results must be converted into a form that obeys the normal distribution, such as logarithmic, square root or exponential form. If the transformation still does not meet the normal distribution requirements, a strong or non-parametric statistical procedure can be used. If the results are relatively scattered and even distributed in a multi-peaked shape, carefully check the measurement methods, test equipment and operating procedures used by each laboratory, find out the reasons and make improvements, and re-measure. 5.4.4 Check and deal with statistical outliers. The deviation of a result is compared with the deviation of other results in the group, or the deviation of a group is compared with the deviation of other groups, whether in terms of precision or accuracy. If the accuracy exceeds the statistical fluctuation tolerance of the given frequency distribution, then this single result or this group of results should be suspected to be a statistical outlier. The judgment and treatment of statistical outliers shall be carried out in accordance with GB/T1883. 5.5 Statistical calculations
Let X, be the result reported by laboratory i
P is the number of data groups
n is the number of data reported in each group
Total average
Total average The standard deviation of the mean (X) is:
P(P-1)
The confidence interval of the total mean (x) is ±-a(P1)S where -a(P-1) is the 1-/2 quantile of the t distribution of the degree of freedom (P-1) 5.6 Representation of the result of fixed value
5.6.1 The standard value is rounded off according to GB/TB170. The standard deviation is rounded off according to the principle of only rounding up and not rounding down, and its digits are aligned with the standard value digits, generally retaining 1 to 2 significant figures, GB/T15000.3-94
5.6.2 The result of the determination is composed of the standard value and uncertainty, which can be expressed in one of the following ways. 5.6.2.1 Expressed by the standard value and confidence interval; 2 Expressed by the standard value and statistical tolerance interval: 5. 6. 2. 2
3 The average value of the test data of each laboratory and each test method is regarded as a single test value. The result of the determination is expressed by the standard value and the standard deviation of the single test value, and the number of test data groups involved in the determination is given. 1
Number of measurements
GB/T 15000.3—94
Appendix A
1Value table
Table Alt(u)Numerical value
Appendix B
K value table
Table B1K. Value
Pe= 0. 99
P,= 0. 95
Measurement number
P,= 0. 95
GB/T 15000.3—94
Continued Table B1
P,= 0. 99
Pe= 0. 99
P,=0, 90
Additional remarks:
This standard is proposed by the State Administration of Technical Supervision. GB/T15000.3—94
This standard is under the jurisdiction of the National Technical Committee for Standards. This standard was drafted by the Secretariat of the National Technical Committee for Standards. This standard is interpreted by the Secretariat of the National Technical Committee for Standards. The main drafter of this standard is Zhang Guangwei, member of the National Technical Committee for Standards.
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