Accuracy (trueness and precision) ofmeasurement methods and results?Part 2:Basic method for the determination of repeatability and reproducibility of a STANDARD measurement method
Some standard content:
ICS03.120.30
National Standard of the People's Republic of China
GB/T6379.2—2004/ISO5725-2:1994 Partially replaces GB/T6379—1986
GB/T11792-1989
Accuracy (trueness and precision) of measurement methods and results-Part 2.Basic method for the determination of repeatability andreproducibility of a standard measurement method (ISO5725-2:1994, IDT)
2004-06-02 Issued
Digital Film Drink
General Administration of Quality Supervision, Inspection and Quarantine of the People's Republic of China Standardization Administration of China
2005-01-01 Implementation
Normative references
Parameter estimation in basic model
5 Requirements for precision test
5.1 Test arrangement
5.2 Laboratory recruitment
Material preparation
Personnel involved in precision test
Leading group
Responsibilities of statistical experts
Executive responsibilities Responsibilities of the person in charge
Measurement manager
6.5 Operator
7 Statistical analysis of precision test
7.1 Preliminary considerations
Results tabulation and symbols used
Consistency of test results and outlier check
7.4 Calculation of overall mean and variance.
Order, order
7.5 Establishment of functional relationship between precision value and average level m7.6 Steps of statistical analysis procedure...
7.7 Report to the leadership team and decision made by the leadership team8 Statistical value tables·
Appendix A (Normative Appendix) Symbols and abbreviations used in GB/T 6379Appendix B (Informative Appendix) Precision test Examples of statistical analysis...GB/T6379.2—2004/ISO5725-2:199413
B.1 Example 1: Determination of sulfur content in coal (multi-level, excluding missing values and outlier data)B.2 Example 2: Softening point of asphalt (multi-level, including missing value data)B.3 Example 3: Thermal titration of creosote (multi-level, including outlier data)Appendix C (Informative Appendix)References
GB/T6379.2—2004/ISO5725-21994GB/T6379 "Accuracy (Trueness and Precision) of Measurement Methods and Results" is divided into six parts, and its expected structure and corresponding international standards are:
Part 1 Division: General principles and definitions (ISO5725-1: 1994, IDT) Part 2: Basic methods for determining the repeatability and reproducibility of standard measurement methods (ISO5725-2: 1994, IDT) Part 3: Intermediate measures of the precision of standard measurement methods (corresponding to ISO5725-3: 1994) Part 4: Basic methods for determining the correctness of standard measurement methods (corresponding to ISO5725-4: 1994) Part 5: Alternative methods for determining the correctness of standard measurement methods (corresponding to ISO5725-5: 1998) - Part 6: Practical application of accuracy values (corresponding to ISO5725-6: 1994) This part is Part 2 of GB/T 6379.
This part of GB/T6379 is equivalent to the international standard ISO5725-2:1994 "Accuracy (Trueness and Precision) of Measurement Methods and Results Part 2: Basic Methods for Determining Repeatability and Reproducibility of Standard Measurement Methods" and the technical amendment to the 1994 version of ISO5725-2 issued by ISO on May 15, 2002.
GB/T6379 Parts 1 to 6 replace GB/T6379-1986 and GB/T11792-1989 as a whole. The original precision is expanded in the standard, and the trueness is added; in addition to the repeatability and reproducibility conditions, the intermediate precision conditions are added. Appendices A and B of this part are normative appendices, and Appendix C is an informative appendix. This part is proposed by the China National Institute of Standardization. This part is under the jurisdiction of the National Technical Committee for Standardization of Statistical Methods and Applications. This part was drafted by: China National Institute of Standardization, Institute of Mathematics and Systems Science, Chinese Academy of Sciences, Liaoning Exit-Entry Inspection and Quarantine Bureau, Guangzhou Exit-Entry Inspection and Quarantine Bureau.
The main drafters of this part are: Yu Zhenfan, Feng Shiyong, Liu Wen, Jiang Jian, Ding Wenxing, Wang Douwen, Xiao Hui, Li Chengming. This part was first published in 2004.
GB/T6379.2—2004/IS05725-2:1994 Introduction
0.1GB/T6379 uses the two terms "trueness" and "precision" to describe the accuracy of a measurement method. Trueness refers to the degree of agreement between the (arithmetic) mean of a large number of test results and the true value or accepted reference value, while precision refers to the degree of agreement between test results. 0.2General considerations for the above quantities are given in GB/T6379.1 and are not repeated in this part of GB/T6379. GB/T 6379.1 should be read in conjunction with all other parts of GB/T 6379 (including this part) because GB/T 6379.1 gives basic definitions and general principles. 0.3 This part of GB/T 6379 only considers the estimation of the standard deviation of repeatability and the standard deviation of reproducibility. Although other types of tests (such as split-level tests) can also be used to estimate precision in some cases, this part of GB/T 6379 does not cover this aspect, which will be discussed in ISO 5725-5: This part of GB/T 6379 also does not consider any other intermediate measurement issues between the two main measurements of precision, which will be the subject of GB/T 6379.3. 0.4 In some cases, test data obtained for the purpose of estimating precision can also be used to estimate trueness. The estimation of trueness is also not considered in this part, and all contents related to the estimation of trueness will be the objective of GB/T 6379.4. IV
1 Scope
GB/T6379.2—2004/ISO5725-2:1994 Accuracy of measurement methods and results (trueness and precision)
Part 2: Basic methods for determining the repeatability and reproducibility of standard measurement methods
1.1 This part of GB/T6379
gives some general principles to be followed in the design of experiments to obtain numerical estimates of the precision of measurement methods through collaborative testing and inter-laboratory testing. It provides a detailed and practical description of the basic methods commonly used to estimate the precision of measurement methods. It provides guidance for all those concerned with the design, execution and analysis of experiments. NOTE 1 Certain modifications of the basic methods for specific purposes are given in other parts of GB/T6379. Annex B provides some practical examples of estimating the precision of measurement methods through experiments. 1.2 The measurement methods covered in this part of GB/T 6379 refer specifically to measurement methods that measure continuous quantities and take only one measurement value as the test result each time, although this value may be the result of a calculation of a set of observations. 1.3 It is assumed that all the principles given in GB/T 6379.1 have been followed in the design and execution of the precision test. The basic method is to use the same number of test results in each laboratory and to analyze the same level of the test sample in each laboratory, that is, to conduct a balanced uniform level test. The basic method is applicable to those procedures that are standardized and routinely used in many laboratories. Note 2: The standard appendix gives several practical examples to illustrate balanced and consistent test results. In one example, the number of replicates in the unit varies (unbalanced design); in another example, some data are missing. This is because a balanced design experiment may eventually become unbalanced. Drift and outliers are also considered.
1.4 The statistical model in Chapter 5 of GB/T6379.1-2004 is used as the basic model for interpreting and analyzing test results, and the test results are considered to be approximately normally distributed.
1.5 The basic method for estimating the precision of the test method in this part of GB/T6379 is used in the following situations: a) It is necessary to determine the precision of the test method in GB/T6379.1) when the repeatability and reproducibility standard deviations are defined; b) when the materials used are homogeneous, or the effects of inhomogeneity can be included in the precision value; when a balanced homogeneous design can be used. 1.6 The same method can also be used to make preliminary precision estimates for measurement methods that have not yet been standardized or are not routinely used. 2 Normative references
The clauses in the following documents become clauses of this part through reference in this part of GB/T 6379. For any dated referenced document, all subsequent amendments (excluding errata) or revised versions are not applicable to this part, however, parties to an agreement based on this part are encouraged to study whether the latest versions of these documents can be used. For any undated referenced document, the latest version applies to this part. ISO 3534-1:1993 Statistical vocabulary and symbols Part 1: Probability and general statistical terms GB/T 6379.1-2004 Accuracy (trueness and precision) of measurement methods and results Part 1: General principles and definitions 3 Definitions
The definitions given in ISO 3534-1 and GB/T 6379.1 are still applicable in this part of GB/T 6379. The symbols used in GB/T 6379 are given in Appendix A. 1
GB/T 6379.2—2004/ISO5725-2:1994 4 Parameter estimation in basic models
4.1 The procedures given in this part of GB/T 6379 are based on the statistical models in Chapter 5 of GB/T 6379.1--2004, which are described in detail in 1.2 of GB/T 6379.1-2004. In particular, these procedures are based on equations (2 to (6) in Chapter 5 of GB/T 6379.1-2004. The basic model is:
y=m+B+e
where, for a given test material:
m——total mean value (expected);
B——laboratory component of bias under repeatability conditions; e——random error generated by each measurement under repeatability conditions. 4.2 Equations (2) to (6) in Chapter 5 of GB/T 6379.1-2004 represent the overall standard deviation of the considered material. The true value of the standard deviation. In actual situations, the exact values of these standard deviations are unknown, and the estimated value of precision is obtained by sampling a small number of laboratories from the population of all laboratories. Within these laboratories, the estimate is obtained from a small sample of all possible test results. 4.3 In statistical practice, if the true value of the standard deviation is unknown, it is estimated and replaced by the sample. In this case, the symbol is replaced by , indicating the estimated value of . The following estimates can be obtained based on equations (2) to (6) of GB/T6379.1-2004: si: inter-laboratory variance Estimated value:
sw: Estimated value of intra-laboratory variance:
s: The arithmetic mean of s, and is the estimated value of repeatability variance; this arithmetic mean is calculated for all laboratories participating in the accuracy test after eliminating outliers. : Estimated value of reproducibility variance:
5 Requirements for precision test
5. Test arrangement
5.1.1 When the basic method is used for test arrangement, samples taken from batch Q of materials represent 9 different test levels and are divided into p laboratories. Each laboratory The laboratory obtains the same n repeated test results for each level under repetitive conditions. This test is called a balanced level test.
5.1.2 These measurements should be organized under the following rules: The preliminary inspection of any equipment should be carried out as specified in the standard method. a)
A set of n measurements at the same level should be carried out under repetitive conditions, that is, at short time intervals, by the same operator; 6)
No recalibration of the equipment is allowed during the measurement process unless it is part of the entire measurement process. c) It is very important that a set of n tests be carried out independently under repetitive conditions, just like n tests on n different materials. However, in fact, the operator will know that he is testing the same material. It should be emphasized in the instructions that the whole intention of the test is to examine how much the test results can vary in actual testing. Despite this reminder, in order to avoid the influence of previous test results on subsequent tests and thus affect the repeatability variance, it is possible to consider requiring n independent test samples at each level in all 9 levels, and mixing the numbers so that the operator does not know which level the test is performed. However, such a procedure may also cause another problem, that is, whether it can be guaranteed that the repeatability conditions apply to these repeated tests. The above conditions can only be guaranteed when all n measurements can be completed in a very short time.
It is not necessary to require that all 9 groups of n measurements be carried out strictly within a short period of time; measurements of different groups may not be carried out on the same day;
e) All q levels of measurement will be made by the same operator. In addition, the n measurements made at a given level will use the same equipment from beginning to end;
CB/T6379.2—2004/ISO5725-2:1994If an operator cannot complete all measurements during the measurement process for some reason, then another operator can continue the remaining f
measurements, as long as this personnel change does not occur on the same level and the same group of n measurements, but on two different groups in the q group. Any such personnel change must be reported together with the test results. A time limit should be given, and all measurements should be completed within this time interval. g) Limit this time to the date of receipt of the sample and the date the measurement is completed;
h) All test samples should be labeled with the test name and the sample number. 5.1.3 Explain the "operator" in 5.1.2 and the rest of this part of GB/T 6379. For some measurements, it may actually be carried out by a group of operators, each of whom performs a certain part of the measurement procedure. In this case, the group of operators will be collectively referred to as "operators", and any changes in the group will be regarded as different "operators". 5.1.4 In commercial practice, the rounding of test results may be very rough. However, in precision tests, the test results should have at least one more significant digit than specified in the standard method. If the method does not specify the number of significant digits, the rounding error should not exceed 1/2 of the estimated repeatability standard deviation. When the precision depends on the level m, different levels require different rounding degrees. 5.2 Laboratory solicitation
5.2.1 The general principles for soliciting laboratories for inter-laboratory collaborative testing are given in 6.3 of GB/T 6379.1-2004. When soliciting the required number of collaborative laboratories, the conditions of these laboratories should be clearly specified. Figure 1 shows an example of a laboratory survey solicitation.
5.2.2 A "laboratory" is considered to be a combination of operators, equipment and test sites in this part of GB/T 6379. A test site or a laboratory in the general sense can generate several "laboratories" as long as it can provide independent instruments and test sites for several operators.
5.3 Material preparation
5.3.1 The key points to be considered when selecting materials for precision testing are given in 6.1 of GB/T 6379.1-2004. 5.3.2 When deciding the amount of materials in the test site, it should be taken into account that accidental wine and weighing errors may occur when obtaining certain test results, thus requiring additional materials. The quantity of materials to be prepared should be sufficient for the test and allow for appropriate reserves. Questionnaire for inter-laboratory collaborative research
Name of measurement method (with copies of relevant materials)1. Our laboratory will participate in this standard measurement and method precision test is
No topic
2. As participants, we understand that;
(check the corresponding box)
a) All necessary instruments, chemicals and other conditions specified in the method must be prepared in our laboratory at the beginning of the project:
b) The time requirements specified, including the start date, the order of sub-test samples and the completion time of the project must be strictly followed:
c) The test must be carried out strictly in accordance with the method requirements:d) The samples must be handled according to the instructions e) The measurement must be completed by a qualified operator. We have carefully studied the test method and have also made a reasonable assessment of our capabilities and equipment. We believe that we have sufficient strength to participate in the collaborative test of this method. 3. Comments
(Signature)
(Company or laboratory)
Questionnaire for collaborative research between laboratories
GB/T6379.2—2004/ISO5725-2:19945.3.3 Consideration should be given to whether it is desirable for some laboratories to obtain some preliminary test results in order to become familiar with the measurement method before obtaining formal test results. If so, consideration should also be given to whether additional material (non-precision test samples) should be provided. 5.3.4 When a material must be homogenized, it should be homogenized in the most appropriate manner for that material. When the material to be tested is not homogenous, it is important to prepare the samples in the manner specified in the method, preferably using different batches of commercial material for each level. For unstable materials, special storage and handling instructions should be given. 5.3.5 If there is a risk that the material will deteriorate once the container is opened (e.g., by oxidation, loss of volatile or hygroscopic material), then n different containers should be used for each test laboratory for each level of sample. In the case of unstable materials, special storage and handling instructions should be given. Precautions should be taken to ensure that the samples are identical until the measurement is made. If the material to be measured consists of a mixture of powdered materials of different relative densities or of particles of different sizes, special attention should be paid to the possibility that separation may occur due to vibration (for example during transportation). When the test sample may react with air, the sample can be sealed in a glass bottle that is evacuated or filled with an inert gas. For perishable materials such as food or blood samples, it is necessary to send them to the participating laboratories in a frozen state and to explain the thawing procedure in detail. 6 Personnel involved in precision testing
Note 3: Different laboratories have different operating methods. Therefore, the content of this chapter is only a guide and can be modified appropriately in specific circumstances. 6.1 Leadership team
6.1.1 The leadership team should consist of experts who are familiar with the measurement method and its application. 6.1.2 The tasks of the leadership group are: a) plan and coordinate the test: b) determine the number of laboratories required, their level and the number of measurements required, as well as the number of significant figures required; b) designate one of the members to assume statistical responsibilities (see 6.2); e) designate one of the members as the executive person in charge (see 6.3); d) consider issuing operating instructions other than the standard measurement method to the measurement person in charge of each laboratory: decide whether to allow some operators to make a small number of informal measurements in order to regain experience in the measurement method after a long break (these measurement results should not be used as formal samples for collaborative testing); f) discuss the statistical analysis report after the test results analysis is completed; g) determine the final values of the standard deviation of the repeatability and the standard deviation of the reproducibility: i) quickly determine whether further measures need to be taken to improve the measurement method standards and for those laboratories whose test results are rejected as outliers.
6.2 Duties of the Statistical Expert
At least one member of the leadership team should have experience in statistical design and test analysis. His tasks are: a) Use professional knowledge to design the test;
b): Analyze the data;
c) Submit a report to the leadership team in accordance with the provisions of 7.7.1. 6.3 Duties of the Executive Person in Charge
6.3.1 Entrust the actual organization of the test to a laboratory. The leadership team appoints a member of the laboratory as the executive person in charge, who is fully responsible for this work.
6.3.2 The tasks of the executive director are:
Collect the necessary number of cooperating laboratories and appoint the measurement director of each laboratory, a)
Organize and supervise the preparation of test materials and samples and the distribution of samples; for each level, sufficient spare b)
materials should be reserved;
Draft operating instructions covering the key points a) to h) in 5.1.2, and distribute the instructions to the measurement directors of each laboratory as early as possible so that they can give their opinions on them and ensure that the selected operators can correctly perform the routine operations. 4
GB/T6379.2—2004/ISO5725-2:1994d) Design appropriate forms for operators to use for work records and for measurement supervisors to use for reporting test results; (The form may include the operator's name, the date of receipt and measurement of the sample, the equipment used and other relevant information, etc.): Deal with problems encountered by each laboratory in the measurement operation; e
Pay attention to the progress of the test so that the test is carried out according to the prescribed schedule: f)
g) Collect data tables and submit them to statistical experts. 6.4 Measurement responsible person
6.4.1 Each laboratory participating in the test should designate a member to be responsible for the organization of the actual measurement, work according to the instructions of the responsible person and report the test results.
The tasks of the measurement supervisor are:
Ensure that the selected operators can perform measurements correctly in daily operations; distribute samples to operators according to the instructions of the execution supervisor (if necessary, provide materials for familiarization with the test operations); supervise the execution of measurements (the measurement supervisor should not participate in measurement operations); e)
Ensure that the operator performs the prescribed number of measurements d)
Ensure that the measurement work is carried out according to the schedule; collect test results, requiring that the number of decimal places recorded in the results is consistent with the requirements, as well as any difficulties encountered during the test, abnormal phenomena and opinions reflected by the operators.
6.4.3 The person in charge of measurements in each laboratory shall prepare a comprehensive report including the following information: a) the original test results, recorded by the operator in legible handwriting on the form provided, and not transcribed or printed (except for results printed out by a computer or testing machine); b) the initial observations or readings (when the test results are calculated from these readings), recorded by the operator in legible handwriting on the form provided, and not transcribed or printed; c) any comments made by the operator regarding the standard of the measurement method; information on any irregularities or interferences that occurred during the measurements, including any changes of operator that may have occurred, indicating which operator made which measurements, and an explanation of the reasons for any missing data; e) the date the samples were received;
the date each sample was measured;
information on relevant equipment used; and
other relevant information.
6.5 Operators
6.5.1 In each laboratory, measurements should be made by a selected operator who is representative of the operators who would normally perform the measurement.
6.5.2 Since the purpose of the test is to determine the precision of the standard measurement method for all operators who use the standard measurement method, it is generally not appropriate to give operators the right to extend the measurement method standard. However, it should be pointed out to the operators that one of the purposes of the test is to discover the variation in test results in practice so that they will not discard or repeat inconsistent test results. 6.5.3 Although operators are not usually responsible for supplementing the standard measurement method, they should be encouraged to comment on the standard, especially whether the instructions in the standard are clear and not ambiguous. 6.5.4 The operator's task is to:
a) perform the measurement according to the standard measurement method; b) report any anomalies and difficulties encountered in the test; reporting an error is more important than adjusting the test results, because missing one or two test results will not ruin the entire test, but in most cases reflect the shortcomings of the measurement standard itself. To evaluate whether the instructions in the standard are appropriate; the operator should report any situation encountered that cannot be tested according to the test instructions at any time, because this also reflects the shortcomings of the standard itself. 5
GB/T6379.2-2004/ISO5725-2:19947 Statistical analysis of precision test
7.1 Preliminary considerations
7.1.1 The analysis of data is a statistical problem that should be solved by statistical experts. It includes the following three consecutive steps: a) Check the data to identify and deal with outliers or other irregular data, and test the suitability of the model, b) Calculate the initial values of precision and mean for each level; determine the final values of precision and mean, and when the analysis shows that there may be a relationship between precision and level m, establish the relationship between them.
7.1.2 For each level, first calculate the estimated values of the following quantities: Repeatability variance: s
Inter-laboratory variance: s
-Reproducibility variance: =+
Mean value m
7.1.3 Statistical analysis includes the systematic application of statistical tests for outliers. There are many methods in the literature that can be used for this part of GB/T 6379. Considering practical applications, these methods are selected and organized into several methods in 7.3. 7.2 Result tabulation and symbols used
7.2.1 Unit
The combination of one laboratory and one level is called a unit of precision testing. Ideally, a test involving q laboratories and q levels would be tabulated as pq units, each containing n replicates, from which the repeatability and reproducibility standard deviations are calculated. However, this ideal situation is not always achieved in practice due to the occurrence of redundant data, missing data and outliers.
7.2.2 Redundant data
Sometimes a laboratory may perform and report more test results than are formally specified. In this case, the person responsible for the measurement should report why this is the case? Which are the correct test results? If the answer is that all the test results are equally valid, then the original number of data should be randomly selected from these test results for analysis. 7.2.3 Missing data
Another situation is that some test results may be missing, for example, because of sample loss or operator error during measurement. The analytical procedure recommended in 7.1 is to simply ignore completely blank units and take partially blank units into account through the standard calculation procedure.
7.2.4 Outliers
Outliers are original test results or some values generated from them, which are very different and inconsistent from other test results or other values generated in the same way. Experience tells us that outliers cannot be completely avoided and must be treated similarly to missing data. 7.2.5 Outlier laboratories
When a laboratory has unexplained abnormal test results at several different levels, and the laboratory variance and (or) systematic error are too large at the test level, it can be regarded as an outlier laboratory. There is reason to discard part or all of the data of the outlier laboratory. This part of GB/T6379 does not provide statistical test procedures for how to judge suspected outlier laboratories. The statistical experts should make a preliminary decision on this, but all excluded laboratories should be reported to the leadership team for further action. 7.2.6 Incorrect data
Data with obvious errors should be verified and corrected or eliminated. 7.2.7 Balanced uniform level test results
The ideal situation is that there are q laboratories (numbered i = 1, 2, p) and q levels (numbered j = 1, 2, q), each level is repeated n times, and a total of pQn test results are obtained. This ideal situation is not always achieved due to missing data (7.2.3), outlier test results (7.2.4), outlier laboratories (7.2.5) or erroneous data (7.2.6). In these cases, the notation in 7.2.8 to 6
ISO5725-2:19947.2.10 and the procedure in 7.4 allow for the number of test results to be different. Figure 2 shows the recommended tabular format of raw data for statistical analysis, which are referred to as A table, B table and C table for convenience. Table A Recommended format for arranging raw data
Laboratory
Laboratory
7.2.8 Original test results
In Table A of Figure 2,
Table B Recommended format for arranging unit averages
Table C Recommended format for arranging dispersion within units
Figure 2 Recommended format for arranging analysis results
is the number of test results of the kth laboratory in the unit at the level; y is the kth test result of the unit (-1, 2*n)P, is the number of laboratories with at least one test result at the level (after eliminating all outliers and erroneous test results). 7.2.9 Unit averages (Table B of Figure 2)
Calculate the unit average from Table A as follows:
GB/T6379.2—2004/IS05725-2:1994 The unit average should have one more significant figure than the test result in Table A. 7.2.10 Unit dispersion (Table C in Figure 2) The unit dispersion is calculated from Table A (see 7.2.8) and Table B (see 7.2.9) according to the following formula: In general, the standard deviation within the unit is used, that is, the above formula is equivalent to
..·(3)
(4)
When using the above formula for calculation, care should be taken to retain enough significant digits during the calculation process. The number of digits required to be retained for each intermediate value should be twice that of the original data.
Note 4: If the unit section contains only two test results, the standard deviation within the unit is: 5g = ym-Yut1//2
Therefore, for simplicity, if all units contain only two test results, the absolute deviation can be used instead of the standard deviation. The standard deviation should have one more significant digit than the result in Table A. If n is less than 2, insert the symbol \- in Table C. 7.2.11 Corrected or Eliminated Data
Because some data may be corrected or eliminated according to the tests mentioned in 7.1.3, 7.3.3 and 7.3.4, the y, n and P used to finally determine the precision and mean may be different from the original test results in Tables A, B and C recorded in Figure 2. Therefore, when reporting the final values of precision and trueness, if there are corrected or eliminated data, it should be indicated. 7.3 Check for consistency and outliers of test results See Reference 3.
Based on the data obtained at multiple levels, the standard deviation of repeatability and reproducibility can be estimated. Since individual laboratories or data may be significantly inconsistent with other laboratories or other data, thus affecting the estimation, these values must be checked. To this end, the following two methods are introduced
a) Graphical method for checking consistency,
b) Checking Numerical methods for outliers.
7.3.1 Graphical method for testing agreement
This method requires two bases of measure called Mandel's h statistic and the statistic. In addition to describing the variation of measurement methods, these two statistics are also useful for laboratory assessment. 7.3.1.1 For each level in each laboratory, calculate the between-laboratory agreement statistic h by dividing the deviation of the unit mean (unit mean minus the overall mean for that level) by the standard deviation of the unit mean: ha
Where, see also 7.2.9 and 7.4.4. p:
each 5)
·(6)
Plot the values of h, in the order of the laboratories, with the different levels of each laboratory as a set of plot points (see B.7, called the h-plot). 7.3.1.2 For each laboratory i, calculate the within-laboratory agreement statistic k by first calculating the combined within-unit standard deviation for each level:5) or the existence of erroneous data (7.2.6), this ideal situation is not always obtained. In these cases, the notation in 7.2.8 to 6
GB/T6379.2—2004/1SO5725-2:19947.2.10 and the procedure in 7.4 allow the number of test results to be different. Figure 2 shows the recommended tabular format of raw data for statistical analysis, which are referred to as A table, B table and C table for convenience. Table A Recommended format for arranging raw data
Laboratory
Laboratory
7.2.8 Original test results
In Table A of Figure 2,
Table B Recommended format for arranging unit averages
Table C Recommended format for arranging dispersion within units
Figure 2 Recommended format for arranging analysis results
is the number of test results of the kth laboratory in the unit at the level; y is the kth test result of the unit (-1, 2*n)P, is the number of laboratories with at least one test result at the level (after eliminating all outliers and erroneous test results). 7.2.9 Unit averages (Table B of Figure 2)
Calculate the unit average from Table A as follows:
GB/T6379.2—2004/IS05725-2:1994 The unit average should have one more significant figure than the test result in Table A. 7.2.10 Unit dispersion (Table C in Figure 2) The unit dispersion is calculated from Table A (see 7.2.8) and Table B (see 7.2.9) according to the following formula: In general, the standard deviation within the unit is used, that is, the above formula is equivalent to
..·(3)
(4)
When using the above formula for calculation, care should be taken to retain enough significant digits during the calculation process. The number of digits required to be retained for each intermediate value should be twice that of the original data.
Note 4: If the unit section contains only two test results, the standard deviation within the unit is: 5g = ym-Yut1//2
Therefore, for simplicity, if all units contain only two test results, the absolute deviation can be used instead of the standard deviation. The standard deviation should have one more significant digit than the result in Table A. If n is less than 2, insert the symbol \- in Table C. 7.2.11 Corrected or Eliminated Data
Because some data may be corrected or eliminated according to the tests mentioned in 7.1.3, 7.3.3 and 7.3.4, the y, n and P used to finally determine the precision and mean may be different from the original test results in Tables A, B and C recorded in Figure 2. Therefore, when reporting the final values of precision and trueness, if there are corrected or eliminated data, it should be indicated. 7.3 Check for consistency and outliers of test results See Reference 3.
Based on the data obtained at multiple levels, the standard deviation of repeatability and reproducibility can be estimated. Since individual laboratories or data may be significantly inconsistent with other laboratories or other data, thus affecting the estimation, these values must be checked. To this end, the following two methods are introduced
a) Graphical method for checking consistency,
b) Checking Numerical methods for outliers.
7.3.1 Graphical method for testing agreement
This method requires two bases of measure called Mandel's h statistic and the statistic. In addition to describing the variation of measurement methods, these two statistics are also useful for laboratory assessment. 7.3.1.1 For each level in each laboratory, calculate the between-laboratory agreement statistic h by dividing the deviation of the unit mean (unit mean minus the overall mean for that level) by the standard deviation of the unit mean: ha
Where, see also 7.2.9 and 7.4.4. p:
each 5)
·(6)
Plot the values of h, in the order of the laboratories, with the different levels of each laboratory as a set of plot points (see B.7, called the h-plot). 7.3.1.2 For each laboratory i, calculate the within-laboratory agreement statistic k by first calculating the combined within-unit standard deviation for each level:5) or the existence of erroneous data (7.2.6), this ideal situation is not always obtained. In these cases, the notation in 7.2.8 to 6
GB/T6379.2—2004/1SO5725-2:19947.2.10 and the procedure in 7.4 allow the number of test results to be different. Figure 2 shows the recommended tabular format of raw data for statistical analysis, which are referred to as A table, B table and C table for convenience. Table A Recommended format for arranging raw data
Laboratory
Laboratory
7.2.8 Original test results
In Table A of Figure 2,
Table B Recommended format for arranging unit averages
Table C Recommended format for arranging dispersion within units
Figure 2 Recommended format for arranging analysis results
is the number of test results of the kth laboratory in the unit at the level; y is the kth test result of the unit (-1, 2*n)P, is the number of laboratories with at least one test result at the level (after eliminating all outliers and erroneous test results). 7.2.9 Unit averages (Table B of Figure 2)
Calculate the unit average from Table A as follows:
GB/T6379.2—2004/IS05725-2:1994 The unit average should have one more significant figure than the test result in Table A. 7.2.10 Unit dispersion (Table C in Figure 2) The unit dispersion is calculated from Table A (see 7.2.8) and Table B (see 7.2.9) according to the following formula: In general, the standard deviation within the unit is used, that is, the above formula is equivalent to
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When using the above formula for calculation, care should be taken to retain enough significant digits during the calculation process. The number of digits required to be retained for each intermediate value should be twice that of the original data.
Note 4: If the unit section contains only two test results, the standard deviation within the unit is: 5g = ym-Yut1//2
Therefore, for simplicity, if all units contain only two test results, the absolute deviation can be used instead of the standard deviation. The standard deviation should have one more significant digit than the result in Table A. If n is less than 2, insert the symbol \- in Table C. 7.2.11 Corrected or Eliminated Data
Because some data may be corrected or eliminated according to the tests mentioned in 7.1.3, 7.3.3 and 7.3.4, the y, n and P used to finally determine the precision and mean may be different from the original test results in Tables A, B and C recorded in Figure 2. Therefore, when reporting the final values of precision and trueness, if there are corrected or eliminated data, it should be indicated. 7.3 Check for consistency and outliers of test results See Reference 3.
Based on the data obtained at multiple levels, the standard deviation of repeatability and reproducibility can be estimated. Since individual laboratories or data may be significantly inconsistent with other laboratories or other data, thus affecting the estimation, these values must be checked. To this end, the following two methods are introduced
a) Graphical method for checking consistency,
b) Checking Numerical methods for outliers.
7.3.1 Graphical method for testing agreement
This method requires two bases of measure called Mandel's h statistic and the statistic. In addition to describing the variation of measurement methods, these two statistics are also useful for laboratory assessment. 7.3.1.1 For each level in each laboratory, calculate the between-laboratory agreement statistic h by dividing the deviation of the unit mean (unit mean minus the overall mean for that level) by the standard deviation of the unit mean: ha
Where, see also 7.2.9 and 7.4.4. p:bzxz.net
each 5)
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Plot the values of h, in the order of the laboratories, with the different levels of each laboratory as a set of plot points (see B.7, called the h-plot). 7.3.1.2 For each laboratory i, calculate the within-laboratory agreement statistic k by first calculating the combined within-unit standard deviation for each level:
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