Accuracy(trueness and precision) of measurement methods and results - Part 3：Intermediate measures of the precision of a standard measurement method
Some standard content:
National Standard of the People's Republic of China
GB/T6379.3—2012/ISO5725-3;1994 Accuracy (trueness and precision) of measurement methods and results-Part 3: Intermediate measures of the precision of a standard measurement method (ISO5725-3; 1994. IDT)
2012-11-05 Issued
General Administration of Quality Supervision, Inspection and Quarantine of the People's Republic of China Administration of Standardization of the People's Republic of China
2013-02-15 Implementation
1 Scope
2 Normative references
3 Terms and definitions
General requirements
Important factors
6 Statistical model
Basic model
6.2 Overall mean station
Component day
6.4 Component BB
Error term
7 Selection of measurement conditions
8 In-laboratory study and analysis of intermediate precision measures8.1 The simplest method
8.2 Optional methods
8.3 Influence of measurement conditions on the final reported results 9 Inter-laboratory studies and analysis of intermediate precision measures Basic assumptions
9.2 The simplest method
Set design experiment
Full set design experiment
9.5 Layered set design experiment
Configuration of elements in set design
9.7 Comparison of the design with the methods given in GB/T 6379.2 Comparison of full set design and staggered set design 9.8
Appendix A (Normative Appendix)
Special symbols and abbreviations used in GB/T 6379
Appendix B (Normative Appendix) Variance analysis of full set design experiment B.1 Three-factor full set design experiment
B.2 Four-factor full set design experiment
Appendix C (Normative Appendix) Variance analysis of double-layer variable design experiment C.1 Three-factor staggered nested design experiment
C.2 Four-factor staggered nested design experiment
C.3 Five-factor staggered nested design experiment
GB/T6379.3—2012/ISO5725-3:1994C.4 Six-factor staggered nested design experiment
Appendix D (Informative Appendix) Examples of statistical analysis of intermediate precision tests References
GB/T 6379.3-2012/ISO 5725-3:1994GB/T 379 Accuracy (accuracy and precision) of measurement methods and results is divided into the following parts, and its test structure and corresponding international standards are
- Part 1: General principles and definitions (ISO 5725-1:1994, IDT)- Part 2 Part: Basic method for repeatability and reproducibility of iodine standard measurement methods (ISO 5725-2: 1994, IDT) Part 3: Intermediate measure of precision of standard measurement methods (ISO5725-3: 1994 IDT) Part 4: Basic method for determining the accuracy of standard measurement methods (ISO.5725-4: 1994, IDT) - Part 5: Alternative methods for determining the precision of standard measurement methods (ISO5725-5.1998, IDT) Part 6: Practical application of accuracy values (ISO.5725-6: 1994 IDT) This part is Part 3 of GB/T 6379 Part 1, 1-20-09 planning drafting
This part is in accordance with GB
This part is equivalent to the international standard ISO5725-3: 1994 Accuracy (trueness and precision) of measurement methods and results Part 3: Intermediate measures of precision of standard measurement methods and the technical amendment to the 1994 version of ISO 5725-3 issued by [SO on October 15, 2001. The following changes and corrections are made to the errors of ISO 5725-3: 1994. The inaccurate description of the estimation of repeatability standard deviation, reproducibility standard deviation and intermediate precision standard deviation in 9.4 is modified according to the complete set of designed tests.
In Table D.5 of Appendix D, the value of s(, at the 6th level is corrected from 9.545×10 to 8. 020×10-1GB/T6379 Part 1 to Part 6 replace GB/T6379-1986 and GB/T11792-1989 as a whole. The standard expands the original precision concept and adds the concept of correctness, which is collectively referred to as accuracy; in addition to the repeatability and reproducibility conditions, the intermediate precision is added
This part is proposed and managed by the National Technical Committee for Standardization of Statistical Methods (SAC/TC21). Drafting units of this part: China National Institute of Standardization, Institute of Mathematics and Systems Science, Chinese Academy of Sciences, Shenzhen Huafu Testing Co., Ltd., Hainan Product Quality Supervision and Inspection Institute, Wuxi Product Quality Supervision and Inspection Institute, Guangzhou Exit-Entry Inspection and Quarantine Bureau. The main drafters of this part: Yu Zhenfan, Feng Shiyong, Ding Wenxing, Zhu Ping, Huang Yan, Chen Huaying, Wu Jianwei, Li Chengming. This part was first published in 2012
0.1GB/T6379 uses 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. 2 GB/T 6379. 1 gives general considerations for the above quantities and will not be repeated in this part. It must be emphasized that GB/T6379.1 should be read in conjunction with all other parts of GB/T6379 (including this part), because GB/T6379.1 provides basic definitions and general principles
0. 3 Many different factors (besides the differences between assumed identical samples) can cause the variation of the results of the measurement method, including:
a) operator +
b》the equipment used,
c calibration of the equipment +
d》environment (temperature, temperature, air pollution, etc.); e) batches of reagents
time interval between different measurements
measurements made by different operators and on different equipment are generally more variable than those made by the same operator using the same equipment in a short period of time. 0.4 The two conditions of precision, namely repeatability and reproducibility, are necessary and are useful in many practical situations to describe the variation of the measurement method. Under repeatability conditions, the factors a) to 1 listed in 0.3 remain unchanged and do not produce variation, while under reproducibility conditions, these conditions are all changing and can cause variation in the test results. Therefore, repeatability and reproducibility are two extreme cases of precision conditions, the former describing the minimum variation of the test results, while the latter describing the maximum variation of the test results. Intermediate conditions exist between these two extremes, i.e., the precision in the factors a) and D is usually expressed as the standard deviation
. They can be used in certain specific circumstances. 0.5 This standard mainly discusses the intermediate precision measures of a measurement method. Since the values of these measures are between the two extreme precision measures of the measurement method (repeatability standard deviation and reproducibility standard deviation), they are called intermediate precision. To illustrate the necessity of these intermediate precision measures, consider the current operation of a laboratory related to a production workshop. In this laboratory, three shifts are implemented. The measurements are performed by different operators on different equipment. Therefore, operators and equipment are some of the factors that can cause the variation of test results. They must be taken into account when evaluating the precision of the secondary measurement method. 0.6 The intermediate precision scale defined in this standard is first used in the following situations: in order to improve, standardize and control the measurement method within the laboratory, an intermediate precision estimate is required; in an inter-laboratory study of a specific section, an intermediate precision estimate is also required. However, due to the reasons stated in 1.3 and 9.1, these measures should be interpreted and applied with caution. 0.7 The four factors most likely to affect the precision of a quantitative method are: a) time: whether the time interval between consecutive measurements is long or short. b) calibration: whether the same equipment is recalibrated between consecutive sets of measurements. c) operator: whether consecutive measurements are made by the same operator. d) equipment: whether the same equipment (or the same batch of test samples) is used in the measurement. 0.8 Next, we introduce M factors with different intermediate precision conditions (M = 1, 2,3 or 4) to take into account the variation of measurement conditions (time, calibration, operator and equipment) within the laboratory M = 1: only one of the four factors is different;
b>M = 2: two of the four factors are different:) M-3, three of the four factors are different
d) M = 4, all four factors are different, GB/T6379.3-2012/IS05725-3:1994 Different intermediate precision conditions produce different intermediate precision standard deviations, denoted as w. The specific conditions corresponding to them are clearly marked in parentheses, for example, Siro represents the intermediate precision standard deviation for different operators at different times, 0.9 For measurements under intermediate precision conditions, one or more of the factors listed in 0.7 is different. Under repeatability conditions, those factors are assumed to be constants
The standard deviation of the test results obtained under repeatability conditions is generally smaller than the standard deviation of the test results obtained under intermediate precision conditions. Generally, in chemical analysis, the standard deviation under intermediate precision conditions will be 2~~3 times the standard deviation under repeatability conditions. When hot, it should not be greater than the reproducibility standard deviation.
In a collaborative experiment involving 35 laboratories to determine the copper content of ore, it was found that whether using electrolytic pycnometric method or Na.S,0 titration method, under the condition of intermediate precision with a different factor (different time but the same operator and equipment), the standard deviation obtained was 1.5 times greater than the standard deviation under the condition of repeatability. Scope
Accuracy (Trueness and Precision) of Measurement Methods and Results Part 3: Intermediate Measures of Precision of Standard Measurement Methods 1.1 This part specifies four intermediate measures of precision that arise from variations in laboratory observation conditions (time, calibration, operator and equipment). These intermediate measures can be generated in a defined laboratory experiment or through inter-laboratory experiments. In addition, this part of GB/T 6379:
8) discusses the meaning of the definition of intermediate measures of precision: b) provides guidance on the interpretation and application of estimates of intermediate measures of precision in practical work: ) does not provide any measure for estimating the error of intermediate measures of precision. It does not involve how to determine the trueness of the measurement method itself, but discusses the relationship between trueness and measurement conditions. 1.2 This part applies to measurement methods involving continuous quantities, and each measurement takes only one value as the measurement result, although this value may be the result of a calculation of a set of observations. 1.3 The essence of determining these intermediate measures of precision is to express quantitatively the ability of the measurement method to repeat the test results under specified conditions. The statistical methods described in this part of ISO 15001 are based on the premise that information from "similar" measurement conditions can be combined to obtain more accurate information about an intermediate precision measure. This premise is valid as long as the so-called "similar" is really similar. However, this premise is difficult to meet when estimating an intermediate precision measure through interlaboratory studies. For example, in order to make the information from different laboratories meaningful, it is necessary to make all participating laboratories "similar" by controlling for "time" effects or "operator" effects. Therefore, caution should be exercised in using the results of interlaboratory studies of intermediate precision. Intralaboratory studies also rely on the above premise, but in this case the premise is easier to meet because the analyst knows more about the actual effect of a factor and how to control it .... Intralaboratory studies also rely on the above premise, but in this case the premise is easier to meet. Intralaboratory studies also rely on the above premise, but in this case the premise is easier to meet 6379.6). This part does not claim to provide the only method for estimating intermediate precision measures in a particular laboratory. Note: This part is based on knowledge of experimental design, such as set design. Appendices B and C list relevant basic information. 2 Normative references The following documents are indispensable for the application of this document. For any dated reference, only the dated version applies to this document. For any undated reference, the latest version (including all amendments) applies to this document. GB/T3358.1-2009
(ISO 3534-1;2006,IDT)
GB/T6379-1-2004
(ISO5725-1:1994,IDT)
R/T6370
Part 1 Part: General statistical terms and terms used in probability Statistical vocabulary and symbols
Accuracy (trueness and precision) of measurement methods and results
Uncertainty (trueness and precision) of measurement methods and results Part 1: General principles and definitions
Part 2: Basic methods for determining the repeatability and reproducibility of standard measurement methods (ISO 5725-2, 1994, IDT) ISO 3534-1:1993 Statistical vocabulary and symbols Part 1: Probability and general statistical terms ISO Guide 33, 1989 Use of certified reference materials ISO Guide 35; 1989 General principles and statistical principles for the determination of reference materials 3 Terms and definitions
For the purposes of this document, the terms and definitions defined in GB/T 6379.1 and ISO 3534-1 and the following terms and definitions apply. The symbols used in GB/T 6379 are in Appendix A General requirements
To ensure consistency in the measurement methods, standardized cold methods should be used. All measurements that form part of a specific laboratory test or an inter-laboratory test should be carried out according to standard methods. 5 Important factors
5.1 The four factors of laboratory measurement conditions (time, calibration, operator and equipment) are considered to be the main causes of variation in measurement results (see Table 1).
Table 1 Four important factors and their states
State 1 (same)
Measurements performed at the same time
No calibration between measurements
Same operator
Same equipment not recalibrated
Measurement equipment in the laboratory
State 2 (different)
Measurements performed at different times
Calibration between measurements
Different operators
Different equipment
5.2 “Same time measurements” include those performed in the shortest possible time with the aim of minimizing changes in test conditions (e.g., where constant environmental conditions cannot be guaranteed)
“Different time measurements” " refers to measurements made over a longer period of time, which may be affected by changes in environmental conditions.
"Calibration" here does not refer to calibration as an integral part of the procedure for obtaining test results as specified by the measurement method, but refers to the calibration process performed at regular intervals between different groups of measurements within a laboratory. 5.4 For some types of operations, "operator" may in fact refer to a group of operators, each of whom performs a specified part of the measurement procedure. In this case, "operator" refers to this group of operators, and any changes in the personnel or assigned tasks in this group of operators should be regarded as different "operators".
5.5 Equipment \ in fact often refers to a complete set of equipment. Any change in any significant part of the complete set of equipment will be regarded as different "equipment". As to what is a significant part, it can be judged by common sense that a change of thermometer will be regarded as a different significant part, while replacing water with a slightly different container will be regarded as insignificant. The use of different batches of reagents should be considered a significant component change, which will be considered as the use of different "equipment"; if this change occurs after a calibration, it will be considered as a recalibration. 5.6 Under repeatability conditions, all four factors are in state 1 of Table 1. For the intermediate precision conditions, one or more factors are in state 2 in Table 1, which is called "precision conditions with ~M factors in different states", where M is the number of factors in state 2. Under the reproducibility condition, the measurement results are obtained by different laboratories, so not only are all four factors in state 2, but there will also be additional effects due to differences in laboratory management and maintenance, operator overall training level, stability and verification of test results.
5.7 For the intermediate precision conditions with M factors in different states, it is necessary to indicate which factors are in state 2 in Table 1 and indicate them with the corresponding subscripts. For example:
intermediate precision standard deviation with different time, Skm! intermediate precision standard deviation with different calibration, Sxo1 intermediate precision standard deviation with different operators, Ska intermediate precision standard deviation with different time and operator, Stre intermediate precision standard deviation with different time, operator and equipment, 5xTok1. Similar representation methods are used for other situations. 6 Statistical model
6.1 Basic model
To estimate the accuracy (trueness and precision) of the measurement method, it is assumed that each test result y is the sum of the following three components: Among them, for a given variable test material:
Total mean value (expected):
y=m+B+e
B——Laboratory component of bias under repeatability conditions + random error generated by each measurement under repeatability conditions The following discusses each component in the model and the generalization of the basic model. 6.2 Total mean value m
The total mean value m is the total mean value of all test results. The values obtained in a collaborative study (see GB/T 6379.2) are only 6.2.
The total average value for a particular test material is called the "test level" based on the "true value" and the measurement method, rather than the laboratory, equipment, operator and time factors used to obtain these test results; for example, samples of a chemical with different purities or different materials (such as different types of pots) correspond to different levels.
In many cases, the concept of the true value of the test characteristic is applicable, for example, the true value of a solution being titrated The actual accuracy level is not always equal to the true value. The difference m is called the "bias of the measurement method". In some cases, the test level depends entirely on the measurement method used. In this case, the concept of an independent true value no longer applies. For example, the Vickers hardness of steel and the Micum drum index of coke belong to this type of situation. The bias is represented by & (when the true value does not exist, 8-0), and the overall mean m can be expressed as m=e+8
Note: A discussion of the bias and similar data for trueness tests are given in GB/T 6379, 4. 2
6.2.2 When checking the differences between test results obtained by the same measurement method, the bias of the measurement method will not affect it and can be ignored unless it depends on the test level. When comparing test results with a specified value or standard value in a contract, the specified value or standard value in the contract refers to the true value μ and not the test level m. When measuring a measurement method, and when comparing test results obtained by different measurement methods, the bias of the measurement method must be taken into account.
6.3 Component B
6.3.1 The component B represents the laboratory bias with respect to m due to various reasons. It is independent of the random error e that occurs in every test. Under
conditions of repeatability within a laboratory, B is considered to be a constant and is called the "laboratory component of bias". 6.3.2 However, when a measurement method is used routinely, the value of the laboratory bias B obviously includes many effects, such as those caused by the operator, the equipment used, etc. The effects of equipment, calibration of equipment, and changes in the environment (temperature, wakefulness, air quality, etc.). In this way, the statistical model of formula (1) can be changed to:
=#+B+Bm+Ba++e
-（3)
y-u+a+B,+Bo+B++e
where B is composed of components such as Ba, Bons, Bun, etc., and is explained by a variety of intermediate precision factors. In practice, the research objectives and the sensitivity of the measurement method determine the complexity of the model. In many cases, a simplified form of the model is sufficient.
6. 4 Components Bo, Btn, B2, etc.
These components are constants under repeatability conditions and are part of the bias of the test results. Under intermediate precision conditions, B, is the constant effect of the language factor that remains the same (Table 1D in Table 1): while Bm, B(m, etc. are the random effects of the factors that change (Table 1 State 2). They do not increase bias, but they do increase the intermediate precision standard deviation to a value greater than the repeatability standard deviation. 6.4.2 Operator effects arise from differences between operators, including personal habits in the operation of the measurement method (e.g., reading the scale). Some of these differences should be eliminated by standardizing the measurement method, especially by providing clear and accurate technical instructions. Even if the test results are obtained by the same operator, this component of the error is not always constant (e.g., the size of the error may vary with the mental or physical condition of the operator on the day). However, this part of the bias cannot be completely corrected and should be corrected by using clearly stated operating manuals and training. The effects caused by different operators can be regarded as random. Reducing this type of bias
6. 4.3 Equipment effects are caused by differences between different equipment. They include the effects caused by different equipment installation locations, especially the passive effects caused by pointers or recorders. Some of these effects can be eliminated by accurate calibration. Differences caused by systematic reasons between equipment should be corrected by calibration. The standard measurement method should include such calibration procedures. For example, when replacing a batch of reagents during the execution of the effect, the above method can be used to accept the reference value. In this regard, reference should be made to ISO Guide 33 and ISO Guide 35. The residual effects brought by equipment that has been calibrated with standard materials will be considered as random effects6. 4.4 Time effects are caused by differences in the environment at different times (e.g. changes in room temperature, humidity, etc.). This effect should be minimized as much as possible by standardizing environmental conditions. The effects caused by the skill or fatigue of individual operators can be regarded as the interaction effect between operator and time: the performance of a set of equipment may be different when it is first used and after many hours of use. This is an example of the interaction effect between equipment and time. When the number of operators is small and the number of equipment is even smaller, the effects of these factors can be regarded as fixed (non-random) effects. 6.4.6 The method given in GB/T 6379.2 is based on the assumption that the laboratory component of the reliability is approximately normally distributed. But in practice, for most distributions, as long as they are unimodal, the method can be used. B The variance is called the \inter-laboratory variance\ and is expressed as: Var(B)=dt
However, this variance still includes the effects caused by operator, equipment, time and environmental changes. In a precision test conducted by different operators, at different measurement times and in different environments, the intermediate precision variance can be calculated using a nested design. Var(B) is considered to be composed of independent variance components such as laboratory, operator, test date, and environment: Var(B) -Var(B.)+Var(Bn,) +Var(Btas)+ -The above variance is recorded as
Var(B,)=dta
Var(Bau)-dla
Var(Bo)=oia
In practice, Var(B) is estimated by S, and similar intermediate precision estimates can be obtained through appropriately designed experiments. 6.5 Error term.
6.5.1 The error term represents the random error included in each test result. In the methods given in this standard, this error variable is always assumed to be approximately normally distributed, but in practice, it is sufficient as long as the distribution is unimodal. 6.5.2 Within a single laboratory, the error variance is called the intra-laboratory variance and is expressed as: Var(e)-d
m（8）
6.5.3 Due to differences in operator skills between laboratories, it can be expected that the values of % will vary from one laboratory to another. However, in this standard, it is assumed that the differences in intra-laboratory variances between different laboratories are small through reasonable standardization of the measurement method. It is reasonable to determine a common value for the intra-laboratory variance for all laboratories using the standard measurement method. This common value is estimated as the average value of the intra-laboratory variances of each laboratory, called the "repeatability variance", and is expressed as, -Varke)
e4r+1+itei
This average is obtained for all laboratories participating in the accuracy test outside the group laboratory. 7 Selection of two-quantity conditions
7.1. When measuring with a residual method, many measurement conditions can be imagined in a laboratory, for example: a) Repeatability conditions (all four factors are constant): several intermediate precision conditions with one factor different 625
several intermediate precision conditions with two factors different: several intermediate precision conditions with one factor different: e) Intermediate density conditions with four factors different, m (9)
In the measurement method standard, although the repeatability standard deviation should always be given, it is not necessary (as far as is practicable) to give all possible precision measures. In general industry practice, for intermediate precision measures, the measurement conditions that are usually encountered should be stated. It is sufficient to specify only the appropriate intermediate precision measure while specifying the specific measurement conditions that correspond to them. The measurement conditions that may change should be carefully stated, especially for intermediate precisions that vary in time, the actual average time interval between consecutive measurements should be specified 7.2 We assume that the reliability of a standardized measurement method is as small as possible and that the inherent bias of the measurement method itself has been dealt with by technical means. Therefore, this section only discusses the bias caused by measurement conditions. Any change in the measurement conditions (time, calibration, operator and equipment) in the repeatability condition (i.e., from state 1 to state 2 in Table 1) will increase the variation of the test results. However, the bias of the average of multiple test results will be smaller than the bias under repeatability conditions. Therefore, instead of using a single test result, the average of multiple replicate test results as the final reported test result can overcome the increase in standard deviation under the intermediate precision signature.
7.4 Some practical considerations of most laboratories, such as the required precision (standard deviation) of the final reported result and the cost of conducting the test, will determine the number of factors and the selection of factors that affect the test conditions in the standardization of the measurement method. The simplest method for in-laboratory study and analysis of intermediate precision
The simplest method for estimating the standard deviation of intermediate precision within a laboratory is to take a sample (or for destructive testing, a group of samples that are assumed to be identical, that is, the same) and make repeated measurements on it a number of times. The number of factors that change between the different measurements is recommended to be at least 15. For laboratories, this requirement may not be met, and compared with other methods, this method is not very efficient for estimating in-laboratory intermediate precision. However, its analysis is simple and this method is useful for studying the intermediate precision at different times by measuring a sample on consecutive days or studying the effect of different calibrations on the measurement. To detect outliers in the data, it is recommended to use a pair of plots of the test data, where is the last test result of the repeated test results and is the average of the repeated test results. More formal methods for detecting outliers include the Grubbs test given in 7.3.4 of GB/T 6379.2-2004. When the M factors are different, the estimate of the standard deviation of the intermediate precision is given by: (10)
The symbol indicating the intermediate precision condition should be marked in the subscript brackets. 8.2 Alternative method
8.2.1 Another alternative method is to consider t groups of measurements, each of which includes n repeated test results. For example, in a laboratory, a group of 10 materials, each of which is weighed, the intermediate precision factor is changed, and the material is re-weighed, and this procedure is repeated until each material obtains a test result. The n test results in each group should be measured on the same sample (for destructive testing, from the same group of samples assumed to be the same). The materials tested do not have to be identical. The only requirement is that all materials are within the same test level range. For a material, as long as one value of the intermediate precision standard deviation for the M factors is within the range, the material can be considered to be within the test level range. The value of element 1) is at least 15. After a single measurement is made, the first operator repeats this process, and an estimate of the intermediate precision can be calculated by a third operator. 8.2.2 To detect potential outliers in the data, it is recommended to use a plot of y-y, against the number of materials, where yμ is the th test result for the th material, and y is the average of the th test results for the th material. More formal methods for detecting outliers include GB/T 6379.2
2004, 7, 3, 4 The Grubbs test is given. This test can be used to test each group of results separately or to test all t results as a whole. The estimate of the intermediate precision difference for different materials is given by the following formula: n
For n=2 (there are 2 test results for each material), the above formula is simplified to:)
8.3 Effect of measurement conditions on the final reported results.
8.3.1 Time. Different combinations of calibration, operator and equipment factors have different expected values, even if only one of the four factors is changed. This limits the use of the average value, which is reported as the final result in chemical analysis or physical testing; for commercial raw materials, this final reported result is often used as an assessment of the quality of the raw material and greatly affects the price of the product. Example: In the international trade of coal, the transaction volume is more than 70,000 tons, of which the ash content is determined by only one or so test quantities. If the contract stipulates that the price per ton of coal will differ by $1.5 for every 1% difference in the content, then every 1 mg difference in the mass of the carbon on the chemical level will correspond to a difference of 0.1% in the ash content, or a difference of $0.15 per ton of coal. The total price of this batch of transactions will differ by more than $10,500 (0.1 × 1.5 × 70,000).
8.3.2 Therefore, the results of the chemical analysis and physical tests in the final report should be sufficiently accurate, highly reliable, and especially universal and reproducible. For commercial requirements, a final report result that can only be guaranteed under certain operator, equipment and time conditions is not good enough.
9 Interlaboratory Studies and Analysis of Intermediate Precision Measures 9.1 Basic Assumptions
The estimate of intermediate precision obtained from an interlaboratory study relies on the assumption that the effect of any particular factor is the same across all laboratories, e.g., a change of operator in one laboratory has the same effect as a change in operator in another laboratory, and that changes due to time are the same for all laboratories. If this assumption is not true, the concept of an intermediate measure of precision and the techniques for estimating intermediate precision measures given in the following sections are meaningless: Outliers (which are not necessarily excluded) must be carefully watched because they help to detect deviations from the assumption that the information obtained from all experiments can be combined. An effective technique for detecting potential outliers is to present the measurement results as a function of the levels of the factors or the laboratories involved in the study and to present them graphically. 9.2 The simplest approach
is to send the material for each of the β levels to β laboratories, each of which makes 1 measurement on each of the β levels, varying the intermediate precision conditions between the 1 measurements within each level. The analysis is performed in the same way as described in GB/T 6379.2, except that an intermediate precision standard is obtained instead of an estimate of the repeatability standard deviation. 9.3 Set of designed tests
Another way to ensure the same precision in the test is to conduct more sophisticated and complex tests. Possible methods include full set of designed tests and staggered set of designed tests (see GB/T 3358.3 for the definition of set of designs). The advantage of using a set of designs is that, through a single inter-laboratory test, estimates of both the repeatability standard deviation and the reproducibility standard deviation can be obtained at the same time, as well as estimates of one or more intermediate precision standard deviations. However, there are some areas that must be paid special attention to when using a set of designed tests, which will be explained in 9.8. 9.4 Full set of designed tests
Figure 1 is a schematic diagram of a full set of designed tests at a specific test level. Guo'an
Therefore, the test is released
.
Three-factor full design experiment
b) Four-factor full design experiment
Figure 1 Schematic diagram of three-factor and four-factor full design experimentsYaz
Based on the three-factor full design experiment conducted in collaboration with several laboratories, the estimates of the repeatability standard deviation Sk, the intermediate precision standard deviation Sk and the reproducibility standard deviation S# can be obtained by estimating and. Similarly, based on the piezo full design experiment, the estimates of the repeatability standard deviation S, the two intermediate precision standard deviations Skp.Si1as and the reproducibility standard deviation S. can be obtained simultaneously. In Figure 1a), the three-factor full design experiment, the subscripts 1J and dot of the data represent (for example) the laboratory, the test date and one repetition under the repeatability condition, respectively.
In Figure 1b), the subscripts J, and (, represent (for example) the laboratory, the test date, the operator and one repetition under the repeatability condition, respectively. The analysis of the results of the full set design test is carried out on each level of the test using the "analysis of variance (ANOVA)" method in statistics. This is described in detail in Appendix B. 9.5 Split-layer set design test
Figure 2 is a schematic diagram of the split-layer set design test under a specific test level. Comparison
Figure 2 Schematic diagram of the four-factor split-layer set design test A laboratory! Get 3 debugging results. The test results y and ya should be obtained under the repeatability condition; y should be obtained under M factors with different intermediate precision conditions (M-1,2,3), for example, under different intermediate precision conditions of time, in a four-element staggered nested design experiment with different operators and different labor dates, yu should be obtained under M different intermediate precision conditions (M ≥ 2). For example, under different intermediate precision conditions of time-operator (i.e., changing the conditions of date and operator). The analysis of the results of the staggered nested design experiment for each factor is performed on each level of the test using the "analysis of variance" (ANOVA) method in the design. The details of this are given in the following section. 9.6 Configuration of factors in the nested design
The factors in the nested design should be arranged as follows: the factors mainly affected by systematic effects should be placed at the highest level, and the factors mainly affected by random effects should be placed at the lowest level. The factors in the lowest level are regarded as residuals, and the order from high to low is (0, 1, -). For example, in the four-factor design experiment in Figure 1b) and Figure 2, factor 0 may be the laboratory, factor 1 may be the operator, factor 2 may be the date of measurement, and factor 3 is the repetition. In the complete nested design, due to the symmetry of the design, the way of configuring the factors does not seem to be important. 9.7 Comparison of the nested design with the method given in GB/T6379.2 The method given in GB/T6379.2 is to analyze each test level (of the test material) separately, which is actually a complete nested design with two factors. , and finally two standard deviations are obtained, namely the repeatability standard deviation and the reproducibility standard deviation. Among the two factors, factor 0 is the laboratory and factor 1 is the repetition. If a factor is added to this design, two operators are arranged in a laboratory, and each operator measures two results under repeatability conditions, then in addition to the repeatability standard deviation and reproducibility standard deviation, the intermediate precision standard deviation between operators can also be determined.
Each laboratory has only
operators, but the tests are carried out on different days. The intermediate precision standard deviation between time can be obtained through this three-factor tight set design experiment. If the experiment adds another factor, two operators are arranged in each laboratory, each operator performs two measurements and the experiment is repeated once at different working days, the experiment arranged in this way can determine the repeatability standard deviation, reproducibility standard deviation, operator-to-operator intermediate precision standard deviation, time-to-operator intermediate precision standard deviation,
9.8 Comparison between full set design and staggered set design A one-factor full set design test requires 2 test results for each laboratory, which may be an excessive requirement for the laboratory. This is the main reason for adopting the staggered set design. Although the analysis of the staggered set design is slightly more complicated, and because the number of required test results is the least, the uncertainty of the standard deviation estimate is larger, but it can obtain the same number of standard deviations with fewer full test results. Appendix A
(Normative Appendix)
Symbols and abbreviations used in GB/T 6379 Relationship: =a+bm The trimming distance
A is used to calculate the coefficient b of the uncertainty of the estimated value. The slope
in the relationship sa+bm represents the deviation component of a laboratory's test results from the total mean (laboratory component of bias). It represents the component of B when all factors remain unchanged under intermediate precision conditions. Be
Bu-Bs represents the component of B when factors change under intermediate sugar density conditions. The component of the American formula Igs=c+digm is the cutting Yang
C.CC test statistic
critical value for statistical test
CD, recovery rate P Critical difference of
CRCritical range of probability P
in the oblique chapter
relationship
random error component occurring in each test resultCritical range coefficient
F,(+) p quantile of F distribution with degrees of freedom and Grubbs test statistic
hMandel's inter-laboratory consistency test statisticMandel's intra-laboratory consistency test statisticLower control limit (action limit or warning limit)
Total mean of the test characteristic: water sharing
MNumber of factors considered in the intermediate precision conditionNumber of interactions
Number of test results of laboratories at one level (i.e., in one unit)Number of laboratories participating in the inter-laboratory trial
4Number of levels of the test characteristic in the inter-laboratory trialRepeatability limit
RReproducibility limit
RM Standard material
Estimated value of standard deviation
Predicted value of standard deviation
Total
t. Number of test targets or groups
Upper control limit (action limit or city limit)
Weight in weighted regression
Range of a group of test results
Number used for Grubbs test
Test results
Arithmetic mean of three test results
Test Total mean of test results
aSignificance level
Type II error rate
Ratio of reproducibility standard deviation to repeatability standard deviation ()4Estimate of laboratory bias
8Estimate of measurement method bias
8Detectable difference between two laboratory biases or two measurement method biasesTrue value or acceptance reference value of the test characteristic
Degrees of freedom
. Detectable ratio between the repeatability standard deviations of method A and method B. True value of standard deviation
Represents the detectable ratio of the square root of the mean square between laboratories of Method A and Method B in the component of variation in test results caused by time change since the last calibrationQuantile of the distribution with degrees of freedom
Symbols used as subscripts:
CCalibration - different
EEquipment - different
Laboratory identification
Intermediate measure of precision: The intermediate situation type T in brackets indicates the level of identification (GB/T 6379.2); Identification of test or factor (GB/T6379:3)Laboratory, level, identification of test resultsInter-laboratory
mIdentification of detectable bias
MBetween samples
OOperator-different
Repeatability
RReproducibility
TTime-different
WWithin laboratory
1,2.3…．Test results are numbered in the order in which they are obtained (1),2),.C3),Test results are numbered in ascending order according to numerical value10
Appendix B
(Normative Appendix)
Analysis of variance for complete set of designed experiments
The analysis of variance described in this appendix must be performed separately for each test level in the inter-laboratory test. For simplicity, the subscripts indicating the test level are not marked on the test data. It should be noted that in this part, the subscripts are used to denote factor 1 (factor 0 represents the laboratory), and in other parts of GB/T 6379, the subscripts represent the test level. The data should be checked for consistency and outliers using the method described in 7.3 of GB/T 6379.2-2004. When some test results from one laboratory are missing, accurate analysis of the data will be very complicated using the design described in this annex. If some test results from a laboratory are determined to be outliers or high-level values and should be eliminated in the analysis, it is recommended that all data (of the corresponding level) from this laboratory should be excluded in the analysis. B.1 Three-factor complete set of designed experiments
The data obtained in the experiment are denoted as y, and the mean and range are! 5, =(+y)
Here, force is the total sum of squares of the number of laboratories participating in the inter-laboratory test SST can be decomposed into:
55T-222(0u -3) -S0+ 1 + se
SS0-2-)=420-5)-40-4p()
51-0-200
Because the degrees of freedom of the sum of squares SS0, SS1, and SSe are 1, p, and 2p respectively, the designed variance analysis table is shown in Table B.1. Table B,1 Analysis of variance table for three-factor complete set design experiment Source
Sum of squares
Degrees of freedom
MS0-50/(p1)
MSI-SSi/p
MSe- SSe/(2p)
The expected value of mean square
The unbiased estimates of oma are sea and product, respectively. These estimates can be calculated from mean square MSo, MSI, MSe according to the following formula
e-(MSOMS1)
(MS1-MSe)
The estimates of repeatability variance, intermediate precision variance of one factor, and reproducibility variance are: a+a
s+s+so
B.2 Four-factor full set design test
The data obtained in the test is recorded as 3u, and the mean and range are y=2(yi+y）
J-ta+y)
Wg-ly-yar
Wa—13—3l
w.,=[,—ya]
where β is the number of laboratories participating in the inter-laboratory test. The total sum of squares SST can be decomposed into
SSTsS0 +s$1+2+SSe
S50 -22220-0-820)-8p0)
SS12220-4220-22
SS20-220,2
Because the degrees of freedom of the sum of squares SS0,SS1,SS52,SSe are p-1,p,2 and 4p respectively. The variance analysis table of the design is shown in Table B, 2:
Table B, 2 Variance analysis table of four-rate complete set design experiment from
Easy Service Institute
Degrees of freedom
MS0o/(—1)
MS1-SS1/P
MSeSSe/L4p)
Expected value of the mean square
#+20a+4otu+80am
af+2adia+4au
the unbiased estimates of aati are ssns and, respectively. These estimates can be calculated from the mean squares MS0, MS1, MS2 and MSe according to the following formula:
=(MSO- MSI)
s0)—(MS1-MS2)
s-↓(MS2—MSe)
et-MSe
The estimated values of repeatability variance, one-factor-unchanged intermediate precision variance, two-factor-unchanged intermediate precision variance and reproducibility variance are:
skn= &+ sa
ka= $+ +sin,
=s$+sn+so+s
Appendix C
(Normative Appendix)
Analysis of variance for nested design experiments
The analysis of variance described in this manual must be performed separately for each test level in the inter-laboratory trial. For simplicity, subscripts indicating test levels are not marked on the test data. It should be noted that in this part, subscripts are used to indicate repetitions within a laboratory; while in other parts of GB/T 6379, j represents the test level. The method described in 7.3 of GB/T 6379.2-2004 should be used to check the consistency and outliers of the data. With the design described in this annex, when some test results of a laboratory are missing, the accurate analysis of the logarithm will be very complicated. If some test results from a laboratory are determined to be outliers or outliers and should be eliminated in the analysis, it is recommended that all data (of the corresponding level) from this laboratory should be eliminated in the analysis. C.1 Three-factor staggered nested design experiment
The data obtained in laboratory 1 in the experiment are recorded as y, (j-1,2,3), and the mean and range are Jan(+ya)
m-+(a+y+)
wan-lya—yal
Wae, =[3a, -al
where P is the number of laboratories participating in the inter-laboratory test. The total sum of squares SST can be decomposed into:
sT-(y)sso+ss1+sse
SS0-3 20am)-3p(6)
Because the degrees of freedom of the sum of squares SSo, SS1, SSe are p-I, p and P respectively, the variance analysis table of the design is shown in Table C.1. Table C.1 Variance analysis table of three-factor staggered nest design experiment Source
Sin square and
degrees of freedom
sso/(p-1)
The expected value of the mean square
diaal,. The unbiased estimates of the mean squares are sm+n and. These estimates can be calculated from the mean squares MSoMS1 and MSe according to the following formula
te-IMSO-MS1+1MSe
a-=MS1- is MSe
The repeatability variance, the estimated values of the intermediate precision variance and the reproducibility variance of a factor are: sn= $+device
most=sample+a+,
C.2 National Factor Staggered Layer Design Experiment
In the experiment, the data obtained in the laboratory! is recorded as y. (j-1,2,3.4), the mean and range are: Jan(a+y)
J=+(y,+ya+ya)
Wxu =lya-yal
Ye-+(g +y,+ya+y,)-lyay
Where force is the number of laboratories participating in the inter-laboratory test. The variance analysis table of the design is shown in Table C.2. Table C.2 Variance analysis table of four-factor staggered layer design experiment Source
Sum of squares
C.3 Five-factor staggered layer design experiment
Degrees of freedom
SS/The unbiased estimates of are sm+n and sm+n, respectively. These estimates can be calculated from the mean square MSoMS1 and MSe according to the following formulas:
te-IMSO-MS1+1MSe
a-=MS1- is MSe
repeatability variance, the estimates of intermediate precision variance and reproducibility variance for different factors are: sn= $+instrument
most=sample+a+,
C.2 In the country's inductive staggered layer nested design test
the data obtained in the laboratory are recorded as y. (j-1,2,3.4), the mean and range are: Jan(a+y)
J=+(y,+ya+ya)
Wxu =lya-yal
Ye-+(g +y,+ya+y,)-lyay
where force is the number of laboratories participating in the inter-laboratory test. The variance analysis table of the design is shown in Table C.2. Table C.2 Variance analysis table of four-factor staggered forest design experiment Source
Sum of squares
C.3 Five-factor staggered nested design experiment
Degrees of freedom
SS/The unbiased estimates of are sm+n and sm+n, respectively. These estimates can be calculated from the mean square MSoMS1 and MSe according to the following formulas:
te-IMSO-MS1+1MSe
a-=MS1- is MSe
The repeatability variance, the intermediate precision variance and the reproducibility variance of different factors are estimated as follows: sn= $+instrument
most=sample+a+,
C.2 In the country's inductive staggered layer design test
the data obtained in the laboratory are recorded as y. (j-1,2,3.4), the mean and range are as follows: Jan(a+y)
J=+(y,+ya+ya)
Wxu =lya-yal
Ye-+(g +y,+ya+y,)-lyay
where force is the number of laboratories participating in the inter-laboratory test. The variance analysis table of the design is shown in Table C.2. Table C.2 Variance analysis table of four-factor staggered forest design experiment Source
Sum of squares
C.3 Five-factor staggered nested design experiment
Degrees of freedom
SS/The sum of 1% and 1% is shown in Table D.1. The analysis is performed using the method given in 8.2. % (m/m)
Tel: 88895555899
Figure D.1 is a dot plot of the data [the sample number T for each day's test result that is higher than the mean of the test result (>,-5) corresponds to the sample number T. From this scatter plot or by using Cochran's test, it can be found that the samples ranked 20 and 24 are outliers. There is a big difference between the test results of these two samples on two days, and the main reason may be the error in recording the data. When calculating the intermediate precision standard deviation ssTa for different times and operators, the duplicate test values of these two samples should be excluded. Calculated by formula (12): to-/2×22 =2.87×10
6/Signature
Group Product No.:
Figure D.1 Carbon content in steel - Deviation of daily test results from the mean of two-day test results Corresponding sample number D.2 Example 2 Standard deviation of intermediate precision obtained by time-varying test D.2.1 Back-measurement
) Measurement method: Vanadium content in steel was determined by ion absorption spectrometry as described in the test description. The test results were expressed in mass percentage.
Source: ISO/TC 17, Steel/SC 1, Methods for determination of chemical composition and tests conducted in May 1985. b)
Test design: In a three-factor staggered nested design involving 20 laboratories, each laboratory reported one test result obtained under repeatability conditions on the first day and another test result obtained and reported on the second day at each of the six levels included in the test. All measurements in each laboratory were performed by the same operator using the same measuring equipment. D.2. 2 Analysis
The data for all six levels are given in Table D.2, but only the analysis of variance for level 1 is given. Figure D.2 shows a plot of the data (results of the subtests on the first and second days versus the laboratory number). It can be seen from this figure that laboratory number 20 is a high-ranking laboratory. There is a large difference between the mean of the test results of this laboratory on the second day and the mean of the test results on the first day, which is very large compared to the differences in the test results of the other laboratories. When calculating the density measure, the test results of this laboratory are excluded.
Based on Appendix C, C.1, wt and y+ are calculated and the results are given in Table D.3. 19
Laboratory number
BBDBBD
A day's wing once Muzhan Jinghu
Laboratory number!
Figure D. 2 Carbon content in steel - level 1 The test results of the first and second days correspond to the laboratory number Table D.2
Original data of vanadium content
Yongping 10.01%)
First level
Second level
.010.2
Water 2 (0.04%)
First level
Second level
X(m/m)
Benping 30.1%)
Second day| |tt||First tip
#98989
###9####
##9####S
Laboratory No.
as6789nuD3#55n398
Shuifu 4 (0.2%
First day
Second day
National#######5###
###Service has#
Experiment Business No.
1234562
83DnBIHR#II Company
Table D.2 (continued)
Water rate 50.5 yuan 3
First day
###359
#9#5#5#8#9#
Second day
%(o/m)
Level 60.75%)
First day
Second*
Tongguo######################
##Duonanqin
########55595
##9##5599
##8839885#89
Table D.3ancn and am values
tan and ue, the sum of squares and the average value are calculated as follows: 2wl =5. 52×10~
Z12.44×10
Z(G)*-1 832. 16×10
5-125u: =0 009 798 25
Using the above results, the sum of squares SSO, SS1 and SSe can be obtained, as shown in Table D. 4 is the corresponding variance analysis table. The unbiased estimates of the variance between different laboratories, the unbiased estimates of the variance in the same laboratory and on different dates, and the unbiased estimates of the repeatability variance are:
se-0.278X10
t=0.218×10~
0.145×10-6
The reproducibility standard deviation, the intermediate precision standard deviation5 and the repeatability standard deviation5 at different times are: =/2++s=0.801×102
—/:+=0.603×10-1
3,=0.381×10-
Table D.5 is the calculation results of the estimated values of the standard deviation of vanadium content in steel under 6 test levels; Figure I.3 is a graphical representation of the calculation results. Table D.4 Variance analysis table of vanadium content in steel Data from
0(laboratory)
1(day)
Average
24:16×10-
2.76×10-bzxz.net
35.21×10-
Free bond
1.342×10-
0.4.36×10-
0.145×10~
Expected mean square
+f+3m,
sweet+→
Table D.56 The estimated values of standard deviation of steel content sskn and sx in steel at the test level are outliers. The actual reported room number is
1) in 1SO.5725-3:19
calculated as average value/%
0.381×10
0.820×10--
1.739×10~
3.524×10-s
6.237×10
9.545×10~2
.603×10
0.902X10~
4.730×10-1
6.436×104
0.8 01x10-
0.954×10-
2.650×10
4.826X10-1
9.412×10~1
15.962×10~
GB/T6379.3-2012/1SO5725-3:1994 Barren level/%
Figure D.3 Vanadium content in steel - Relationship between repeatability standard deviation, time-varying intermediate precision standard deviation m and reproducibility standard deviation s and vanadium content level References
[1] GB/T 3358.2—2009 Statistical vocabulary and symbols Part 2 Applied statistics. [2] GB/T 3358.3-2009 Statistical vocabulary and symbols Part 3 Experimental design [3] ISO 5725-4.1994 Accuracy (trueness and precision) of measurement methods and results - Part 4, Basic methods for the determination of the correctness of a standard measurement method [4] ISO 5725-5:1998 Accuracy (trueness and precision) of measurement methods and results — Part 5: Alternative methods for the determination of the precision of a standard measurement method [5] ISO 5725-6: 1994 Accuracy (trueness and precision) of messurement methods results — Part 6 Use in practice of accuracy values.
nexperimental designMeGraw-Hill,1952[6]WINER.BJStat
Unrincinlesi
[7]SNEDECORG.W.andCOCHRANW.G.SuatisticealmethodslowaUniversitypress1967All rights reserved
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