GB/T 22554-2010 Linear calibration based on standard samples GB/T22554-2010 Standard download decompression password: www.bzxz.net
This standard specifies the general principles for the calibration of measurement systems and the maintenance of the calibrated measurement systems in a state of statistical control. This standard specifies the basic method for the following purposes: a) Estimation of the linear calibration function under two assumptions of measurement variability; b) Verification of the assumptions of linearity of the calibration function and measurement variability; c) Estimation of the new unknown quantity after the measured value is transformed based on the calibration function. This standard gives the control method for the use cycle of the calibration function, which is used for: a) Verification of when the calibration function needs to be updated; b) Uncertainty assessment of the measured value after the calibration function is transformed. This standard specifies two alternative methods to the basic method under specific conditions, and gives examples of the basic method and the control method. This standard applies to measurement systems for which reference samples are available and for which a linear calibration function is assumed, and provides methods for verifying the assumption of linearity. This standard is not applicable to situations where the calibration function is known to be nonlinear, unless the "clamping technique" described in 8.3 is used. This standard does not distinguish between various types of reference samples and assumes that there is no error in the accepted values ​​of reference samples used for measurement system calibration.
class="f14" style="padding-top:10px; padding-left:12px; padding-bottom:10px;"> This standard is modified and adopted ISO11095:1996 "Linear calibration using reference materials".
The main differences between this standard and ISO11095:1996 are as follows:
———The foreword of the international standard is deleted;
———The statement form of typical introductory words is used in the scope, and some corresponding editorial modifications and adjustments are made under equivalent conditions;
———The Chinese standard adopting the international standard is quoted;
———The Appendix A "Symbols used" in the original international standard is adjusted to 3.2 of this standard;
———The Appendix B "Basic method when the number of repetitions is not equal" in the original international standard is adjusted to Appendix A of this standard.
Appendix A of this standard is a normative appendix.
This standard is proposed and managed by the National Technical Committee for Standardization of Statistical Methods (SAC/TC21).
The drafting units of this standard are: Liaoning Entry-Exit Inspection and Quarantine Bureau, China National Accreditation Service for Conformity Assessment, Beijing University of Technology, China National Institute of Standardization, China National Institute of Metrology, and Qinghai Entry-Exit Inspection and Quarantine Bureau.
The main drafters of this standard are: Wang Douwen, Song Guilan, Zhang Mingxia, Niu Xingrong, Xie Tianfa, Zhang Fan, Liu Zhimin, Chen Zhimin, Li Liantong, Chen Zhenyi.
The clauses in the following documents become the clauses of this standard through reference in this standard. For all dated referenced documents, all subsequent amendments (excluding errata) or revisions are not applicable to this standard. However, the parties who reach an agreement based on this standard are encouraged to study whether the latest versions of these documents can be used. For all undated referenced documents, the latest versions are applicable to this standard.
GB/T3358.1 Statistical vocabulary and symbols Part 1: General statistical terms and terms used in probability (GB/T3358.1—2009, ISO3534-1:2006, IDT)
GB/T3358.2 Statistical vocabulary and symbols Part 2: Applied statistics (GB/T3358.2—2009, ISO3534-2:2006, IDT)
GB/T15000.2 Guidelines for working with reference samples (2) Common terms and definitions for reference samples (GB/T15000.2—1994, ISOGuide30:1991, NEQ)
Foreword I
Introduction II
1 Scope 1
2 Normative references 1
3 Terms and definitions, symbols 1
4 General3
5 Basic method3
5.1 Overview3
5.2 Assumptions3
5.3 Calibration experiment3
5.4 Data analysis strategy4
6 Steps in the basic method4
6.1 Plotting the data collected during the calibration experiment4
6.2 Estimation of the linear calibration function under the assumption of constant residual standard deviation5
6.3 Plotting the calibration function against the residuals6
6.4 Estimation of the calibration function under the assumption of proportional residual standard deviation and plotting the calibration function against the residuals7
6.5 Assessment of underfit of the calibration function8
6.6 Transformation of the calibration function for subsequent measurements9
7 Control method10
7.1 Overview10
7.2 Calculation of upper and lower control limits 10
7.3 Data acquisition and plotting 10
7.4 Determination of system status

ICS 03.120.30
National Standard of the People's Republic of China
GB/T22554--2010
Linear calibration using reference materials (ISO110951996, MOD)
Published on September 2, 2010
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
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Implemented on April 1, 2011
GB/T 22554-2010
Normative references
Terms and definitions, symbols
Basic method
Calibration experiment
Data analysis strategy
6 Steps of the basic method
6.1 Plotting the data collected during the calibration experiment6.2
Estimation of linear calibration function under the assumption of constant multiplied residual standard deviationPlotting calibration function and residuals
Estimation of calibration function under the assumption of proportional residual standard deviation and plotting calibration function and residuals6.4
Evaluation of underfit of calibration function
6.6 Subsequent measurements Transformation of calibration function
7 Control method
.[-Calculation of control limit and lower control limit-
7.3 Data acquisition and drawing….
Determination of system state··
Uncertainty assessment of transformation value:
8 Two alternative methods to the basic method
Overview·
Single-point calibration method
Forcing technology
9 Examples
9.1 Overview…
0.2 Basic method·bzxZ.net
9.3 Control method
Appendix A (Normative Appendix)
Repeat Basic method when the numbers are not equal
References
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This standard is modified by IS)110951996 "Linear calibration using reference malerials"
The main differences between this standard and IS011095:1996 are as follows: the foreword of the international standard is deleted;
- The statement form of typical introductory words is used in the scope, and some corresponding edits are made under equivalent conditions The following are the modifications and adjustments: - The Chinese standard that adopts the international standard is quoted; - The symbols used in Appendix A of the original international standard are adjusted to 3.2 of this standard; - Appendix B of the original international standard, the basic method for unequal repetition numbers, is adjusted to Appendix A of this standard. Appendix A of this standard is a normative appendix.
This standard was proposed and coordinated by the National Technical Committee for Standardization of Statistical Methods (SAC/TC21). The drafting units of this standard are: Liaoning Exit-Entry Inspection and Quarantine Bureau, China National Accreditation Service for Conformity Assessment, Beijing University of Technology, China National Institute of Standardization, China National Institute of Metrology, Qinghai Exit-Entry Inspection and Quarantine Bureau. The main drafters of this standard are: Xia Douwen, Song Jialan, Zhang Mingsuan, Niu Xingrong, Xie Tiantai, Zhang Fan, Liu Zhimin, Chen Zhimin, Li Liantong, and Chen Zhenyi.
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Calibration is the core link in most measurement procedures. It is a set of operations under specified conditions to establish the relationship between the values ​​given by the measurement system and the values ​​accepted by the "standard material". A standard sample is a substance or product whose one or more properties have been fully established to confirm the measurement system. There are several types:
Internal standard samples are developed by the user for internal use; external standard samples are provided by the outside:
Certified standard samples , issued and valued by recognized competent institutions. http://foodmate.net1Scope
Linear calibration based on standard samples
GB/T22554—2010
This standard specifies the general principles for the calibration of measurement systems and the maintenance of calibrated measurement systems in a state of statistical control. This standard specifies the basic methods for the following purposes: a) Estimation of linear calibration functions under two assumptions of traceability variability; b) Verification of the assumptions of linearity of the calibration function and measurement variability; c) Estimation of new unknown quantities after the measured value is transformed based on the calibration function. This standard gives This standard specifies two alternatives to the basic method under specific conditions and gives examples of the basic method and the control method. This standard is applicable to measurement systems for which standard samples are available and measurement systems that assume a linear calibration function, and provides methods for verifying the linearity assumption.
This standard is not applicable to situations where the calibration function is known to be nonlinear, unless the "cool technique" described in 8.3 is used. This standard does not distinguish between various types of standard samples and assumes that the standard samples used for measurement system calibration are There is no error in the accepted value of the product. 2 Normative references
The clauses in the following documents become clauses of this standard through reference in this standard. For any referenced document with a date, all subsequent amendments (excluding errata) or revisions are not applicable to this standard. However, parties to an agreement based on this standard are encouraged to study whether the latest versions of these documents can be used. For any undated referenced document, the latest version applies to this standard, ([3/T3358.1 Statistical Vocabulary and Symbols Part 1: - Statistical Terms and Terms Used in Probability (GB/T3358.1-2009, IS0 3534-1,2006,IDT)
GB/T3358.2 Statistical vocabulary and symbols Part 2: Applied statistics (GB/T3358.2—2009, ISO3534-2.2006,IDT) GB/I15000.2 Standard sample T. Guidance (2) Common terms and definitions of standard samples (GB/I15000.21994, ISOGuide 30:1991,NEQ)
3 Terms and definitions, symbols
GIB/T3358.1 and GF/T3358.2 and the following terms and definitions, symbols apply to this standard. 3.1 Terms
Standard sample reference Material
Standard samples are a batch of samples with sufficiently uniform one or more chemical, physical, biological, engineering or sensory properties, which have been technically identified and are accompanied by a certificate describing the relevant performance data. Note 1: Standard samples can be pure or mixed gases, liquids or liquids, or a product or image. Most standard samples are batch identified, that is, a small part that can meet the requirements is randomly selected from a batch of materials, which can represent the performance value of the batch within the specified uncertainty limit; a few standard samples are single products identified individually; and some standard samples cannot be explained by established chemical structures and other reasons due to their properties. For example, their characteristics cannot be expressed by composition, quality and quantity, nor can they be determined by strictly defined test methods. This type of standard sample includes some biological, engineering and/or sensory standard products. Note 2: The standard samples in this standard are also called reference materials, standard materials, certified reference materials, certified standard materials, reference materials, etc. in other application fields. Note 3: Modified from the definition in GB/T 15200.2. 1
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3.2 Symbols
Number of standard samples
K or K,
Number of repeated measurements for each standard sample
Total number of measurements for all standard samples
Acceptance value of standard sample
Acceptance value of blank sample
Average of all accepted values
Reciprocal of acceptance value of standard sample (1/)
Average of reciprocals of all accepted values
Measured value of standard sample
Blank measurement
Average of all measurements
Average of the values ​​measured for a particular standard sample
Ratio of the measurement of a standard sample to the acceptance value of that standard sample (3/z) β—Intercept of the calibration function under the assumption of the required residual standard deviation (see 6.2.4)—Slope of the calibration function under the assumption of the proportional residual standard deviation (see 5.2.4)…—Slope of the calibration function under the assumption of the proportional residual standard deviation·Departure between the measurement and the mean under the assumption of the constant residual standard deviation and linearity.-proportional residual standard deviation and deviation from the mean e under the assumption of linearity
residuals under the band residual standard deviation and linearity assumptionproportional residual standard deviationweighted residuals under the linearity assumptionconstant residual variance (variance of e)
pure error variance under the constant residual standard deviation assumptionunderfit error variance under the constant residual standard deviation assumptionproportional residual variance (variance of /)
pure error variance under the proportional residual standard deviation assumptionunderfit error variance under the proportional residual standard deviation assumptionsum of squares of residuals e
sum of squares of weighted residuals||tt ||SSTWSST
SSR,WSSR-
is the total sum of squares of deviations under the assumption of band or proportional residual standard deviation respectively. The sum of squares of deviations of the errors under the assumption of constant or proportional residual standard deviation respectively. The semi-sum of squares of deviations given by the calibration function under the assumption of constant or proportional residual standard deviation respectively. α-significance level
[—αconfidence level
Fr:（n:，n）is the quantile ti-t(:) of the F distribution with degree n and n-
is the quantile ti-t(:) of the t distribution with degree n-
U- Upper control limit L under constant residual standard deviation assumption:----Lower control limit under constant residual standard deviation assumption ti
Upper control limit under proportional residual standard deviation assumption Lower control limit under proportional residual standard deviation assumption Control value under constant residual standard deviation assumption Control value under proportional residual standard deviation assumption htt
4 General
GB/T22554—2010
Calibration A procedure used to determine whether there are systematic differences between a measurement system and a “standard” system, where the “standard” system is represented by standard samples and their acceptance values. This The system defined in the standard (measurement system or standard system) represents not only the measuring instrument, but also the procedures, operators and environmental conditions associated with the instrument. The output of the calibration procedure is the calibration function, which is used to transform the subsequent measurement results. The term "transformation" in this standard refers to: - the correction made to the subsequent measurement when the observed value has the same units as the accepted value of the standard sample, or - the conversion of the units of the measured value into the units of the standard sample. The validity of the calibration function depends on two conditions: a) the measurements for which the calibration function is calculated represent the operation of the measurement system under normal conditions; and b) the measurement system is in a state of control.
The design of the calibration experiment should meet the above requirements and the control method should be able to identify the system out of control as early as possible. The procedures in this standard are only applicable to measurement systems that are linearly related to their standard system. In order to check whether the linearity assumption is valid, more than two standard samples should be used during the calibration experiment, as described in the basic method. By using several standard samples, the basic method gives strategies and techniques for analyzing the data obtained in the calibration experiment. If the linearity assumption is valid, a single-point method that is more simple than the basic method can be used to estimate the linear calibration function. This "single point calibration" method (based on 0-level-transformation) is a quick method for "recalibrating" the system, because it has been fully studied in previous experiments, so no assumption test is required; if the linear assumption does not hold, an alternative method called "delimitation" can be used. The basic method and the single point method are based on the assumption that the calibration implemented during the process stability period is effective. To study the validity period of calibration, the control force method should be used. The control method should be designed to detect changes in the system to determine whether to investigate and/or recalibrate. The control method also gives a simple method for determining the precision of the transformation value of the calibration function. The clamping method is more complicated, but it gives better accuracy for the determination of unknown values. This method uses 2 standard samples to cover (sandwich) each unknown quantity as tightly as possible, and obtains the transformation value of the known quantity from the measurement of the unknown quantity and the 2 standard sample values. It makes an assumption about the short-term stability of the measurement process (the stability of the unknown quantity value and the 2 standard sample values ​​during the measurement), and only makes a linear assumption for the interval of the 2 standard sample values:
5 Basic method
5.1 Overview
This chapter describes how to estimate and use a linear calibration function when several (2 to 1) standard samples are available. The linearity of the calibration function can only be verified by using several standard samples. 5.2 Assumptions
5.2.1 The accepted values ​​of the standard samples are free of error (this assumption is not tested in this standard). In practice, the accepted values ​​of the standard samples and their uncertainties are given simultaneously. If the uncertainty of the accepted values ​​of the standard samples is small compared to the errors in the measured values ​​of the standard samples, the assumption that the accepted values ​​of the standard samples are free of error is considered valid (see reference [1]. Note: If the standard samples are chemically treated or, in some cases, physically treated before the instrument reading is given, this standard may underestimate the uncertainty of the transformed value of the new measurement result.
5.2.2 The calibration function is linear (this assumption needs to be tested). 5.2.3 The repeated measurements of the standard samples are independent and normally distributed with a variance of \frac{\squared variance}” (this standard does not test the assumptions of independence and normality).
5.2.4 The residual standard deviations are all equal or proportional to the accepted values ​​of the standard samples (referred to as "constant residual standard deviation" or "proportional residual standard deviation", this assumption needs to be tested).
5.3 Calibration experiment
5.3.1 Experimental conditions
The experimental conditions should be the same as the normal operating conditions of the measurement system. For example, if more than one operator uses the measuring equipment, all three operators should participate in the calibration experiment.
5.3.2 Selection of standard samples
The value range of the selected standard samples should cover the range of the measurement under the normal operating conditions of the measurement system as much as possible. The composition of the selected standard samples should be as close as possible to the composition of the sample being measured. The standard sample values ​​should be distributed approximately equidistantly over the entire measurement range under the normal operating conditions of the measurement system. 5.3.3 Number of Standard Samples N
The number of standard samples evaluated with the calibration function should be at least 3. For the initial evaluation of the calibration function, it is recommended that more than 3 standard samples be used (if the linearity of the calibration function is suspected, the number of standard samples in all sub-intervals should be at least 3).
5.3.4 Number of Repetitions K
Each standard sample should be measured at least twice (it is recommended to repeat as many times as practical). The number of replicates for all standard samples should be equal
The coverage of the time and conditions used for the replicate measurements should be as wide as possible to ensure representativeness of all operating conditions. 5.4 Data Analysis Strategy
5.4.1 Plot the data to investigate:
a) the state of control of the measurement system during the calibration experiment;
Linearity assumptions:
c) the variation of the measured values ​​as a function of the acceptance values ​​of the standard samples. 5.4.2 Estimate the linear calibration function under the assumption of constant residual standard deviation. 5.4.3 Plot the calibration function and residuals. The residual plot is an important indicator for judging whether there is a deviation from the linear assumption or the constant residual standard deviation assumption. If the assumption of constant residual standard deviation is established, skip 5.4.4 and continue with 5.4.5. Otherwise, execute 5.4.4. 5.4.4 Under the assumption of proportional residual standard deviation, estimate the linear calibration function and plot the calibration numbers and residuals. 5.4.5 Assess the lack of fit of the calibration function. If the variation caused by the lack of fit is greater than the variation caused by repeated measurements, investigate the procedures implemented during the calibration experiment and re-examine the assumption of linearity of the calibration function. If the assumption of linearity is not established, use the clamping technique described in 8.3.
Note: Other techniques can be used to fit the data of quadratic or higher order curves, but they are not within the scope of this standard (see reference L2_ and reference [3]>). 5.4.6 Use the calibration function to transform the subsequent measured values. The six steps of this strategy are shown in Chapter 6. Examples of the basic method are shown in Chapter 9. 6 Basic method steps
6.1 Plotting the data collected during the calibration experiment Figure 1 is a scatter plot of the acceptance value and the measured value of the calibration sample. Figures 1 and 2~ Figure 5 was drawn using simulated data. These five graphs illustrate the type of information that can be obtained from such graphs. Complete examples of data, plotting, and analysis are provided in Chapter 8. 70
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Standard sample acceptance value (total phosphorus to disk ratio) Figure 1 Schematic diagram of the data obtained during the calibration experiment
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Figure 1 The main transformer is used for white measurement to check whether there are any anomalies in the measurement system during the calibration experiment, and identify possible outliers. If possible, plot the order of the data points and look for obvious time trends. If some data are considered suspicious or obvious time trends are found, the cause of the anomaly should be investigated. Once the anomaly is eliminated, the calibration experiment should be repeated and new data should be collected.Establish calibration coefficients. If the causes of one or a few outliers are found and these causes do not affect other measurements, the outliers are removed. At this point, the calibration experiment becomes unbalanced, that is, K in each standard sample is replaced by an unequal number of measurements K. However, the estimation of calibration coefficients can be carried out in a similar way to 6.2, 6.4 and 6.5, just replace the formulas with the formulas given in Appendix A. Figure 1 can also be used to diagnose the linearity assumption of the calibration function and to make a preliminary judgment on the assumption of a constant residual standard deviation. The linearity of the calibration function can be checked by observing whether the plotted points through the data in Figure 1 form a straight line (the data in Figure 1 seem a bit curved). The assumption of a constant residual standard deviation is checked by observing the spread of the data points under the standard sample in Figure 1. If this spread increases with the acceptance value of the standard sample, the assumption of a constant residual standard deviation may be incorrect (this phenomenon does not exist in Figure 1). 6.3 A more complex plot for testing linearity and constant residual standard deviation is given
6. 2 Estimation of the linear calibration function under the assumption of constant residual standard deviation 6.2.1 Model
The model under the assumptions of linearity of the calibration function and constant residual standard deviation can be expressed as: Where:
Yue=βeBita Fema
The acceptance value of the nth standard sample (-N
The nth measured value of the nth standard sample (-1,,K); The expected value of the measured value of the nth standard sample;
The expected deviation from the measured value of the nth standard sample (assuming that these deviations are independent of each other and follow a normal distribution with mean ○ and variance).
Three parameters to be estimated based on the data obtained during the calibration: the intercept of the calibration function;
The slope of the calibration function;
2. A measure of the precision of the measurement system.
6.2.2 Parameter estimation
The estimation of parameters β and can be calculated using the following formula, or by using a linear regression software package, conjugating two columns of equal length, one column a and the other column y.
Note: The estimated values ​​of the parameters in this standard are marked with - to distinguish them from their unknown parameters. Formula
-)(yh —3)
>(un—)2
(NK-2)
NK-NXK;
3.B.-βa,;
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CB/T 22554—2010
6. 3 Plotting calibration function and residuals
It is recommended to plot Figures 2 and 3 to check whether there is a deviation from the assumptions made by the model in 6.2. 6.3.1 Plotting calibration function
The estimated calibration function is plotted in 1 to form Figure 2. 70
× First Repeat data
42nd update data
03rd repeat data
Acceptance value of standard sample (total phosphorus weight to length ratio)Figure 2 Schematic diagram of calibration curve
Figure 2 can be used to check the calculation results in 6.2.2, and can also be used to visually check the linearity assumption of the calibration function. 6.3.2 Plotting residuals against fitted values
Plotting the residuals against the fitted values ​​(Figure 3) is an effective tool for checking whether there is a deviation from the linearity and constant residual standard deviation assumptions. If these two assumptions are true, Figure 3 should show randomly distributed points centered at 0. If there is a systematic pattern between the residuals and the fitted values, it indicates a deviation from the linearity assumption (as shown in Figure 3). If the data spread increases or decreases with the fitted values, it indicates a deviation from the constant residual standard deviation assumption. In Figure 3, the residual spread of the fitted values ​​is equal, so it is believed that the assumption of constant residual standard deviation is valid.
Note: Figure 8 shows that the assumption of constant residual standard deviation is not valid. 3
■1st Recall
42nd Recall
?3rd Recall
Figure 3 Residual Schematic
50 Fitted Values
If the assumption of constant residual standard deviation is not valid, the data obtained during the calibration experiment should be reanalyzed. Plotting the standard deviation of the repeated measurements of the standard sample against the acceptance value of the standard sample can show whether the assumption of proportional residual standard deviation is valid, as shown in Figure 9. a) If the assumption of proportional residual standard deviation is valid, reanalyze the data according to the steps in 5.1. If the assumption of proportional residual standard deviation is not valid, and there is another relationship between the residual standard deviation and the acceptance value of the standard sample station (e.g., inverse proportion), then a method similar to that in 6.4 can be used. If the linear assumption is not valid, then the clipping technique in 8.3 can be used. Note: Other techniques can be used to fit the data for quadratic or higher-order lines (see references 27 and 3]). This is beyond the scope of this family of studies. 554—2010
Finally, the test of the assumptions of independence and normality of the values ​​is not within the scope of this standard. These two assumptions are important for the validity of 6.5 and can also be tested by studying the residuals. For example, the normal probability plot of the residuals can be used to test the stability of the normality, and the residual plot against time can be used to test the assumption of independence of the measured values. For details, see reference [.31. 6.4 Estimation of the calibration function under the assumption of proportional residual standard deviation and plotting of the calibration function and residuals 6.4. 1 Model
When the calibration function is linear, but the residual standard error increases with the acceptance value of the standard sample, the following model can be used to replace the model given in 6.2.1. The model is expressed as:
Y—Y-?t, + 7ne
Where:
the acceptance value of the nth standard sample (n-1,,N); Yn
the nth measured value of the nth standard sample (-1,,K); the expected value of the nth standard sample measurement;
the deviation from the expected value of the nth standard sample measurement (assuming that these deviations and are independent of each other and follow a stationary distribution with mean 0 and variance To
proportional to), that is, ar)var() =, and
are the three parameters to be estimated based on the data obtained before the calibration period: where, and are the intercept and slope of the calibration function respectively; is a measure of the relative precision of the measurement system. This model can be transformed into the model given in 6.2.1, that is, with the corresponding error variance. The transformation only requires dividing both sides by 1+10, thus obtaining:
in.. Ye +. + a
or equivalently
2n =Y1 +Yeu, -En?
where:
Ent - After the correct substitution of each item, the new model can be analyzed according to 6.2. 6.4.2 Parameter Estimation The estimates of parameters %, and can be calculated using the following formula, or run the weighted linear regression software package, input three columns of data of the same length, one column for definition, another column for main, and the third column for weights (= input, directly input the second and third columns:
NK=NXK;
). The same output can also use the linear regression software package: It is not necessary to consider the input of weights 2
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GB/T 22554—2010
,=+wa+
Un = zat
6.4.3 Plotting the calibration function against the residuals
As in 6.3, it is recommended to plot two plots:
2) Using the data in Figure 1, plot the estimated calibration function + b) plot the weighted residuals against the weighted fitted values. The interpretation of these plots is equivalent to Figures 2 and 3.6.5 Assessment of poor fit of the calibration function
6.5.1 Overview
Construct an analysis of variance (ANOVA) table to compare the following two variations: a) variation due to poor fit of the model selected in 6.2 or 6.4; and b) variation due to pure error that cannot be accurately repeated by the measurement system. This comparison is possible because each standard sample is measured repeatedly. The choice of significance level depends on the specific circumstances of the application and is determined by the user of this standard. 6.5.2 Constant Residual Standard Deviation Model (see 6.2) 6.5.2.1 The ANOVA table shown in Table 1 can be obtained using the following formula or from the output of most linear regression software packages. Table 1 ANOVA table comparing underfit and pure error under the assumption of constant residual standard deviation Source
Calibration function
Residual error
Underfit error
Pure error
Degrees of freedom F
NK—1
SSE given in 6,2,2
Sum of squares SS
SSR-SST-SSE
SSE---SSP
Mean square SS/DF
SSE-SSH
6.5.2.2 The pure error variance estimate is independent of the model that fits the data (y-β+β), and the underfit variance estimate is 8
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