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National Metrology Technical Specification of the People's Republic of China JJF1135--2005
Evaluation of Uncertainty in Chemical Analysis Measurement2005-09-05Published
200512-05Implemented
Published by the General Administration of Quality Supervision, Inspection and QuarantineJJF11352005
Evaluation of Uncertainty in Chemical Analysis Measurement
Evaluation of Uncertainty in Chemical Analysis Measurement
JJF1135—2005
This specification was approved by the General Administration of Quality Supervision, Inspection and Quarantine on September 5, 2005, and will be implemented on December 5, 2005
Responsible unit:
Drafting unit:
National Technical Committee for Physical and Chemical Metrology
National Center for Standardized Materials
This specification is under the responsibility of the National Technical Committee for Physical and Chemical Metrology. The main drafters of this specification are:
Ni Xiaoli
Participating drafters:
Shao Mingwu
Lu Xiaohua
Song Xiaoping
JJF 1135—2005
(National Research Center for Standardized Materials)
(National Research Center for Standardized Materials)
(National Research Center for Standardized Materials)
(National Research Center for Standardized Materials)
Scope of Application+
References
Basic Terms and Definitions
JJF 1135—2005
Main sources of uncertainty in chemical analysis measurement results 4.1
Description of the measured object
Sample preparation
Choice of reference materials for the measurement system
Instrument verification/calibration
Analytical measurement
Data processing
Procedure for evaluating the uncertainty of chemical analysis measurement results 5.1
Detailed description of the measured object
Identification of sources of uncertainty
Quantification of uncertainty
Calculation of the combined standard uncertainty
5.5 Determination of the expanded uncertainty
6 Expression of the results of the uncertainty evaluation for chemical measurements 1 Expression of standard uncertainty
6.2 Expression by expanded uncertainty
6.3 Effective mathematical expression of uncertainty of measurement result
Appendix A. Schematic diagram of uncertainty evaluation procedure for chemical analysis measurement Appendix B. Distribution function and standard uncertainty calculation Appendix B. Distribution function and standard uncertainty calculation at different confidence probabilities and degrees of freedom (values) (1)
JJF 1135—2005
Evaluation of uncertainty in chemical analysis measurement
This technical specification follows the basic principles of the Guide to the Expression of Uncertainty in Measurement (CUM) and the Guide to the Evaluation of Uncertainty in Chemical Analysis (EURACHEMCITAC Guide Quantifying Uncertainty in Analytical Measurement), combines the characteristics of chemical analysis measurement, and establishes an evaluation model from the perspective of scientificity, standardization and practicality to standardize the evaluation and expression methods of chemical analysis measurement uncertainty. 1 Scope of application
This specification is applicable to chemical analysis measurements with all accuracy requirements and various fields from basic research to routine analytical measurement. For example:
a) Establishment of national chemical metrology base, standards and international comparison; 6) Development of reference materials;
c) Development and evaluation of chemical measurement methods, capability verification; 1) Verification/calibration of chemical analysis instruments, type evaluation; e) Chemical measurement research, development and product inspection; ) Quality control and quality assurance in scientific research and production, etc. 2 References
JF1059-1999 "Evaluation and Expression of Uncertainty in Measurement" JF1001-1998 "General Metrology Terms and Definitions" JJF1071-2000 "Rules for the Preparation of National Measurement Calibration Specifications" EURACHEM/CITAC Guide Quuritifying Uncertainty in Analytical Measurementrnent (Guidelines for the Evaluation of Uncertainty in Chemical Analysis)
IS0 5725 Accuracy of measurement methods and results When using this specification, the current valid versions of the above references should be used. 3 Basic terms and definitions
3.1 Uncertainty [of measurement] Characterizes the dispersion of the values that can reasonably be attributed to the measurand, a parameter associated with the measurement result. Note:
1 This prime number can be, for example, the standard deviation (or its multiple), or describes the half-width of a confidence interval. 2 Measurement uncertainty consists of several components, some of which can be estimated from the statistical distribution of the measurement results and are characterized by the experimental standard deviation. Other components are estimated using probability distributions assumed based on experience or other information and are also characterized by standard deviations. 3 The measurement result should be understood as the best estimate of the value of the measurand, with all uncertainty components contributing to the dispersion, including those introduced by systematic effects, such as those associated with corrections and reference measurement standards. 3.2 Standard uncertainty u(x) standard uncertainty The uncertainty of a measurement result expressed in terms of standard deviation. 1
J.FF1135—2005
3.3 Type A evaluation of uncertainty (Type A uncertainty evaluation) uxtypeAevaluation of uncertainty The standard uncertainty is evaluated by a method other than a statistical analysis of the observation series. 3.4 Type B evaluation of uncertainty (Type B uncertainty evaluation) \typeBevaiuationofuncertainty The standard uncertainty is evaluated by a method other than a statistical analysis of the observation series. 3.5 Combined standard uncertainty When the measurement result is obtained from the values of several other quantities, the standard uncertainty is calculated by combining the variance and covariance of the other quantities.
3.6 Expanded uncertainty/rxpandedlumcertainty The quantity that determines the range of the measurement result, and the reasonable assumption that the distribution of the values of the measured value is expected to be included in this interval. :
1 This part can be used as the coverage rate or confidence interval. 2 In order to relate the specific risk level to the interval defined by the expanded uncertainty, it is necessary to clearly state or explain the assumptions underlying the measurement results and the probability distribution represented by the combined standard uncertainty. The confidence level assigned to this interval can only be understood to the extent that these assumptions are correct.
3 Combined standard uncertainty 4, and the included expanded uncertainty 3.7 Inclusion factor crveragefaclor
The numerical factor by which the combined standard uncertainty is multiplied to obtain the expanded uncertainty. Note:
1 The inclusion factor is equal to the ratio of the expanded uncertainty to the combined standard uncertainty. 2 The inclusion factor is generally 2 or 3.
3.8 Degrees of freedom
In the calculation of variance, the number of terms in the sum minus the number of restrictions. 3.9 Confidence level pconfidence level; level of confidence probability value related to confidence interval or statistical inclusion interval: 3.10 Arithmetic mean xarithnetic mean (or average) arithmetic mean of a limited number of measurement results.
experimental standand deviation sexperimental standand deviation 3.111
The standard deviation of π measurement results is an estimate of the population standard deviation. The quantity that characterizes the dispersion of the measurement results when n measurements are made on the same measured object can be calculated as follows: Where: ——the result of the nth measurement;
%——the arithmetic mean of n measurements:
3.12 Standard deviation of the mean s yuan standlard deviatian ot average2
JJF 11352005
The standard deviation of the mean x of n independent results taken from the population is: n
3.13Relative standard deviation HS
related standard deviation
Experimental standard deviation divided by the mean value of the sample. Often expressed as coefficient of variation (CV), also often expressed as a percentage, RSD =
4Main sources of uncertainty in chemical analysis measurement results$
General analytical measurement process: Description of the object to be measured - Sampling - Sample preparation
- Selection of standard materials (CRM) for the measurement system - Instrument verification/calibration - Analytical measurement - Data acquisition - Data processing Result presentation and necessary description,
4.1 Description of the object to be measured
a) Incomplete understanding of the object to be measured, such as the lack of a precise structural description of the substance to be measured; b) Sample homogeneity and stability.
4.2 Sampling
a) Sample representativeness:
h) Effects of specific sampling methods (e.g. random, directional, etc.);
c) Effects of sample movement (e.g. density);
d) Physical state of matter (solid, liquid, gas);
f) Effects of sampling process on components (e.g. different adsorption in the sampling system). 4.3 Sample preparation
a) Effects of homogeneous and/or secondary sampling:
c) Pulverization;
d) Dissolution;
e) Extraction;
f) Contamination (particularly prominent in quantitative analysis);
h) Inactivation (biological samples);
i) Dilution;
j) Enrichment;
k) Weighing and panning equipment;
1) Effects of environmental conditions or measurements.
4.4 Selection of standard materials for measurement system a) Uncertainty of standard materials;
bh) Matching of standard materials with samples.
4.5 Instrument verification/calibration
a) Instrument verification/calibration process;
JJF 1135--2005
b) Verification/calibration standard materials and their uncertainty; d) Matching of samples with verification/calibration standard materials; d) Instrument repeatability and reproducibility.
4.6 Analytical measurement
) Limitations of the analytical method itself;
b) Response lag of the analyzer:
c) Resolution, sensitivity, stability, noise level, instrument bias, etc. of the instrument:
d) Effects of operation (such as color difference, parallax and other system effects);
e) Effects of interference, background subtraction, reagents or other analytes:
g) Instrument parameter settings (such as integration parameters);
h) Repeatability of analytical measurement:
i) Random effects in the analytical process.
4.7 Data processing
a) Obtaining average values (such as arithmetic mean, median, etc.);
b) Reference, conversion constants or other parameters;
c) Data rounding;
dl Statistics:
e) Certain approximations and assumptions in the analytical method and process;
f) Selection of processing mathematical models (such as linear least squares method). The contribution of all these factors affecting uncertainty to the total uncertainty needs to be comprehensively analyzed and evaluated. However, sometimes these four factors are not necessarily independent, so the contribution of the influence of each other on the uncertainty must be considered, that is, covariance must be considered.
5 Uncertainty evaluation process of chemical analysis measurement 5.1 Detailed description of the measured quantity
On the basis of a comprehensive understanding of the measurement process, clarify the relationship between the measured quantity and the input quantity it depends on (such as the measured quantity, constant, calibration standard value, etc.). Determine the relationship between the measured quantity and its parameters, and make corrections for known systematic effects. Establish a functional relationship between the measured object and the input quantity: \(,,,), then the uncertainty is given by the uncertainty of each input quantity such as \, 2,,, etc. Pay attention to the influence of the function or correction factor on the measurement result. a) For parameter measurements with definite physical meanings and classical chemical analysis measurements. The measurement process has a definite measurement model or mathematical model. In this case, the uncertainty can be calculated or estimated based on the model and the uncertainty propagation method.
For example: Use potassium hydrogen phthalate standard substance to calibrate the concentration of sodium hydroxide solution. Then: 4
JJF 1135—2005
1 000mxl*Pkr (mol/L)
CNaOH -
MxHP·V
Ekson—--Concentration of NaOH solution, mol/L; where:
1000---Conversion coefficient from mL to L.; mrHp—Mass basis of potassium hydrogen phthalate standard substance, name; P--Purity of potassium hydrogen phthalate standard substance,; MxHp——Molar mass of potassium hydrogen phthalate standard substance, gmol; V.—Titration volume of NaOH solution, mL. (1)
h) In instrumental analysis, some measured quantities are estimated by comparison with corresponding standard substances, and the measurement mathematical model can be obtained according to the influencing quantity.
For example, in gas chromatography analysis, to measure the molar fraction of a certain alkane gas, use the same type of gas standard material with the most similar content to calibrate the gas chromatograph (for example, measure the chromatographic peak area), then use the calibrated gas chromatograph to measure the gas (measure the chromatographic peak area), the measured value is: A
Csample=CvalueAvalue
where: C is the molar fraction of the gas to be measured; C is the molar fraction of the gas standard material (known); A is the chromatographic peak area of the standard gas;
A is the chromatographic peak area of the gas to be measured. (2)
c) In instrumental analysis, some measurements first use a series of standard materials with different concentrations to make a working curve, then measure the sample and obtain its value, and then build a mathematical model. For example, to determine the concentration of a solution by atomic absorption spectroscopy, first use five standard solutions with different concentrations to fit a working curve of concentration and absorbance. The equation is: A= R,α+ P,www.bzxz.net
or: A——absorbance of the solution; concentration of the solution; B, slope of the standard line; B, intercept of the standard curve. From the above formula, we can get: Using the original absorption spectrometer to measure the absorbance of the solution to be measured, the concentration of the solution to be measured can be obtained by formula (3). If it is difficult to establish a functional relationship, it is necessary to estimate the influence of these quantities on the measured quantity through experiments or other means, and integrate them to give the uncertainty of the measured quantity. 5.2 Identify the sources of uncertainty List possible sources of uncertainty, including sources that contribute to the uncertainty of the parameters in the above relationship, and may also include other sources, especially those produced by chemical assumptions. S JJF1135-2005 It is also possible to draw a cause-and-effect diagram of the relevant uncertainty sources for easy identification and verification. For example, potassium hydrogen phthalate standard substance is used to calibrate sodium hydroxide solution. The concentration of the liquid, the cause-and-effect diagram of the related uncertainty sources is shown in Figure 1.
Reproducibility
5.3 Quantitative uncertainty
+Reduction
Measure or estimate the size of each identified uncertainty component. Estimate the contribution of each component to the combined uncertainty. According to the measurement requirements, components with a contribution less than 1/10 of the maximum component can be discarded to simplify the list of uncertainty components.
5.3.1 Evaluation of standard uncertainty type A
The uncertainty component estimated from the dispersion experiment of repeated measurements, the standard uncertainty (u) of a single measurement result is characterized by the experimental standard deviation s(). For the averaged results, the standard uncertainty of the mean [μ, (using the standard deviation of the mean value |s(). The calculation formula is as follows: s(x))
5.3.2 Evaluation of standard uncertainty type B
ux=s(x)
5(2)= 3(α)
()=s(x)
Class B uncertainty generally does not require repeated observation of the measured value under statistical control (repeatability or reproducibility conditions) but is evaluated based on existing information. The general calculation formula for Class B uncertainty evaluation is as follows: ug=cloud
Where:
Half-width of the interval of possible values of the measured value:
Inclusion factor.
Where: The information sources are:
Previous measurement data;
Experience and general knowledge:
Technical instructions;
J.JF 1135—2005
——Calibration certificate, verification certificate, test report and other materials;——Manual reference materials.
a) If the uncertainty estimate U (,) derived from the results and data given in the relevant technical data is times the standard deviation, and the size of the coverage factor is specified, then the standard uncertainty () = (,. b) If the uncertainty estimate is a confidence interval under a confidence probability (expressed as ± under p%), it is generally considered according to the normal distribution, and the standard uncertainty () = (),, where the relationship between the confidence probability and the coverage factor is shown in Table 1. Table 1 Relationship between confidence probability and coverage factor * under normal distribution.
) If only ± upper and lower limits are given without confidence level, and it is assumed that each value is equally likely to fall anywhere between the upper and lower limits, that is, rectangular distribution or uniform distribution, the standard deviation is e (,)a. d) If only ±u upper and lower limits are given without confidence level, but if the probability of the measured value occurring near the center of the range from ±u to ±u is known, it is generally assumed to be a blue angle distribution with a standard deviation of 2h (x) = ut6.
e) The calculation of the standard uncertainty estimate of the most common distribution function in chemical measurements is shown in Appendix B. f) In the documentation of these methods, according to the specified measurement conditions, when the repeatability limit of the difference between two measurement results of the same laboratory and the reproducibility limit R of the difference between the average values of the measurement results of two laboratories are clearly stated, the standard uncertainty of the measurement result is: z(x,) = r/2.83 or u() = R/2.83 (see IS05725Aceurayufmeasure-mcnt methods and results).
5.4 Calculation of combined standard uncertainty
On the basis of the above quantitative standard analysis, determine the specific contribution of each uncertainty component to the total uncertainty. Regardless of whether these contributions are related to a single uncertainty source or the combined effect of several uncertainty sources, they should be converted into standard deviations and combined according to the combination rules to give the combined standard uncertainty. When the measured quantity has only one influencing factor, then: (x,)=/ +u
When the measured quantity is the coefficient of ten directly measured quantities x,2,…,, that is, =x,,,), then:
u(x) +2
Where: (y)——standard uncertainty of af.
-u.(x,)
tli-t+
JJF 1135—2005
u（a;)——standard uncertainty of x;
(,)—covariance between and.
When x: 稚, are independent of each other, then
u(y) =
According to the above formula, the uncertainty synthesis formulas corresponding to formulas (1), (2), and (3) are: \\
u(cor)
-{“[
Change formula (14) to: SR=
In the formula:
T[A, - (B。+ Bie,)J
Number of measurements of the measured solution:
Number of measurements of the five standard solutions:
Concentration value of the standard solution:
Measured value of the absorbance of the standard solution;
Average value of the standard solution concentration.
1 In formula (14), a standard solution with a concentration of , is prepared, and the absorbance A,,,A, is measured m times. The fitting drop is regarded as m points (e, A), (e, An). So the total number of fitting points is nzo2. The condition for the validity of formula (14) is that the influence of the uncertainty of the standard concentration can be neglected: as long as the most direct measurement x is obtained, by analyzing the uncertainty of type A and type B, t () can be obtained, and the uncertainty of the sensitive measurement can be obtained,
5.5 Expanded uncertainty is given by
Multiply () by the coverage factor of the "probability" to obtain the expanded uncertainty U. U=ku
The value is related to the degree of freedom and the confidence probability P, (16)
is given by the critical value of the t distribution (referred to as t value, see Appendix C), =t, μ), and has nothing to do with the distribution of r. When y is close to the normal distribution, the p value is generally 95% or 99%. For most measurements, p = 95%, k = 2; for measurements that meet the highest benchmark or high quality requirements, P = 99%, k = 3 can be used. 6. Representation of chemical analysis measurement results
When a complete analytical measurement result is given, the measurement result and its uncertainty should be reported so that the user can correctly
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