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GB/T 27419-2018 English PDF

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GB/T 27419-2018: Guide to the evaluation and expression of uncertainty in measurement -- Supplement 1: Propagation of distributions using a Monte Carlo method
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GB/T 27419-20181404 Add to Cart 5 days Guide to the evaluation and expression of uncertainty in measurement -- Supplement 1: Propagation of distributions using a Monte Carlo method Valid

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Basic data

Standard ID: GB/T 27419-2018 (GB/T27419-2018)
Description (Translated English): Guide to the evaluation and expression of uncertainty in measurement -- Supplement 1: Propagation of distributions using a Monte Carlo method
Sector / Industry: National Standard (Recommended)
Classification of Chinese Standard: A50
Classification of International Standard: 17.020
Word Count Estimation: 74,736
Date of Issue: 2018-05-14
Date of Implementation: 2018-12-01
Regulation (derived from): National Standards Announcement No. 6 of 2018
Issuing agency(ies): State Administration for Market Regulation, China National Standardization Administration

GB/T 27419-2018: Guide to the evaluation and expression of uncertainty in measurement -- Supplement 1: Propagation of distributions using a Monte Carlo method


---This is a DRAFT version for illustration, not a final translation. Full copy of true-PDF in English version (including equations, symbols, images, flow-chart, tables, and figures etc.) will be manually/carefully translated upon your order.
Guide to the evaluation and expression of uncertainty in measurement--Supplement 1. Propagation of distributions using a Monte Carlo method ICS 17.020 A50 National Standards of People's Republic of China Measurement Uncertainty Assessment and Representation Supplementary Document 1. Distribution propagation based on Monte Carlo method (ISO /IEC Guide 98-3/Suppl.1.2008, Uncertaintyofmeasurement-Part 3. Published on.2018-05-14 2018-12-01 implementation State market supervision and administration China National Standardization Administration issued

Content

Foreword V Introduction VII 1 Scope 1 2 Normative references 2 3 Terms and Definitions 2 4 conventions and symbols 5 5 Basic Principles 6 5.1 Main stage of uncertainty assessment 6 5.2 Distribution spread 7 5.3 Obtaining Report Information 7 5.4 Implementation of distributed communication 8 5.5 Report Results 8 5.6 GUM uncertainty framework 9 5.7 GUM uncertainty framework effective conditions for linear models 10 5.8 GUM uncertainty framework effective conditions for nonlinear models 10 5.9 Distribution and Results Reporting Based on Monte Carlo Method 11 5.10 Conditions for Effective Use of MCM 12 5.11 Comparison of GUM uncertainty framework and Monte Carlo method 13 6 probability density function of input quantity 14 6.1 Overview 14 6.2 Bayesian theory 14 6.3 Principle of Maximum Information Entropy 15 6.4 Determination of the probability density function under common conditions 15 6.4.1 Overview 15 6.4.2 Rectangular distribution 16 6.4.3 Rectangular distribution with uncertain boundary values 17 6.4.4 Trapezoidal distribution 17 6.4.5 Triangle distribution 18 6.4.6 Arcsine (U-shaped) distribution 19 6.4.7 Normal distribution 19 6.4.8 Multivariate normal distribution 19 6.4.9 t distribution 20 6.4.10 Exponential distribution 21 6.4.11 Gamma distribution 22 6.5 Determining the probability distribution from previous uncertainty calculations 22 7 Monte Carlo method of calculation 22 7.1 Overview 22 7.2 Monte Carlo test times 22 7.3 Sampling from the probability distribution 23 7.4 Calculation of the model 23 7.5 Discrete representation of the output distribution function 23 7.6 Estimated output and its standard uncertainty 24 7.7 Output range includes 24 7.8 Calculation time 24 7.9 Adaptive Monte Carlo Program 25 7.9.1 Overview 25 7.9.2 Value tolerances associated with a value 25 7.9.3 Purpose of the adaptive procedure 25 7.9.4 Adaptive procedure 26 8 Verification of results 27 8.1 Verification of the GUM uncertainty framework using the Monte Carlo method 27 8.2 Acquisition of Monte Carlo method results based on verification purposes 27 9 Case 27 9.1 Description of relevant aspects of this standard 27 9.2 Addition model 28 9.2.1 Formula 28 9.2.2 Input quantity obeys normal distribution 28 9.2.3 Inputs are subject to a rectangular distribution of the same width 30 9.2.4 Inputs are subject to a rectangular distribution of different widths 31 9.3 Weight Calibration 33 9.3.1 Equation 33 9.3.2 Communication and reporting results 34 9.4 Comparison loss of microwave power meter calibration 35 9.4.1 Equation 35 9.4.2 Communication and Reporting Results. Zero Covariance 36 9.4.3 Communication and reporting results. non-zero covariance 40 9.5 Gauge Block Calibration 42 9.5.1 Equation 42 9.5.2 Formula. Determination of distribution 43 9.5.3 Communication and reporting results 46 9.5.4 Result 46 Appendix A (informative) Historical Perspectives 48 Appendix B (informative) Sensitivity and uncertainty contribution 49 Appendix C (informative) Sample 50 from the probability distribution Appendix D (informative) Continuous approximation of the output distribution function 55 Appendix E (informative) The quadratic convolution of the rectangular distribution contains the interval 57 Appendix F (informative) Comparative loss problem 58 Appendix G (informative appendix) Main symbol summary table 61 References 64

Foreword

This standard was drafted in accordance with the rules given in GB/T 1.1-2009. This standard uses the translation method equivalent to ISO /IEC Guide 98-3/Suppl.1.2008 "Measurement uncertainty - Part 3. Measurement Guide to Uncertainty Representation (GUM..1995) Supplementary Document 1. Distribution Propagation Based on the Monte Carlo Method. This standard has the following editorial changes compared to ISO /IEC Guide 98-3/Suppl.1.2008. --- Modified the standard name. This standard is proposed and managed by the National Certification and Accreditation Standardization Technical Committee (SAC/TC261). This standard was drafted. China Metrology University, China Institute of Metrology, Zhejiang Institute of Metrology, Shanghai Metrology and Testing Research Institute, Guangzhou Institute of Metrology and Measurement Technology, Hangzhou Quality and Technology Supervision and Inspection Institute, Binzhou College, Shaanxi Institute of Metrology, China Measurement (Beijing) Institute of Inspection and Testing. The main drafters of this standard. Song Mingshun, Gao Wei, Shao Li, Xu Shengjian, Fang Xinghua, Zhou Lubin, Tong Jun, Huang Lefu, Wang Wei, Zhang Junliang, Yin Zhijun.

Introduction

0.1 Overview This standard is a supplement to the “Guidelines for the Expression of Measurement Uncertainty” (GUM), mainly through the establishment of measurement models, using Monte Carlo The method (abbreviation. MCM) performs probability distribution propagation and evaluates the measurement uncertainty [ISO /IEC Guide 98-3.2008, 3.1.6]. The The method is applied to models with multiple inputs and a single output. In the following two cases, it is valuable to use MCM instead of GUM uncertainty framework for uncertainty evaluation [ISO /IEC Guide98-3..2008, 3.4.8]. a) a nonlinear model; b) The probability density function (PDF) of the output clearly deviates from the normal distribution or the t-distribution, such as a significant asymmetry in the distribution. In a), the estimation of the output and its standard uncertainty using the method in the GUM uncertainty framework may be unreliable; In b), use the method in the GUM uncertainty framework to get the inclusion interval of the output (ie, the extension in the GUM uncertainty framework) The degree of certainty" may not be practical. GUM [ISO /IEC Guide 98-3.2008, 3.4.8] "provides a method for assessing uncertainty" based on uncertainty Degree propagation law [ISO /IEC Guide 98-3.2008, Chapter 5] and characterization of output with normal distribution or t-distribution [ISO /IEC Guide98- 3.2008, G.6.2, G.6.4]. In this method, the uncertainty propagation law provides a method for propagation uncertainty through the model. specifically, It gives the best estimate of the output and the standard uncertainty under the following conditions. a) the best estimate of each input; b) the standard uncertainty of the estimated values of each input; c) the degree of freedom associated with these standard uncertainties, where possible; d) Non-zero covariance between inputs. In this method, the inclusion interval under the specific inclusion probability of the output is given by the PDF of the output. The best estimate, standard uncertainty, covariance, and degrees of freedom are the information available for the input. The method in this standard, the input amount The information available is the input quantity PDFs, which is the PDF of the output volume obtained by the transmission of the input quantity PDFs. Given the limitations of the GUM uncertainty framework, distributed propagation always yields output consistent with the input PDFs. PDF. The input quantity of PDFs describes the knowledge of the input quantity, and the output quantity PDF determined by the input quantity knowledge describes the output quantity. knowledge. Once the output PDF is obtained, the output can use its expectation, its best estimate, and its standard deviation, ie the standard The quasi-uncertainty is summarized; and the inclusion interval of the output with the given probability can be obtained from the PDF. The use of PDFs in this standard is consistent with the concept implicit in GUM. A quantity of PDF indicates the knowledge state of the quantity, ie It quantitatively reflects the degree of credibility that is given to the quantity based on the available information. These available information usually include raw statistics, measurements Volume results or other relevant scientific descriptions and professional judgments. In order to construct a quantity of PDF, Bayesian theory can be applied based on a series of observations of this quantity [27, 33]; For proper information about system effects, an appropriate PDF can be determined using the principle of maximum information entropy [51, 56]. Distribution propagation has a wider range of applications than the GUM uncertainty framework. It takes advantage of the best estimate and standard uncertainty (More effective degrees of freedom and covariance, as appropriate). Decimal point symbol. The decimal point symbol is represented by the dot in the English version of the text, and is indicated by the period in the French version. (see 4.12) Appendix A gives some perspectives based on history. Note 1. GUM gives a method when linearization is insufficient [ISO /IEC Guide 98-3.2008, 5.1.2 Note]. The drawback of this method is. only used The main nonlinear term in the model Taylor series expansion, and the input is considered to be a normal distribution. Note 2. Strictly, GUM characterizes the statistical properties of the variable (Yy)/u(y) with a t-distribution, where Y is the output, y is the estimated value of Y, and u(y) is the estimate. The standard uncertainty of the value y [ISO /IEC Guide 98-3.2008, G.3.1]. This feature is also applicable in this standard. [Actually, GUM The medium variable is (yY)/u(y). ] Note 3. A quantity of PDF cannot be understood as frequency density. Note 4. “Uncertainty assessment is neither procedural nor purely mathematical. It depends on the properties being measured, the measurement methods and procedures used, etc. Detailed knowledge. Therefore, the quality and utility of the uncertainty quoted by the measurement depends on the understanding of the information contributing to the assessment, a rigorous analysis and Its integrity. "[17] 0.2 JCGM Background Information Since.1993, the "Guide to Measurement Uncertainty" has been developed (Guidetotheexpressionofuncertaintyinmeasure- Ment, GUM) and "International vocabulary basic terms" (Internationalvocabularyofbasicandgeneraltermsin Metrology, VIM), seven international organizations, founded the Joint Commission on Metrology Guidelines in.1997 (JointCommitteefor GuidesinMetrology, JCGM), by the Bureau of International Bureau of Metrology (BureauInternationaldesPoidsetMesures, BIPM) The long-term chairman. JCGM took over the development of these two standards from ISO 's Fourth Technical Advisory Group (TAG4). The Joint Commission is composed of BIPM and the International Electrotechnical Commission (IEC ). International Federation of Clinical Chemistry (International Federation of Clinical Chemistry and Laboratory Medicine, IFCC), International Laboratory Accreditation Cooperation (ILAC), International Standard International Organization for Standardization (ISO ), International Union of Theoretical and Applied Chemistry (Interna- tionUnionofPureandAppliedChemistry, IUPAC), International Union of Theoretical and Applied Physics (InternationalU- nionofPureandAppliedPhysics, IUPAP) and the International Organization of Legal Metrology (InternationalOrganizationof LegalMetrology, OIML) and other organizations. JCGM has two working groups. The first working group is the “Measurement Uncertainty Representation Working Group”, and the task is to promote the use and system of GUM. Add supplemental files and files from other GUM extension applications. Working Group II is working on the International Generalized Metrology Terminology (VIM) Add GUM supplemental documents including this standard to provide an assessment of uncertainty not explicitly addressed in GUM The guidance of the aspect enhances the value of GUM. These additional guidelines will be as consistent as possible with the common probabilistic basis in GUM. Measurement Uncertainty Assessment and Representation Supplementary Document 1. Distribution propagation based on Monte Carlo method

1 Scope

This standard provides a general numerical method for the measurement uncertainty assessment, which is consistent with the GUM general principle. [ISO /IEC Guide 98-3.2008, G.1.5]. Suitable for multiple inputs and single outputs that can be characterized by specific PDFs Volume model [ISO /IEC Guide 98-3.2008, G.1.4, G.5.3]. As in GUM, this standard mainly deals with physically defined quantities—that is, measured values that can be characterized by unique values. Representation of uncertainty [ISO /IEC Guide 98-3..2008, 1.2]. This standard is also unsatisfied or unable to determine whether the GUM uncertainty framework condition is met [ISO /IEC Guide 98-3.2008, G.6.6] provides guidance on the uncertainty assessment. It can be used to make the GUM uncertainty framework difficult to apply, such as the complexity of the model. Case. This standard gives a method guide for computer execution. This standard obtains a PDF of the output and determines the following parameters. a) an estimate of the output; b) the standard uncertainty of the estimate; c) The inclusion interval of the output corresponding to the given inclusion probability. Known (i) the relationship model between input and output, (i) input quantity PDFs, then the output has a unique PDF. Usually output The amount of PDF cannot be determined analytically. Therefore, the purpose of this method in this standard is to. without introducing a non-quantitative approximation, The above a), b) and c) are determined within the specified numerical tolerances. For a given inclusion probability, this standard can be used to determine the corresponding inclusion interval, including the interval of the probability symmetry and the shortest Contains intervals. This standard applies to two types of inputs, one of which is independent of each other and can be characterized by an appropriate PDF; The other type is that the inputs are not independent of each other, ie some or all of these inputs can be characterized by a joint PDF. This standard applies to the uncertainty of assessing the following typical conditions. --- The magnitude of each uncertainty component is not similar [ISO /IEC Guide 98-3.2008, G.2.2]; --- When applying the uncertainty propagation law, it is difficult or inconvenient to calculate the partial derivative of the model [ISO /IEC Guide 98-3.2008, Chapter 5]; --- The output of the PDF is not a normal distribution or t distribution [ISO /IEC Guide98-3.2008, G.6.5]; --- The estimated value of the output is approximately the same as its standard uncertainty [ISO /IEC Guide 98-3.2008, G.2.1]; --- Model is complex [ISO /IEC Guide98-3.2008, G.1.5]; --- Asymmetry of PDFs for each input [ISO /IEC Guide 98-3.2008, G.5.3]. This standard provides a verification method to check whether the GUM uncertainty framework is applicable. Apparently suitable in the GUM uncertainty framework In the case of use, it is still the main method of uncertainty assessment. It is usually sufficient to keep one or two significant figures for the uncertainty report. This standard gives a calculation guide, reasonable assurance basis The valid figures reported by the provided information are correct. This standard provides a detailed case description. This standard is a supplement to GUM and should be used in conjunction with GUM. Other methods that are basically consistent with GUM can also be used instead. this The standard user is the same as the GUM user. Note 1. This standard does not consider the case of a model that is not a single output (for example, a solution involving a quadratic equation, and no root is specified). Note 2. This standard does not consider the situation in which the output a priori PDF can be obtained, but the treatment method of this standard is applicable to this case [16].

2 Normative references

The following documents are indispensable for the application of this document. For dated references, only dated versions apply to this article. Pieces. For undated references, the latest edition (including all amendments) applies to this document. ISO /IEC Guide 98-3.2008 Measurement uncertainty - Part 3. Guidance guide to measurement uncertainty (GUM..1995) [Uncertaintyofmeasurement-Part 3. Guidetotheexpressionofuncertaintyin measurement (GUM..1995)] ISO /IEC Guide 99.2007 International Metrology Vocabulary Basic and General Concepts and Related Terminology (VIM) [Internationalvo- cabularyofmetrology-Basicandgeneralconceptsandassociatedterms(VIM)]

3 Terms and definitions

Unless otherwise stated, this standard uses the terms and definitions in ISO /IEC Guide 98-3 and ISO /IEC Guide 99. among them The definitions most relevant to this standard in the above documents are given below (see 4.2). More definitions are also given below, including from other collars. An definition adopted by the domain and important to this standard. A summary of the main symbols is given in Appendix G. 3.1 Probability distribution probabilitydistribution Gives a (random variable) function that takes a random variable to take any given value or a probability that takes a given set. Note. The probability that a random variable takes all the values in the set is equal to 1. [quoted from ISO 3534-1..19931.3; ISO /IEC Guide 98-3..2008, C.2.3] Note 1. When the probability distribution is related to a single (scalar) random variable, it is called a univariate probability distribution; if the probability distribution is related to multiple random variables, it is called Multivariate probability distribution. Multivariate probability distributions can also be referred to as joint distributions. Note 2. A probability distribution can be in the form of a distribution function or a probability density function. 3.2 Distribution function distributionfunction For each value ξ, a function is given for the probability that the random variable X is less than or equal to ξ, which is. GX(ξ)=Pr(X≤ξ) [quoted from ISO 3534-1..19931.4; GUM..1995 C.2.4] 3.3 Probability density function probabilitydensityfunction The derivative of the distribution function, if the derivative exists, the function is. gX(ξ)=dGX(ξ)/dξ Note. gX(ξ)dξ is the “probability unit”. gX(ξ)dξ=Pr(ξ \u003cX\u003cξ dξ) [quoted from ISO 3534-1..19931.5; ISO /IEC Guide 98-3..2008, C.2.5] 3.4 Normal distribution normaldistribution The probability distribution of the continuous random variable X, whose probability density function is. gX(ξ)= σ 2π Exp - (ξ-μ 2é Êê Úú , -¥< ξ< ¥ Note. μ is the expectation of the random variable X, and σ is the standard deviation of the random variable X. [quoted from ISO 3534-1..19931.37; ISO /IEC Guide 98-3..2008, C.2.14] Note. Normal distribution is also known as Gaussian distribution. 3.5 t distribution t-distribution The probability distribution of the continuous random variable X, whose probability density function is. gX(ξ)= Γ......
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