1、Basic concepts in metrology Evaluating measurements of a single measurand and expression of uncertainty ICs 17.020 - DIN - 1319-3 Descriptors: Metrology, uncertainty, evaluation. Grundlagen der Metechnik - Teil 3: Auswertung von Messungen einer einzelnen Megre, Meunsicherheit This standard, together
2、 with the January 1995 edition of DIN 1319-1, supersedes August 1983 edition. In keeping with current practice in standards published by the International Organization for Standardization (ISO), a comma has been used throughout as the decimal marker. Contents Page Page 1 Scope and field of applicati
3、on . 2 AppendixA Examples of evaluating and expressing measurement results and their uncertainties 14 2 Normative references 2 3 Concepts . 2 Appendix B Computer-assisted evaluations 17 Principles of evaluating measurements Appendix C Limitations of evaluation method . 18 Appendix D The maximum unce
4、rtainty . 18 5 Simplified evaluation of direct measurements 4 Appendix E Symbols used in this standard . 19 6 Evaluating indirect measurements 7 Explanatory notes. . 20 . Foreword The August 1983 edition of this standard has been revised by the Normenausschu Einheiten und Formelgren (Quantities and
5、Units Standards Committee) in order to take into account the publication of the IS0 Guide to the expression of uncertainty in measurement l. The DIN 1319 series of standards comprises the following parts: Part 1 General concepts Part 2 Part 3 Part 4 Terminology relating to the use of measuring instr
6、uments Evaluating measurements of a single measurand and expression of uncertainty Evaluating measurements of more than one measurand and treatment of uncertainty Amendments The following amendments have been made to the August 1983 edition of DIN 1319-3: a) The standard has been revised to take DIN
7、 1319-4 and publication l into account. b) Basic concepts are now defined in DIN 1319-1. Previous editions DIN 1319: 1942-07, 1962-01, 1963-12; DIN 1319-3: 1968-12, 1972-01, 1983-08. Continued on pages 2 to 20. Translation by DIN-Sprachendienst. In case of doubt, the German-language original should
8、be consulted as the authoritative text. O No part of this translation may be reproduced without the prior permission of DIN Deutsches Institut fr Normung e. V., Berlin. Beuth Verlag GmbH, D-10772 Berlin, has the exclusive right of sale for German Standards(D1N-Normen) Ref. Nr. DIN 1319-3: 1996-05 Pr
9、eisgr. 13 Vertr.-Nr. 1113 08.98 Page 2 DIN 131 9-3 : 1996-05 1 Scope and field of application This standard specifies methods of determining the uncertainty of measurements of a single measurand, whether performed directly or derived from measurements of other quantities. It applies by analogy to co
10、mputer-assisted measurements. DIN 131 9-4 covers the evaluation of uncertainty for interlaboratory test comparisons and simultaneous indirect measure- ments of several measurands. 2 Normative references This standard incorporates, by dated or undated reference, provisions from other publications. Th
11、ese normative references are cited at the appropriate place in the text and the titles of the publications are listed below. For dated references, subsequent amendments to or revisions of any of these publications apply to this standard only when incorporated into it by amendment or revision. For un
12、dated references, the latest edition of the publication referred to applies. DIN 1313 DIN 1319-1 DIN 131 9-2 DIN 131 9-4 DIN 1333 DIN 13303-1 DIN 13303-2 DIN 53804-1 DIN 55350-21 DIN 55350-22 DIN 55350-23 DIN 55350-24 Physical quantities and equations - Concepts and nomenclature Basic concepts in me
13、trology - General concepts Basic concepts in metrology - Terminology relating to the use of measuring instruments Basic concepts in metrology - Evaluating measurements of more than one measurand and treatment of uncertainty Presentation of numerical data Probability theory, common fundamental concep
14、ts of mathematical and of descriptive statistics - Concepts and symbols Mathematical statistics - Concepts and symbols Statistical evaluation - Measurable (continuous) characteristics Terminology in quality assurance and statistics - Concepts relating to random variables and probability distribution
15、s Terminology in quality assurance and statistics - Concepts relating to special probability distributions Terminology in quality assurance and statistics - Concepts relating to descriptive statistics Terminology in quality assurance and statistics - Concepts relating to inferential statistics IS0 3
16、534-1 : 1993 Statistics -Vocabulary and symbols - Part 1 : Probability and general statistical terms l Guide to the Expression of Uncertainty in Measurement. Geneva: International Organization for Standardization, 1993. 2 (BSI) PD 6461 -1 : 1995 Vocabulary of metrology - Part 1: Basic and general te
17、rms (international) (French/English). (Identical with International vocabulary of basic and general terms in metrology (VIM) published by IS0 in 1993; German/English version also available*). 3 Weise, K. and Wger, W., A Bayesian theory of measurement uncertainty. Meas. Sci. Technol., 1993: 4, 1-1 1.
18、 3 Concepts General metrological concepts are defined in DIN 1319-1. For further definitions, see IS0 3534-1 and publications l and 2. Translators note. Much of the terminology used in this translation has been taken from the English language version of l. 3.1 Meacurand Physical quantity subject to
19、measurement (from DIN 1319-1). NOTE: Although the output quantity (cf. subclause 3.2) is normally considered to be the measurand, the input quantities (cf. subclause 3.3) -especially influence quantities and calibration factors - may also be viewed as measurands in many cases. 3.2 Output quantity (o
20、f an evaluation) Quantity (.e. measurand) representing the outcome of the evaluation of measurement results. Denoted in this standard and l as Y, with its estimate being denoted by y. To be differentiated from the output quantity of measuring instruments (cf. DIN 1319-1, subclause 4.9). 3.3 Input qu
21、antity (of an evaluation) Any quantity, including influence quantities, used in the evaluation of a measurement. Denoted in this standard and l as X, while estimates of input quantities are denoted by X. To be differentiated from the input quantity of measuring instruments (cf. DIN 1319-1, subclause
22、 4.8). *) Obtainable from Beuth Verlag GrnbH, Burggrafenstrae 6, D-10787 Berlin. Page 3 DIN 1319-3 : 1996-05 3.4 Model (of an evaluation) An equation (e.g. function) describing the mathematical relationships between all quantities involved in the evaluation of a measurement. 3.5 Uncertainty (of meas
23、urement) Parameter obtained from measurements and which -together with the result of measurement - is an estimate of the range within which the true value of the measurand lies (cf. l and DIN 1319-1). NOTE 1: Uncertainty is a measure of the accuracy of a measurement and represents the extent to whic
24、h the value of the measurand cannot be known 3. NOTE 2: The uncertainty of measurement is to be distinguished from the error of measurement, which is the deviation of a measured value from the true value of the measurand. The error can be equal to zero, without this being known. This unknown factor
25、is expressed by the uncertainty, which is always positive. NOTE 3: In general, uncertainty can also be associated with a quantity that is not the measurand, Y. When the uncertainty is expressed in terms of a standard deviation, it is called the standard uncertainty l (cf. subclauses 5.3 and 6.2.1).
26、The standard uncertainty has the same dimension as the measurand. The uncertainty of measurement can also be a single component of a combined uncertainty (cf. subclause 3.6). NOTE 4: For other parameters describing the accuracy of a measurement, see subclause 5.4.2 and Appendix D. 3.6 Combined uncer
27、tainty For the purposes of this standard, the uncertainty of the results obtained for a pair of quantities. It describes the range of values within which the true values of the two quantities will lie. NOTE: This range of values is two-dimensional. The combined uncertainty is a measure of the mutual
28、 dependence of the two quantities and may relate to other quantities than the measurand. 3.7 Estimate The value of an estimator obtained as result of an estimation (quoted from IS0 3534-1). 3.8 Estimator A statistic used to estimate a population (quoted from IS0 3534-1). 4 Principles of evaluating m
29、easurements 4.1 Objective of a measurement The objective of every measurement is to determine the true value of the measurand as nearly as possible. For definitions relating to measuring equipment, measuring procedures and objects of measurement, see DIN 1319-1. Measurements can also be simulated wi
30、th the help of a computer. The evaluation of results and other relevant data is an aspect of every measurement. A standardized method of evaluating measurements allows the effective comparison and processing of results. Given the numerous factors, or influence quantities (cf. DIN 1319-l), that can h
31、ave an effect on the measurement, errors of measurement cannot be avoided. For this reason, the true value of a measurand cannot in practice be precisely known. The measurement result actually serves as an estimate,y, of the true value of the measurand, Y, and is always expressed together with its a
32、ssociated uncertainty, uk), in what is referred to in this standard as the complete expression of results. Measurements in which the result for the measurand is displayed by the measuring instrument are sometimes referred to as direct measurements. The evaluation of a series of direct measurements,
33、based on a simple mathematical model and considering the systematic error, is described in clause 5. In most cases, however, the results are obtained by means of an indirect measurement involving the direct or indirect measurement of several input quantities. The calculation of the complete result o
34、f such measurements involves setting up a more complex model describing the relationships between all input quantities, influence quantities and systematic errors. This type of evaluation is described in clause 6. 4.2 The four steps of evaluation It is recommended that evaluations of both direct and
35、 indirect measurements be performed in the following four steps: 1. Set up a mathematical model that describes the relationship of all relevant quantities, including input and influence 2. Prepare the measured results, as well as all other available data. 3. Calculate the result and uncertainty of m
36、easurement based on the prepared data and established model. 4. Draw up a complete expression of results, giving the output quantity and its associated uncertainty. quantities. Page 4 DIN 131 9-3 : 1996-05 5 Simplified evaluation of direct measurements 5.1 Setting up the model Often, the measurand Y
37、 is directly measured in several independent measurements performed under prescribed repeatability conditions. The systematic error, which is a result of the various influence quantities, is accounted for in the evaluation. In this case, a simplified mathematical model will suffice. Let input quanti
38、ty XI be the uncorrected indication and input quantity X, the systematic error. The output quantity (here, the measurand), Y, is then the corrected indication, as shown in equation (l), which is the model for the evaluation: 5.2 Preparation of data 5.2.1 The results of a series of n measurements, uJ
39、 (where j = 1 ,., n) will be dispersed due to the effect of random quantities on the measurement. Such results are therefore considered to be realisations of a random variable, V, attributed to XI. Each random variable is associated with a probability distribution that is characterized by the expect
40、ed value, p, and the standard deviation, u(or variance, 4). However, XI is not itself a random variable and therefore is not equal to V. The expected value p is equal to the true value of XI; where there is no systematic error (.e. X, = O), it is also equal to the true value of the measurand, Y. The
41、 standard deviation is a measure of the dispersion of single results around the expected value, or of the dispersion of the random errors around zero. Since the expected value and standard deviation are not precisely known, the next step in the evaluation is to find estimates for these parameters ba
42、sed on the set of measured values, uJ. Normally, the mean of results, V, (calculated as in equation (2) is taken as the estimate for p (and consequently also for XI): Mean and standard deviation of results where x1 is the uncorrected result of measurement (.e. estimate for XI). The experimental stan
43、dard deviation of the mean, S, serves as the estimate for u (cf. equation (3). (For other means of calculating these parameters, see DIN 53804-1 .) Because the measured values are realisations of V, their mean, E, can deviate randomly from the expectation, p; likewise, the experimental standard devi
44、ation, S, can deviate from u, the standard deviation. Thus, V and s are also realisations of random variables and are treated as estimators. Let V be the estimate, xl, for XI; the uncertainty, u(x,), is then given by the empirical standard deviation of the mean, s(V), as shown in equation (4): The u
45、ncertainty of XI (that is, the expected value, p) thus decreases with an increasing number of results. If the systematic error cannot be disregarded, then u(x1) is only one component of the uncertainty for measurand Y. If the experimental standard deviation, so, of the distribution of results has al
46、ready been established in several earlier measurements carried out on the same or a similar measurand under the same conditions, then equation (5) can be used where there is a limited number of results, n: Ubi) = Sg / Jn (5) 5.2.2 Systematic error The systematic error comprises a known and an unknow
47、n component (cf. DIN 1319-1). The known component serves as an estima te, for the systematic error, for this reason, there is always a certain amount of uncertainty associated with the systematic error (.e. (x,). Even when the correction is equal to zero, and therefore does not appear in the result
48、of measurement, this uncertainty still remains (cf. subclause 3.5 Note 2). Whether or not u(x,) can be ignored is to be decided on a case-by-case basis; it is normally represented by the standard deviation of the distribution of values that can reasonably be attributed to the systematic error. In an
49、y case, the actual value of the systematic error cannot be precisely known. As opposed to the distribution of the random variable Vwhich describes the distribution of measured values, the distribution of the random variable W represents the distribution of possible - but not precisely established - values for the systematic error; thus, W serves as an estimate of X,. Page 5 DIN 1319-3 : 1996-05 The estimated systematic error, x, and its uncertainty, U(X,), can be calculated using the equations given in subclause 6.2.5. For instance, if it
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