1、Designation: E2655 14 An American National StandardStandard Guide forReporting Uncertainty of Test Results and Use of the TermMeasurement Uncertainty in ASTM Test Methods1This standard is issued under the fixed designation E2655; the number immediately following the designation indicates the year of
2、original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon () indicates an editorial change since the last revision or reapproval.1. Scope1.1 This guide provides concepts necessary for understand-ing t
3、he term “uncertainty” when applied to a quantitative testresult. Several measures of uncertainty can be applied to agiven measurement result; the interpretation of some of thecommon forms is described.1.2 This guide describes methods for expressing test resultuncertainty and relates these to standar
4、d statistical methodol-ogy. Relationships between uncertainty and concepts of preci-sion and bias are described.1.3 This guide also presents concepts needed for a labora-tory to identify and characterize components of method per-formance. Elements that an ASTM method can include toprovide guidance t
5、o the user on estimating uncertainty for themethod are described.1.4 The system of units for this guide is not specified.Dimensional quantities in the guide are presented only asillustrations of calculation methods and are not binding onproducts or test methods treated.1.5 This standard does not pur
6、port to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to establish appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:2E2
7、9 Practice for Using Significant Digits in Test Data toDetermine Conformance with SpecificationsE122 Practice for Calculating Sample Size to Estimate, WithSpecified Precision, the Average for a Characteristic of aLot or ProcessE177 Practice for Use of the Terms Precision and Bias inASTM Test Methods
8、E456 Terminology Relating to Quality and StatisticsE691 Practice for Conducting an Interlaboratory Study toDetermine the Precision of a Test MethodE1402 Guide for Sampling DesignE2554 Practice for Estimating and Monitoring the Uncer-tainty of Test Results of a Test Method Using ControlChart Techniqu
9、esE2586 Practice for Calculating and Using Basic Statistics2.2 Other Standard:ISO/IEC 17025 General Requirements for the Competenceof Testing and Calibration Laboratories33. Terminology3.1 Definitions:3.1.1 Additional statistical terms are defined in TerminologyE456.3.1.2 accepted reference value, n
10、a value that serves as anagreed-upon reference for comparison, and which is derivedas: (1) a theoretical or established value, based on scientificprinciples, (2) an assigned or certified value, based on experi-mental work of some national or international organization, or(3) a consensus or certified
11、 value, based on collaborativeexperimental work under the auspices of a scientific orengineering group. E1773.1.3 error of result, na test result minus the acceptedreference value of the characteristic.3.1.4 expanded uncertainty, U, nuncertainty reported as amultiple of the standard uncertainty.3.1.
12、5 random error of result, na component of the errorthat, in the course of a number of test results for the samecharacteristic, varies in an unpredictable way.3.1.5.1 DiscussionUncertainty due to random error can bereduced by averaging multiple test results.3.1.6 sensitivity coeffcient, ndifferential
13、 effect of thechange in a factor on the test result.1This guide is under the jurisdiction of ASTM Committee E11 on Quality andStatistics and is the direct responsibility of Subcommittee E11.20 on Test MethodEvaluation and Quality Control.Current edition approved Oct. 1, 2014. Published October 2014.
14、 Originallyapproved in 2008. Last previous edition approved in 2008 as E2655 08. DOI:10.1520/E2655-14.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStandards volume information, refer to the standards
15、Document Summary page onthe ASTM website.3Available from American National Standards Institute (ANSI), 25 W. 43rd St.,4th Floor, New York, NY 10036, http:/www.ansi.org.Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States13.1.7 standard unc
16、ertainty, u, nuncertainty reported as thestandard deviation of the estimated value of the quantitysubject to measurement.3.1.8 systematic error of result, na component of the errorthat, in the course of a number of test results for the samecharacteristic, remains constant or varies in a predictable
17、way.3.1.8.1 DiscussionSystematic errors and their causes maybe known or unknown. When causes are known, systematicerror can sometimes be reduced by incorporating correctionsinto the calculation of the test result.3.1.9 uncertainty, nan indication of the magnitude of errorassociated with a value that
18、 takes into account both systematicerrors and random errors associated with the measurement ortest process.3.1.10 uncertainty budget, na tabular listing of uncer-tainty components for a given measurement process giving themagnitudes of contributions to uncertainty of the result fromthose sources.3.1
19、.11 uncertainty component, na source of error in a testresult to which is attached a standard uncertainty.4. Significance and Use4.1 Part A of the “Blue Book,” Form and Style for ASTMStandards, introduces the statement of measurement uncer-tainty as an optional part of the report given for the resul
20、t ofapplying a particular test method to a particular material.4.2 Preparation of uncertainty estimates is a requirement forlaboratory accreditation under ISO/IEC 17025. This guidedescribes some of the types of data that the laboratory can useas the basis for reporting uncertainty.5. Concepts for Re
21、porting Uncertainty of Test Results5.1 Uncertainty is part of the relationship of a test result tothe property of interest for the material tested. When a testprocedure is applied to a material, the test result is a value fora characteristic of the material. The test result obtained willusually diff
22、er from the actual value for that material. Multiplecauses can contribute to the error of result. Errors of samplingand effects of sample handling make the portion actually testednot identical to the material as a whole. Imperfections in thetest apparatus and its calibration, environmental, and huma
23、nfactors also affect the result of testing. Nonetheless, aftertesting has been completed, the result obtained will be used forfurther purposes as if it were the actual value. Reportingmeasurement uncertainty for a test result is an attempt toestimate the approximate magnitude of all these sources of
24、error. In common cases the measurement will be reported in theform x 6 u, in which x represents the test result and urepresents the uncertainty associated with x.5.2 Practice E177 describes precision and bias. Uncertaintyis a closely related but not identical concept. The primarydifference between c
25、oncepts of precision and of uncertainty isthe object that they address. Precision (repeatability andreproducibility) and bias are attributes of the test method. Theyare estimates of statistical variability of test results for a testmethod applied to a given material. Repeatability and interme-diate
26、precision measure variation within a laboratory. Repro-ducibility refers to interlaboratory variation. Uncertainty is anattribute of the particular test result for a test material. It is anestimate of the quality of that particular test result.5.3 In the case of a quantity with a definition that doe
27、s notdepend on the measurement or test method (for example,concentration, pH, modulus, heat content), uncertainty mea-sures how close it is believed the measured value comes to thequantity. For results of test methods where the target is onlydefinable relative to the test method (for example, flash
28、points,extractable components, sieve analysis), uncertainty of a testresult must be interpreted as a measure of how closely anindependent, equally competent test result would agree withthat being reported.5.4 In the simplest cases, uncertainty of a test result isnumerically equivalent to test method
29、 precision. That is, if anunknown sample is tested, and the test precision is known to besigma, then uncertainty of the result of test is sigma. The termuncertainty, however, is correct to apply where variation ofrepeated test results is not relevant, as in the followingexamples.5.4.1 ExampleThe New
30、tonian constant of gravitation, G,is 6.6742 10-116 0.0010 10-11m3kg-1s-2based on 2002CODATA recommended values (1).40.0010 10-11m3kg-1s-2is the standard uncertainty. The value and the uncertaintytogether represent the state of knowledge of this fundamentalphysical constant. It is not naturally thoug
31、ht of in terms ofvariation of repeated measurements. Both G and its uncertaintyare derived from the analysis and comparison of a variety ofmeasurement data using methods that are an elaboration ofthose presented in this guide.5.4.2 ExampleA length is measured but the result onlyreported to the neare
32、st inch (for example, a measuring rodgraduated in inches was used to obtain the measurement).Precision of the reported value, in the sense of variation ofrepeated measurements, is zero when all reported lengths arethe same. In this case it is not possible to detect randomvariation in the series of r
33、epeated measurements. Uncertaintyof the length is primarily composed of the systematic error of60.5 inch due to the resolution of the measurement apparatus.5.5 The goal in reporting uncertainty is to take account of allpotential causes of error in the test result. In many cases,uncertainty can be re
34、lated to components of variability due tosampling and to testing. Both of these should be taken intoaccount for the uncertainty of the measurement when thepurpose of the result is to estimate the property for the entire lotof material from which the sample was taken. Uncertainty ofthe lot property v
35、alue based on a single determination is then=s121s221u32, where s1is an estimate of the sampling standarddeviation, s2is an estimate of the standard deviation of the testmethod, and u3is standard uncertainty due to factors that affectall measurements under consideration.5.6 A commonly cited definiti
36、on (2, 3) defines uncertaintyas “a parameter, associated with the measurement result, or testresult, that characterizes the dispersion of values that could4The boldface numbers in parentheses refer to the list of references at the end ofthis standard.E2655 142reasonably be attributed to the quantity
37、 subject to measurementor characteristic subject to test.” This definition emphasizesuncertainty as an attribute of the particular result, as opposed tostatistical variation of test results. The uncertainty parameter isa measure of spread (for example, the standard deviation) of aprobability distrib
38、ution used to represent the likelihood ofvalues of the property.55.7 The methodology for uncertainty estimates has beenclassified as Type A and Type B as discussed in (4). Type Aestimates of uncertainty include standard error estimates basedon knowledge of the statistical character of observations,
39、andbased on statistical analysis of replicate measurements. Type Bestimates of uncertainty include approximate values derivedfrom experience with measurement processes similar to the onebeing considered, and estimates of standard uncertainty de-rived from the range of possible measurement values for
40、 agiven material and an assumed distribution of values withinthat range. See Practice E122 for examples (for example,rectangular, triangular, normal) where a standard deviation isderived from a range without data from samples being avail-able. Complex estimates of test result uncertainty are calcu-l
41、ated by combining Type A and Type B component standarduncertainties for factors contributing to error (see Section 8).5.8 Forms of Uncertainty Expression:5.8.1 Standard UncertaintyThe uncertainty is reported asthe standard deviation of the reported value. The report x 6 uimplies that the value shoul
42、d be between x u and x + u withapproximate probability two-thirds, where x is the test result.5.8.2 Relative Standard UncertaintyThe uncertainty isreported as a fraction of the reported value. For a measuredvalue and a standard uncertainty, x 6 u, the relative standarduncertainty is u/x. This method
43、 of expressing uncertainty maybe useful when standard uncertainty is proportional to the valueover a wide range. However, for a particular result, reportingthe value and standard uncertainty is preferred.5.8.3 Expanded UncertaintyThe uncertainty is reported asx 6 U, where the value of U is a multipl
44、e of the standarduncertainty u. The most common multiple used is 2, which isapproximately equal to the 1.96 factor for a 95 % two-sidedconfidence interval for the mean of a normal distribution (see5.8.4).5.8.4 Confidence IntervalsA confidence interval for aparameter (the actual value of the material
45、 property subject tomeasurement) consists of upper and lower limits generatedfrom sample data by a method that ensures the limits bracketthe parameter value with a stated probability 1-, referred to asthe confidence coefficient.5.8.4.1 From statistical theory, a 95 % confidence intervalfor the mean
46、of a normal distribution, given n independentobservations x1, x2, xndrawn from the distribution, is xH6ts/=n where x is the sample mean, s is the standard deviationof the observations, and t is the 0.975 percentile of theStudents t distribution with n-1 degrees of freedom. BecauseStudents t distribu
47、tion approaches the Normal as n increases,the value of t approaches 1.96 as n increases. This is the basisfor using the factor 2 for expanded uncertainty.5.8.4.2 Practice E2586 defines confidence intervals andprovides additional detail on their interpretation.5.8.5 Measurement UncertaintyMeasurement
48、 uncertaintyis uncertainty reported for a test result without taking intoaccount sampling variation or heterogeneity of the material ofinterest. The report of measurement uncertainty then refersspecifically to the particular sample presented for analysis.5.8.6 Reporting Uncertainty with a Bias Compo
49、nentGoodmeasurement practice requires that biases due to environmentaland other factors should be corrected in the reported resultwhen there is a sound basis for correction and the error in thecorrection terms themselves is not greater than the bias. Suchcorrections are part of the calculation of the result within thetest method. The symmetrical form of reporting a measurementwith standard uncertainty, x 6 u, is adequate for measurementswhere bias is absent or corrected. If the measurement processhas a bias for which there is an estimate of magnit
