1、Designation: E2536 09Standard Guide forAssessment of Measurement Uncertainty in Fire Tests1This standard is issued under the fixed designation E2536; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of last revision. A numb
2、er in parentheses indicates the year of last reapproval. Asuperscript epsilon () indicates an editorial change since the last revision or reapproval.INTRODUCTIONThe objective of a measurement is to determine the value of the measurand, that is, the physicalquantity that needs to be measured. Every m
3、easurement is subject to error, no matter how carefullyit is conducted. The (absolute) error of a measurement is defined in Eq 1.All terms in Eq 1 have the units of the physical quantity that is measured. This equation cannot beused to determine the error of a measurement because the true value is u
4、nknown, otherwise ameasurement would not be needed. In fact, the true value of a measurand is unknowable because itcannot be measured without error. However, it is possible to estimate, with some confidence, theexpected limits of error. This estimate is referred to as the uncertainty of the measurem
5、ent andprovides a quantitative indication of its quality.Errors of measurement have two components, a random component and a systematic component.The former is due to a number of sources that affect a measurement in a random and uncontrolledmanner. Random errors cannot be eliminated, but their effec
6、t on uncertainty is reduced by increasingthe number of repeat measurements and by applying a statistical analysis to the results. Systematicerrors remain unchanged when a measurement is repeated under the same conditions. Their effect onuncertainty cannot be completely eliminated either, but is redu
7、ced by applying corrections to accountfor the error contribution due to recognized systematic effects. The residual systematic error isunknown and shall be treated as a random error for the purpose of this standard.General principles for evaluating and reporting measurement uncertainties are describ
8、ed in theGuide on Uncertainty of Measurements (GUM). Application of the GUM to fire test data presentssome unique challenges. This standard shows how these challenges can be overcome. An example toillustrate application of the guidelines provided in this standard can be found in Appendix X1.y 2 Y (1
9、)where: = measurement error;y = measured value of the measurand; andY = true value of the measurand.1. Scope1.1 This guide covers the evaluation and expression ofuncertainty of measurements of fire test methods developedand maintained byASTM International, based on the approachpresented in the GUM.
10、The use in this process of precision dataobtained from a round robin is also discussed.1.2 The guidelines presented in this standard can also beapplied to evaluate and express the uncertainty associated withfire test results. However, it may not be possible to quantify theuncertainty of fire test re
11、sults if some sources of uncertaintycannot be accounted for. This problem is discussed in moredetail in Appendix X2.1.3 Application of this guide is limited to tests that providequantitative results in engineering units. This includes, forexample, methods for measuring the heat release rate ofburnin
12、g specimens based on oxygen consumption calorimetry,such as Test Method E1354.1.4 This guide does not apply to tests that provide results inthe form of indices or binary results (for example, pass/fail).For example, the uncertainty of the Flame Spread Indexobtained according to Test Method E84 canno
13、t be determined.1.5 In some cases additional guidance is required to supple-ment this standard. For example, the expression of uncertaintyof heat release rate measurements at low levels requiresadditional guidance and uncertainties associated with samplingare not explicitly addressed.1.6 This fire s
14、tandard cannot be used to provide quantitativemeasures.1This guide is under the jurisdiction ofASTM Committee E05 on Fire Standardsand is the direct responsibility of Subcommittee E05.31 on Terminology andServices / Functions.Current edition approved Oct. 1, 2009. Published November 2009. Originally
15、approved in 2006. Last previous edition approved in 2006 as E2536-06. DOI:10.1520/E2536-09.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.1.7 The values stated in SI units are to be regarded asstandard. No other units of measurement
16、 are included in thisstandard.2. Referenced Documents2.1 ASTM Standards:2E84 Test Method for Surface Burning Characteristics ofBuilding MaterialsE119 Test Methods for Fire Tests of Building Constructionand MaterialsE176 Terminology of Fire StandardsE230 Specification and Temperature-Electromotive Fo
17、rce(EMF) Tables for Standardized ThermocouplesE691 Practice for Conducting an Interlaboratory Study toDetermine the Precision of a Test MethodE1354 Test Method for Heat and Visible Smoke ReleaseRates for Materials and Products Using an Oxygen Con-sumption Calorimeter2.2 ISO Standards:3ISO/IEC 17025
18、General requirements for the competence oftesting and calibration laboratoriesGUM Guide to the expression of uncertainty in measure-ment3. Terminology3.1 Definitions: For definitions of terms used in this guideand associated with fire issues, refer to the terminologycontained in Terminology E176. Fo
19、r definitions of terms usedin this guide and associated with precision issues, refer to theterminology contained in Practice E691.3.2 Definitions of Terms Specific to This Standard:3.2.1 accuracy of measurement, ncloseness of the agree-ment between the result of a measurement and the true value ofth
20、e measurand.3.2.2 combined standard uncertainty, nstandard uncer-tainty of the result of a measurement when that result isobtained from the values of a number of other quantities, equalto the positive square root of a sum of terms, the terms beingthe variances or covariances of these other quantitie
21、s weightedaccording to how the measurement result varies with changesin these quantities.3.2.3 coverage factor, nnumerical factor used as a mul-tiplier of the combined standard uncertainty in order to obtainan expanded uncertainty.3.2.4 error (of measurement), nresult of a measurementminus the true
22、value of the measurand; error consists of twocomponents: random error and systematic error.3.2.5 expanded uncertainty, nquantity defining an inter-val about the result of a measurement that may be expected toencompass a large fraction of the distribution of values thatcould reasonably be attributed
23、to the measurand.3.2.6 measurand, nquantity subject to measurement.3.2.7 precision, nvariability of test result measurementsaround reported test result value.3.2.8 random error, nresult of a measurement minus themean that would result from an infinite number of measure-ments of the same measurand ca
24、rried out under repeatabilityconditions.3.2.9 repeatability (of results of measurements),ncloseness of the agreement between the results of succes-sive independent measurements of the same measurand carriedout under repeatability conditions.3.2.10 repeatability conditions, non identical test materia
25、lusing the same measurement procedure, observer(s), andmeasuring instrument(s) and performed in the same laboratoryduring a short period of time.3.2.11 reproducibility (of results of measurements), ncloseness of the agreement between the results of measure-ments of the same measurand carried out und
26、er reproducibilityconditions.3.2.12 reproducibility conditions, non identical test ma-terial using the same measurement procedure, but differentobserver(s) and measuring instrument(s) in different laborato-ries performed during a short period of time.3.2.13 standard deviation, na quantity characteri
27、zing thedispersion of the results of a series of measurements of thesame measurand; the standard deviation is proportional to thesquare root of the sum of the squared deviations of themeasured values from the mean of all measurements.3.2.14 standard uncertainty, nuncertainty of the result ofa measur
28、ement expressed as a standard deviation.3.2.15 systematic error (or bias), nmean that would resultfrom an infinite number of measurements of the same measur-and carried out under repeatability conditions minus the truevalue of the measurand.3.2.16 type A evaluation (of uncertainty), nmethod ofevalua
29、tion of uncertainty by the statistical analysis of series ofobservations.3.2.17 type B evaluation (of uncertainty), nmethod ofevaluation of uncertainty by means other than the statisticalanalysis of series of observations.3.2.18 uncertainty of measurement, nparameter, associ-ated with the result of
30、a measurement, that characterizes thedispersion of the values that could reasonably be attributed tothe measurand.4. Summary of Guide4.1 This guide provides concepts and calculation methods toassess the uncertainty of measurements obtained from firetests.4.2 Appendix X1 of this guide contains an exa
31、mple toillustrate application of this guide by assessing the uncertaintyof heat release rate measured in the Cone Calorimeter (TestMethod E1354).5. Significance and Use5.1 Users of fire test data often need a quantitative indica-tion of the quality of the data presented in a test report. Thisquantit
32、ative indication is referred to as the “measurementuncertainty”. There are two primary reasons for estimating theuncertainty of fire test results.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStandards
33、 volume information, refer to the standards Document Summary page onthe ASTM website.3Available from International Organization for Standardization, P.O. Box 56,CH-1211, Geneva 20, Switzerland.E2536 0925.1.1 ISO/IEC 17025 requires that competent testing andcalibration laboratories include uncertaint
34、y estimates for theresults that are presented in a report.5.1.2 Fire safety engineers need to know the quality of theinput data used in an analysis to determine the uncertainty ofthe outcome of the analysis.6. Evaluating Standard Uncertainty6.1 A quantitative result of a fire test Y is generally not
35、obtained from a direct measurement, but is determined as afunction f from N input quantities X1,XN:Y 5 f X1,X2,.,XN! (2)where:Y = measurand;f = functional relationship between the measurand and theinput quantities; andXi= input quantities (i =1N).6.1.1 The input quantities are categorized as:6.1.1.1
36、 quantities whose values and uncertainties are di-rectly determined from single observation, repeated observa-tion or judgment based on experience, or6.1.1.2 quantities whose values and uncertainties arebrought into the measurement from external sources such asreference data obtained from handbooks.
37、6.1.2 An estimate of the output, y, is obtained from Eq 2using input estimates x1, x2,xNfor the values of the N inputquantities:y 5 f x1,x2,., xN! (3)Substituting Eq 2 and 3 into Eq 1 leads to:y 5 Y 15Y 11121 . 1N(4)where:1= contribution to the total measurement error from theerror associated with x
38、i.6.2 A possible approach to determine the uncertainty of yinvolves a large number (n) of repeat measurements. The meanvalue of the resulting distribution ( y ) is the best estimate of themeasurand. The experimental standard deviation of the mean isthe best estimate of the standard uncertainty of y,
39、 denoted byu(y):uy! =s2y! 5s2y!n5(k51nyk2 y!2nn 2 1!(5)where:u = standard uncertainty,s = experimental standard deviation,n = number of observations;yk=kthmeasured value, andy = mean of n measurements.The number of observations n shall be large enough to ensurethat y provides a reliable estimate of
40、the expectation yof therandom variable y, and that s2( y ) provides a reliable estimateof the variance s2( y )=s(y)/n. If the probability distributionof y is normal, then the standard deviation of s ( y ) relative tos ( y ) is approximately 2(n-1)1/2. Thus, for n =10therelative uncertainty of s ( y
41、) is 24 %t, while for n =50itis10%. Additional values are given in Table E.1 in annex E of theGUM.6.3 Unfortunately it is often not feasible or even possible toperform a sufficiently large number of repeat measurements. Inthose cases, the uncertainty of the measurement can bedetermined by combining
42、the standard uncertainties of theinput estimates. The standard uncertainty of an input estimatexiis obtained from the distribution of possible values of theinput quantity Xi. There are two types of evaluations dependingon how the distribution of possible values is obtained.6.3.1 Type A evaluation of
43、 standard uncertaintyA type Aevaluation of standard uncertainty of xiis based on thefrequency distribution, which is estimated from a series of nrepeated observations xi,k(k = 1 n). The resulting equation issimilar to Eq 5:uxi! =s2xi! 5s2xi!n5(k51nxi,k2 xi!2nn 2 1!(6)where:xi,k=kthmeasured value; an
44、dxi= mean of n measurements.6.3.2 Type B evaluation of standard uncertainty:6.3.2.1 A type B evaluation of standard uncertainty of xiisnot based on repeated measurements but on an a priorifrequency distribution. In this case the uncertainty is deter-mined from previous measurements data, experience
45、or generalknowledge, manufacturers specifications, data provided incalibration certificates, uncertainties assigned to reference datataken from handbooks, etc.6.3.2.2 If the quoted uncertainty from a manufacturer speci-fication, handbook or other source is stated to be a particularmultiple of a stan
46、dard deviation, the standard uncertainty uc(xi)is simply the quoted value divided by the multiplier. Forexample, the quoted uncertainty is often at the 95 % level ofconfidence.Assuming a normal distribution this corresponds toa multiplier of two, that is, the standard uncertainty is half thequoted v
47、alue.6.3.2.3 Often the uncertainty is expressed in the form ofupper and lower limits. Usually there is no specific knowledgeabout the possible values of Xiwithin the interval and one canonly assume that it is equally probable for Xito lie anywhere init. Fig. 1 shows the most common example where the
48、 corre-FIG. 1 Rectangular DistributionE2536 093sponding rectangular distribution is symmetric with respect toits best estimate xi. The standard uncertainty in this case isgiven by:uxi! 5DXi=3(7)where:DXi= half-width of the interval.If some information is known about the distribution of thepossible v
49、alues of Xiwithin the interval, that knowledge is usedto better estimate the standard deviation.6.3.3 Accounting for multiple sources of errorThe uncer-tainty of an input quantity is sometimes due to multiple sourceserror. In this case, the standard uncertainty associated with eachsource of error has to be estimated separately and the standarduncertainty of the input quantity is then determined accordingto the following equation:uxi! 5(j51mujxi!#2(8)where:m = number of sources of error affecting the uncertainty ofxi; and
