1、Designation: E 2536 06Standard Guide forAssessment of Measurement Uncertainty in Fire Tests1This standard is issued under the fixed designation E 2536; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of last revision. A nu
2、mber in parentheses indicates the year of last reapproval. Asuperscript epsilon (e) 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. Ever
3、y measurement 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 i
4、s unknown, 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 measu
5、rement 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 ef
6、fect 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 r
7、educed 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 desc
8、ribed 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.ey 2 Y (1)where:e = measurement error;y = measured value of the measurand; andY = true value of the measurand.1. S
9、cope1.1 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. The use in this process of precision dataobtained from a round robin is also discussed.1.2 Application o
10、f this guide is limited to tests that providequantitative results in engineering units. This includes, forexample, methods for measuring the heat release rate ofburning specimens based on oxygen consumption calorimetry,such as Test Method E 1354.1.3 This guide does not apply to tests that provide re
11、sults inthe form of indices or binary results (for example, pass/fail).For example, the uncertainty of the Flame Spread Indexobtained according to Test Method E84cannot be determined.1.4 In some cases additional guidance is required to supple-ment this standard. For example, the expression of uncert
12、aintyof heat release rate measurements at low levels requiresadditional guidance and uncertainties associated with samplingare not explicitly addressed.1.5 This fire standard cannot be used to provide quantitativemeasures.1This guide is under the jurisdiction ofASTM Committee E05 on Fire Standardsan
13、d is the direct responsibility of Subcommittee E05.31 on Terminology andEditorial.Current edition approved Dec. 1, 2006. Published January 2007.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.2. Referenced Documents2.1 ASTM Standards
14、:2E84 Test Method for Surface Burning Characteristics ofBuilding MaterialsE 176 Terminology of Fire StandardsE 230 Specification and Temperature-Electromotive Force(EMF) Tables for Standardized ThermocouplesE 691 Practice for Conducting an Interlaboratory Study toDetermine the Precision of a Test Me
15、thodE 1354 Test Method for Heat and Visible Smoke ReleaseRates for Materials and Products Using an Oxygen Con-sumption Calorimeter2.2 ISO Standards:3ISO/IEC 17025 General requirements for the competence oftesting and calibration laboratoriesGUM Guide to the expression of uncertainty in measure-ment3
16、. Terminology3.1 Definitions: For definitions of terms used in this guideand associated with fire issues, refer to the terminologycontained in Terminology E 176. For definitions of terms usedin this guide and associated with precision issues, refer to theterminology contained in Practice E 691.3.2 D
17、efinitions 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 ofthe measurand.3.2.2 combined standard uncertainty, nstandard uncer-tainty of the result of a measurement when that result isobtained from
18、 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 quantities weightedaccording to how the measurement result varies with changesin these quantities.3.2.3 coverage factor, nnumerical factor used
19、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 value of the measurand; error consists of twocomponents: random error and systematic error.3.2.5 expanded uncertainty, nquantity defini
20、ng 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 to the measurand.3.2.6 measurand, nquantity subject to measurement.3.2.7 precision, nvariability of test result measurementsaround repo
21、rted 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 carried out under repeatabilityconditions.3.2.9 repeatability (of results of measurements),ncloseness of the agreement between the result
22、s of succes-sive independent measurements of the same measurand carriedout under repeatability conditions.3.2.10 repeatability conditions, non identical test materialusing the same measurement procedure, observer(s), andmeasuring instrument(s) and performed in the same laboratoryduring a short perio
23、d 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 under reproducibilityconditions.3.2.12 reproducibility conditions, non identical test ma-terial using the same measurement procedure, but
24、differentobserver(s) and measuring instrument(s) in different laborato-ries performed during a short period of time.3.2.13 standard deviation, na quantity characterizing thedispersion of the results of a series of measurements of thesame measurand; the standard deviation is proportional to thesquare
25、 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 measurement expressed as a standard deviation.3.2.15 systematic error (or bias), nmean that would resultfrom an infinite number of measuremen
26、ts 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 ofevaluation of uncertainty by the statistical analysis of series ofobservations.3.2.17 type B evaluation (of uncertainty), nmethod ofevaluatio
27、n 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 a measurement, that characterizes thedispersion of the values that could reasonably be attributed tothe measurand.4. Summary of Guide4.
28、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 example toillustrate application of this guide by assessing the uncertaintyof heat release rate measured in the Cone Calorimeter (TestMeth
29、od E 1354).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. Thisquantitative indication is referred to as the “measurementuncertainty”. There are two primary reasons for estimating theuncertainty of fire t
30、est results.5.1.1 ISO/IEC 17025 requires that competent testing andcalibration laboratories include uncertainty 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
31、 of the analysis.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 Document Summary page onthe ASTM website.3Available from International Organization f
32、or Standardization, P.O. Box 56,CH-1211, Geneva 20, Switzerland.E25360626. Evaluating Standard Uncertainty6.1 A quantitative result of a fire test Y is generally notobtained 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 = measu
33、rand;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 quantities whose values and uncertainties are di-rectly determined from single observation, repeated observa-tion or judgment based on
34、 experience, or6.1.1.2 quantities whose values and uncertainties arebrought into the measurement from external sources such asreference data obtained from handbooks.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 x
35、1,x2,., xN! (3)Substituting Eq 2 and 3 into Eq 1 leads to:y 5 Y 1e5Y 1e11e21 . 1eN(4)where:e1= contribution to the total measurement error from theerror associated with xi.6.2 A possible approach to determine the uncertainty of yinvolves a large number (n) of repeat measurements. The meanvalue of th
36、e 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, denoted byu(y):uy! =s2y! 5s2y!n5(k51nyk2 y!2nn 2 1!(5)where:u = standard uncertainty,s = experimental standard deviation,n = numb
37、er 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 the expectation yof therandom variable y, and that s2( y ) provides a reliable estimateof the variance s2( y )=s(y)/n. If the prob
38、ability 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 ) 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 no
39、t feasible or even possible toperform a sufficiently large number of repeat measurements. Inthose cases, the uncertainty of the measurement can bedetermined by combining the standard uncertainties of theinput estimates. The standard uncertainty of an input estimatexiis obtained from the distribution
40、 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 standard uncertaintyA type Aevaluation of standard uncertainty of xiis based on thefrequency distribution, which is estimated fro
41、m 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; andxi= 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
42、 xiisnot based on repeated measurements but on an a priorifrequency distribution. In this case the uncertainty is deter-mined from previous measurements data, experience or generalknowledge, manufacturers specifications, data provided incalibration certificates, uncertainties assigned to reference d
43、atataken 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 standard deviation, the standard uncertainty uc(xi)is simply the quoted value divided by the multiplier. Forexample, the quoted uncert
44、ainty 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 value.6.3.2.3 Often the uncertainty is expressed in the form ofupper and lower limits. Usually there is no specific knowledgeabout
45、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 corre-sponding rectangular distribution is symmetric with respect toits best estimate xi. The standard uncertainty in this case i
46、sgiven by:uxi! 5DXi=3(7)where:DXi= half-width of the interval.FIG. 1 Rectangular DistributionE2536063If some information is known about the distribution of thepossible values of Xiwithin the interval, that knowledge is usedto better estimate the standard deviation.6.3.3 Accounting for multiple sourc
47、es 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 equatio
48、n:uxi! 5(j51mujxi!#2(8)where:m = number of sources of error affecting the uncertainty ofxi; anduj, = standard uncertainty due to jthsource of error.7. Determining Combined Standard Uncertainty7.1 The standard uncertainty of y is obtained by appropri-ately combining the standard uncertainties of the
49、input esti-mates x1, x2, xN. If all input quantities are independent, thecombined standard uncertainty of y is given by:ucy! 5(i5lNFfXi|xiG2u2xi! (i5lNciuxi!#2(9)where:uc= combined standard uncertainty, andci,= sensitivity coefficients.Eq 9 is referred to as the law of propagation of uncertainty andbased on a first-order Taylor series approximation of Y = f (X1,X2,XN). When the nonlinearity of f is significant, higher-order terms must be included (see clause 5.1.2 in the GUM fordetails).7.2 When the input quantities a
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