1、Designation: E2536 15E2536 15a An American National StandardStandard 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 revi
2、sion, 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.INTRODUCTIONThe objective of a measurement is to determine the value of the measurand, that is, the physicalquan
3、tity that needs to be measured. Every 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
4、measurement because the true value is 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 referre
5、d to as the uncertainty of the measurement 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 error
6、s cannot be eliminated, but their effect 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 co
7、mpletely eliminated either, but is reduced 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 reportin
8、g measurement uncertainties are described 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 standa
9、rd can be found in Appendix X1.y 2Y (1)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 of uncertainty of measurements of fire test methods developed andmaintained byASTM International, base
10、d on the approach presented in the GUM.The use in this process of precision data obtainedfrom a round robin is also discussed.1.2 The guidelines presented in this standard can also be applied to evaluate and express the uncertainty associated with fire testresults. However, it may not be possible to
11、 quantify the uncertainty of fire test results if some sources of uncertainty cannot beaccounted for. This problem is discussed in more detail in Appendix X2.1.3 Application of this guide is limited to tests that provide quantitative results in engineering units. This includes, for example,methods f
12、or measuring the heat release rate of burning specimens based on oxygen consumption calorimetry, such as Test MethodE1354.1 This guide is under the jurisdiction of ASTM Committee E05 on Fire Standards and is the direct responsibility of Subcommittee E05.31 on Terminology and Services/ Functions.Curr
13、ent edition approved Jan. 1, 2015Oct. 1, 2015. Published January 2015November 2015. Originally approved in 2006. Last previous edition approved in 20142015as E2536-14.E2536-15. DOI: 10.1520/E2536-15.10.1520/E2536-15A.This document is not an ASTM standard and is intended only to provide the user of a
14、n ASTM standard an indication of what changes have been made to the previous version. Becauseit may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current versionof the standard as publi
15、shed by ASTM is to be considered the official document.Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States11.4 This guide does not apply to tests that provide results in the form of indices or binary results (for example, pass/fail). Fore
16、xample, the uncertainty of the Flame Spread Index obtained according to Test Method E84 cannot be determined.1.5 In some cases additional guidance is required to supplement this standard. For example, the expression of uncertainty of heatrelease rate measurements at low levels requires additional gu
17、idance and uncertainties associated with sampling are not explicitlyaddressed.1.6 This fire standard cannot be used to provide quantitative measures.1.7 The values stated in SI units are to be regarded as standard. No other units of measurement are included in this standard.2. Referenced Documents2.
18、1 ASTM Standards:2E84 Test Method for Surface Burning Characteristics of Building MaterialsE119 Test Methods for Fire Tests of Building Construction and MaterialsE176 Terminology of Fire StandardsE230 Specification and Temperature-Electromotive Force (EMF) Tables for Standardized ThermocouplesE691 P
19、ractice for Conducting an Interlaboratory Study to Determine the Precision of a Test MethodE1354 Test Method for Heat and Visible Smoke Release Rates for Materials and Products Using an Oxygen ConsumptionCalorimeter2.2 ISO Standards:3ISO/IEC 17025 General requirements for the competence of testing a
20、nd calibration laboratoriesGUM Guide to the expression of uncertainty in measurement2.3 CEN Standard:4EN 13823 Reaction to fire tests for building products Building products excluding floorings exposed to the thermal attack bya single burning item3. Terminology3.1 Definitions: For definitions of ter
21、ms used in this guide and associated with fire issues, refer to the terminology containedin Terminology E176. For definitions of terms used in this guide and associated with precision issues, refer to the terminologycontained in Practice E691.3.2 Definitions of Terms Specific to This Standard:3.2.1
22、accuracy of measurement, ncloseness of the agreement between the result of a measurement and the true value of themeasurand.3.2.2 combined standard uncertainty, nstandard uncertainty of the result of a measurement when that result is obtained fromthe values of a number of other quantities, equal to
23、the positive square root of a sum of terms, the terms being the variances orcovariances of these other quantities weighted according to how the measurement result varies with changes in these quantities.3.2.3 coverage factor, nnumerical factor used as a multiplier of the combined standard uncertaint
24、y in order to obtain anexpanded uncertainty.3.2.4 error (of measurement), nresult of a measurement minus the true value of the measurand; error consists of twocomponents: random error and systematic error.3.2.5 expanded uncertainty, nquantity defining an interval about the result of a measurement th
25、at may be expected toencompass a large fraction of the distribution of values that could reasonably be attributed to the measurand.3.2.6 measurand, nquantity subject to measurement.3.2.7 precision, nvariability of test result measurements around reported test result value.3.2.8 random error, nresult
26、 of a measurement minus the mean that would result from an infinite number of measurements ofthe same measurand carried out under repeatability conditions.3.2.9 repeatability (of results of measurements), ncloseness of the agreement between the results of successive independentmeasurements of the sa
27、me measurand carried out under repeatability conditions.3.2.10 repeatability conditions, non identical test material using the same measurement procedure, observer(s), and measuringinstrument(s) and performed in the same laboratory during a short period of time.3.2.11 reproducibility (of results of
28、measurements), n closeness of the agreement between the results of measurements of thesame measurand carried out under reproducibility conditions.2 For referencedASTM standards, visit theASTM website, www.astm.org, or contactASTM Customer Service at serviceastm.org. For Annual Book of ASTM Standards
29、volume information, refer to the standards Document Summary page on the ASTM website.3 Available from International Organization for Standardization, P.O. Box 56, CH-1211, Geneva 20, Switzerland.4 Available from European Committee for Standardization (CEN), Avenue Marnix 17, B-1000, Brussels, Belgiu
30、m, http:/www.cen.eu.E2536 15a23.2.12 reproducibility conditions, non identical test material using the same measurement procedure, but different observer(s)and measuring instrument(s) in different laboratories performed during a short period of time.3.2.13 standard deviation, na quantity characteriz
31、ing the dispersion of the results of a series of measurements of the samemeasurand; the standard deviation is proportional to the square root of the sum of the squared deviations of the measured valuesfrom the mean of all measurements.3.2.14 standard uncertainty, nuncertainty of the result of a meas
32、urement expressed as a standard deviation.3.2.15 systematic error (or bias), nmean that would result from an infinite number of measurements of the same measurandcarried out under repeatability conditions minus the true value of the measurand.3.2.16 type A evaluation (of uncertainty), nmethod of eva
33、luation of uncertainty by the statistical analysis of series ofobservations.3.2.17 type B evaluation (of uncertainty), nmethod of evaluation of uncertainty by means other than the statistical analysisof series of observations.3.2.18 uncertainty of measurement, nparameter, associated with the result
34、of a measurement, that characterizes the dispersionof the values that could reasonably be attributed to the measurand.4. Summary of Guide4.1 This guide provides concepts and calculation methods to assess the uncertainty of measurements obtained from fire tests.4.2 Appendix X1 of this guide contains
35、an example to illustrate application of this guide by assessing the uncertainty of heatrelease rate measured in the Cone Calorimeter (Test Method E1354).5. Significance and Use5.1 Users of fire test data often need a quantitative indication of the quality of the data presented in a test report. This
36、quantitative indication is referred to as the “measurement uncertainty”. There are two primary reasons for estimating theuncertainty of fire test results.5.1.1 ISO/IEC 17025 requires that competent testing and calibration laboratories include uncertainty estimates for the resultsthat are presented i
37、n a report.5.1.2 Fire safety engineers need to know the quality of the input data used in an analysis to determine the uncertainty of theoutcome of the analysis.6. Evaluating Standard Uncertainty6.1 A quantitative result of a fire test Y is generally not obtained from a direct measurement, but is de
38、termined as a functionf from N input quantities X1, , XN:Y 5f X1,X2,XN! (2)where:Y = measurand;f = functional relationship between the measurand and the input quantities; andXi = input quantities (i = 1 N).6.1.1 The input quantities are categorized as:6.1.1.1 quantities whose values and uncertaintie
39、s are directly determined from single observation, repeated observation orjudgment based on experience, or6.1.1.2 quantities whose values and uncertainties are brought into the measurement from external sources such as reference dataobtained from handbooks.6.1.2 An estimate of the output, y, is obta
40、ined from Eq 2 using input estimates x1, x2, , xN for the values of the N inputquantities:y 5f x1,x2,xN! (3)Substituting Eq 2 and 3 into Eq 1 leads to:y 5Y15Y111211N (4)where:1 = contribution to the total measurement error from the error associated with xi.6.2 Apossible approach to determine the unc
41、ertainty of y involves a large number (n) of repeat measurements. The mean valueof the resulting distribution y! is the best estimate of the measurand. The experimental standard deviation of the mean is the bestestimate of the standard uncertainty of y, denoted by u(y):E2536 15a3uy!=s2y!5s2 y!n 5!(k
42、51n yk 2y!2nn 21! (5)where:u = standard uncertainty,s = experimental standard deviation,n = number of observations;yk = kth measured value, andy = mean of n measurements.The number of observations n shall be large enough to ensure that y provides a reliable estimate of the expectation y of therandom
43、 variable y, and that s2y! provides a reliable estimate of the variance 2y!5y!/n. If the probability distribution of y isnormal, then standard deviation of s y! relative to y! is approximately 2(n-1)1/2. Thus, for n = 10 the relative uncertainty ofs y! is 24 %t, while for n = 50 it is 10 %. Addition
44、al values are given in Table E.1 in annex E of the GUM.6.3 Unfortunately it is often not feasible or even possible to perform a sufficiently large number of repeat measurements. Inthose cases, the uncertainty of the measurement can be determined by combining the standard uncertainties of the input e
45、stimates.The standard uncertainty of an input estimate xi is obtained from the distribution of possible values of the input quantity Xi. Thereare two types of evaluations depending on how the distribution of possible values is obtained.6.3.1 Type A evaluation of standard uncertaintyA type A evaluati
46、on of standard uncertainty of xi is based on the frequencydistribution, which is estimated from a series of n repeated observations xi,k (k = 1 n). The resulting equation is similar to Eq5:uxi!=s2xi!5s2 xi!n 5!(k51n xi,k 2xi!2nn 21! (6)where:xi,k = kth measured value; andxi = mean of n measurements.
47、6.3.2 Type B evaluation of standard uncertainty:6.3.2.1 A type B evaluation of standard uncertainty of xi is not based on repeated measurements but on an a priori frequencydistribution. In this case the uncertainty is determined from previous measurements data, experience or general knowledge,manufa
48、cturers specifications, data provided in calibration certificates, uncertainties assigned to reference data taken fromhandbooks, etc.6.3.2.2 If the quoted uncertainty from a manufacturer specification, handbook or other source is stated to be a particular multipleof a standard deviation, the standar
49、d uncertainty uc(xi) is simply the quoted value divided by the multiplier. For example, the quoteduncertainty is often at the 95 % level of confidence. Assuming a normal distribution this corresponds to a multiplier of two, thatis, the standard uncertainty is half the quoted value.6.3.2.3 Often the uncertainty is expressed in the form of upper and lower limits. Usually there is no specific knowledge aboutthe possible values of Xi within the interval and one can only assume that it is equally prob
