ASTM E2536-06
(Guide)Standard Guide for Assessment of Measurement Uncertainty in Fire Tests
Standard Guide for Assessment of Measurement Uncertainty in Fire Tests
SIGNIFICANCE AND USE
Users of fire test data often need a quantitative indication of the quality of the data presented in a test report. This quantitative indication is referred to as the “measurement uncertainty”. There are two primary reasons for estimating the uncertainty of fire test results.
5.1.1 ISO/IEC 17025 requires that competent testing and calibration laboratories include uncertainty estimates for the results that are presented in 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 the outcome of the analysis.
SCOPE
1.1 This guide covers the evaluation and expression of uncertainty of measurements of fire test methods developed and maintained by ASTM International, based on the approach presented in the GUM. The use in this process of precision data obtained from a round robin is also discussed.
1.2 Application of this guide is limited to tests that provide quantitative results in engineering units. This includes, for example, methods for measuring the heat release rate of burning specimens based on oxygen consumption calorimetry, such as Test Method E 1354.
1.3 This guide does not apply to tests that provide results in the form of indices or binary results (for example, pass/fail). For example, the uncertainty of the Flame Spread Index obtained according to Test Method E 84 cannot be determined.
1.4 In some cases additional guidance is required to supplement this standard. For example, the expression of uncertainty of heat release rate measurements at low levels requires additional guidance and uncertainties associated with sampling are not explicitly addressed.
1.5 This fire standard cannot be used to provide quantitative measures.
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Designation: E2536 – 06
Standard Guide for
Assessment of Measurement Uncertainty in Fire Tests
This standard is issued under the fixed designation E2536; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision.Anumber in parentheses indicates the year of last reapproval.A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
INTRODUCTION
The objective of a measurement is to determine the value of the measurand, that is, the physical
quantity that needs to be measured. Every measurement is subject to error, no matter how carefully
it 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 be
used to determine the error of a measurement because the true value is unknown, otherwise a
measurement would not be needed. In fact, the true value of a measurand is unknowable because it
cannot be measured without error. However, it is possible to estimate, with some confidence, the
expected limits of error. This estimate is referred to as the uncertainty of the measurement and
provides 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 uncontrolled
manner. Random errors cannot be eliminated, but their effect on uncertainty is reduced by increasing
the number of repeat measurements and by applying a statistical analysis to the results. Systematic
errors remain unchanged when a measurement is repeated under the same conditions. Their effect on
uncertainty cannot be completely eliminated either, but is reduced by applying corrections to account
for the error contribution due to recognized systematic effects. The residual systematic error is
unknown and shall be treated as a random error for the purpose of this standard.
General principles for evaluating and reporting measurement uncertainties are described in the
Guide on Uncertainty of Measurements (GUM). Application of the GUM to fire test data presents
some unique challenges. This standard shows how these challenges can be overcome.
´[ y 2 Y (1)
1.2 Application of this guide is limited to tests that provide
quantitative results in engineering units. This includes, for
where:
example, methods for measuring the heat release rate of
´ = measurement error;
burning specimens based on oxygen consumption calorimetry,
y = measured value of the measurand; and
such as Test Method E1354.
Y = true value of the measurand.
1.3 This guide does not apply to tests that provide results in
the form of indices or binary results (for example, pass/fail).
1. Scope
For example, the uncertainty of the Flame Spread Index
1.1 This guide covers the evaluation and expression of
obtained according to Test Method E84 cannot be determined.
uncertainty of measurements of fire test methods developed
1.4 In some cases additional guidance is required to supple-
andmaintainedbyASTMInternational,basedontheapproach
ment this standard. For example, the expression of uncertainty
presentedintheGUM.Theuseinthisprocessofprecisiondata
of heat release rate measurements at low levels requires
obtained from a round robin is also discussed.
additionalguidanceanduncertaintiesassociatedwithsampling
are not explicitly addressed.
ThisguideisunderthejurisdictionofASTMCommitteeE05onFireStandards
1.5 Thisfirestandardcannotbeusedtoprovidequantitative
and is the direct responsibility of Subcommittee E05.31 on Terminology and
measures.
Editorial.
Current edition approved Dec. 1, 2006. Published January 2007. DOI: 10.1520/
E2536-06.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.
E2536 – 06
2. Referenced Documents 3.2.9 repeatability (of results of measurements),
n—closeness of the agreement between the results of succes-
2.1 ASTM Standards:
siveindependentmeasurementsofthesamemeasurandcarried
E84 Test Method for Surface Burning Characteristics of
out under repeatability conditions.
Building Materials
3.2.10 repeatability conditions, n—onidenticaltestmaterial
E176 Terminology of Fire Standards
using the same measurement procedure, observer(s), and
E230 Specification and Temperature-Electromotive Force
measuring instrument(s) and performed in the same laboratory
(EMF) Tables for Standardized Thermocouples
during a short period of time.
E691 Practice for Conducting an Interlaboratory Study to
3.2.11 reproducibility (of results of measurements), n—
Determine the Precision of a Test Method
closeness of the agreement between the results of measure-
E1354 Test Method for Heat and Visible Smoke Release
mentsofthesamemeasurandcarriedoutunderreproducibility
Rates for Materials and Products Using an Oxygen Con-
conditions.
sumption Calorimeter
3.2.12 reproducibility conditions, n—on identical test ma-
2.2 ISO Standards:
terial using the same measurement procedure, but different
ISO/IEC17025 Generalrequirementsforthecompetenceof
observer(s) and measuring instrument(s) in different laborato-
testing and calibration laboratories
ries performed during a short period of time.
GUM Guide to the expression of uncertainty in measure-
3.2.13 standard deviation, n—a quantity characterizing the
ment
dispersion of the results of a series of measurements of the
3. Terminology same measurand; the standard deviation is proportional to the
square root of the sum of the squared deviations of the
3.1 Definitions: For definitions of terms used in this guide
measured values from the mean of all measurements.
and associated with fire issues, refer to the terminology
3.2.14 standard uncertainty, n—uncertainty of the result of
contained in Terminology E176. For definitions of terms used
a measurement expressed as a standard deviation.
in this guide and associated with precision issues, refer to the
3.2.15 systematic error (or bias), n—meanthatwouldresult
terminology contained in Practice E691.
from an infinite number of measurements of the same measur-
3.2 Definitions of Terms Specific to This Standard:
and carried out under repeatability conditions minus the true
3.2.1 accuracy of measurement, n—closeness of the agree-
value of the measurand.
mentbetweentheresultofameasurementandthetruevalueof
3.2.16 type A evaluation (of uncertainty), n—method of
the measurand.
evaluation of uncertainty by the statistical analysis of series of
3.2.2 combined standard uncertainty, n—standard uncer-
observations.
tainty of the result of a measurement when that result is
3.2.17 type B evaluation (of uncertainty), n—method of
obtainedfromthevaluesofanumberofotherquantities,equal
evaluation of uncertainty by means other than the statistical
to the positive square root of a sum of terms, the terms being
analysis of series of observations.
the variances or covariances of these other quantities weighted
3.2.18 uncertainty of measurement, n—parameter, associ-
according to how the measurement result varies with changes
ated with the result of a measurement, that characterizes the
in these quantities.
dispersion of the values that could reasonably be attributed to
3.2.3 coverage factor, n—numerical factor used as a mul-
the measurand.
tiplier of the combined standard uncertainty in order to obtain
an expanded uncertainty.
4. Summary of Guide
3.2.4 error (of measurement), n—result of a measurement
4.1 Thisguideprovidesconceptsandcalculationmethodsto
minus the true value of the measurand; error consists of two
assess the uncertainty of measurements obtained from fire
components: random error and systematic error.
tests.
3.2.5 expanded uncertainty, n—quantity defining an inter-
4.2 Appendix X1 of this guide contains an example to
val about the result of a measurement that may be expected to
illustrate application of this guide by assessing the uncertainty
encompass a large fraction of the distribution of values that
of heat release rate measured in the Cone Calorimeter (Test
could reasonably be attributed to the measurand.
Method E1354).
3.2.6 measurand, n—quantity subject to measurement.
3.2.7 precision, n—variability of test result measurements
5. Significance and Use
around reported test result value.
5.1 Users of fire test data often need a quantitative indica-
3.2.8 random error, n—result of a measurement minus the
tion of the quality of the data presented in a test report. This
mean that would result from an infinite number of measure-
quantitative indication is referred to as the “measurement
ments of the same measurand carried out under repeatability
uncertainty”. There are two primary reasons for estimating the
conditions.
uncertainty of fire test results.
5.1.1 ISO/IEC17025 requires that competent testing and
calibration laboratories include uncertainty estimates for the
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
results that are presented in a report.
Standards volume information, refer to the standard’s Document Summary page on
5.1.2 Fire safety engineers need to know the quality of the
the ASTM website.
input data used in an analysis to determine the uncertainty of
Available from International Organization for Standardization, P.O. Box 56,
CH-1211, Geneva 20, Switzerland. the outcome of the analysis.
E2536 – 06
6. Evaluating Standard Uncertainty x is obtained from the distribution of possible values of the
i
inputquantity X.Therearetwotypesofevaluationsdepending
i
6.1 A quantitative result of a fire test Y is generally not
on how the distribution of possible values is obtained.
obtained from a direct measurement, but is determined as a
6.3.1 Type A evaluation of standard uncertainty—AtypeA
function f from N input quantities X,…, X :
1 N
evaluation of standard uncertainty of x is based on the
i
Y 5 f ~X ,X ,.,X ! (2)
1 2 N
frequency distribution, which is estimated from a series of n
repeatedobservations x (k= 1… n).Theresultingequationis
i,k
where:
similar to Eq 5:
Y = measurand;
f = functionalrelationshipbetweenthemeasurandandthe
n
~x 2 x !
input quantities; and 2
( i,k i
s ~x !
k51
i
Œ
X = input quantities (i=1… N). u~x ! '=s ~x ! 5Œ 5 (6)
i i i
n n~n 21!
6.1.1 The input quantities are categorized as:
where:
6.1.1.1 quantities whose values and uncertainties are di-
th
x =k measured value; and
rectly determined from single observation, repeated observa- i,k
x = mean of n measurements.
i
tion or judgment based on experience, or
6.3.2 Type B evaluation of standard uncertainty:
6.1.1.2 quantities whose values and uncertainties are
6.3.2.1 A type B evaluation of standard uncertainty of x is
i
brought into the measurement from external sources such as
not based on repeated measurements but on an a priori
reference data obtained from handbooks.
frequency distribution. In this case the uncertainty is deter-
6.1.2 An estimate of the output, y, is obtained from Eq 2
minedfrompreviousmeasurementsdata,experienceorgeneral
usinginputestimates x , x,…, x forthevaluesofthe Ninput
1 2 N
knowledge, manufacturer’s specifications, data provided in
quantities:
calibration certificates, uncertainties assigned to reference data
y 5 f ~x ,x ,., x ! (3)
1 2 N
taken from handbooks, etc.
6.3.2.2 Ifthequoteduncertaintyfromamanufacturerspeci-
Substituting Eq 2 and 3 into Eq 1 leads to:
fication, handbook or other source is stated to be a particular
y 5 Y1´5 Y1´ 1´ 1.1´ (4)
1 2 N
multipleofastandarddeviation,thestandarduncertainty u (x)
c i
where:
is simply the quoted value divided by the multiplier. For
´ = contribution to the total measurement error from the
example, the quoted uncertainty is often at the 95% level of
error associated with x.
i confidence.Assuminganormaldistributionthiscorrespondsto
6.2 A possible approach to determine the uncertainty of y a multiplier of two, that is, the standard uncertainty is half the
involvesalargenumber(n)ofrepeatmeasurements.Themean
quoted value.
valueoftheresultingdistribution( y)isthebestestimateofthe 6.3.2.3 Often the uncertainty is expressed in the form of
measurand.Theexperimentalstandarddeviationofthemeanis upper and lower limits. Usually there is no specific knowledge
the best estimate of the standard uncertainty of y, denoted by about the possible values of X within the interval and one can
i
u(y): onlyassumethatitisequallyprobablefor X tolieanywherein
i
it. Fig. 1 shows the most common example where the corre-
n
sponding rectangular distribution is symmetric with respect to
~y 2 y!
2 (
k
s ~y! k51
Œ
u~y! ' s ~y! 5 5 (5) its best estimate x. The standard uncertainty in this case is
= Œ
i
n
n~n 21!
given by:
where:
DX
i
u~x ! 5 (7)
u = standard uncertainty, i
=
s = experimental standard deviation,
n = number of observations;
where:
th
y =k measured value, and
DX = half-width of the interval.
k
i
y = mean of n measurements.
The number of observations n shall be large enough to ensure
that y provides a reliable estimate of the expectation µ of the
y
random variable y, and that s ( y ) provides a reliable estimate
of the variance s ( y)= s(y)/n. If the probability distribution
of y is normal, then the standard deviation of s ( y ) relative to
1/2
s ( y ) is approximately [2(n-1)]− . Thus, for n=10the
relative uncertainty of s ( y ) is 24 %t, while for n=50itis10
%.Additional 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
performasufficientlylargenumberofrepeatmeasurements.In
those cases, the uncertainty of the measurement can be
determined by combining the standard uncertainties of the
input estimates. The standard uncertainty of an input estimate FIG. 1 Rectangular Distribution
E2536 – 06
If some information is known about the distribution of the 8. Determining Expanded Uncertainty
possiblevaluesof X withintheinterval,thatknowledgeisused
i
8.1 It is often necessary to give a measure of uncertainty
to better estimate the standard deviation.
that defines an interval about the measurement result that may
6.3.3 Accounting for multiple sources of error—The uncer- beexpectedtoencompassalargefractionofthedistributionof
values that could reasonably be attributed to the measurand.
taintyofaninputquantityissometimesduetomultiplesources
Thismeasureistermedexpandeduncertaintyandisdenotedby
error.Inthiscase,thestandarduncertaintyassociatedwitheach
U. The expanded uncertainty is obtained by multiplying the
source of error has to be estimated separately and the standard
combined standard uncertain
...
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