ASTM E2655-08

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Designation: E2655 − 08 AnAmerican National Standard
Standard Guide for
Reporting Uncertainty of Test Results and Use of the Term
Measurement Uncertainty in ASTM Test Methods
This standard is issued under the fixed designation E2655; 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.
1. Scope E141Practice for Acceptance of Evidence Based on the
Results of Probability Sampling
1.1 This guide provides concepts necessary for understand-
E177Practice for Use of the Terms Precision and Bias in
ing the term “uncertainty” when applied to a quantitative test
ASTM Test Methods
result. Several measures of uncertainty can be applied to a
E456Terminology Relating to Quality and Statistics
given measurement result; the interpretation of some of the
E691Practice for Conducting an Interlaboratory Study to
common forms is described.
Determine the Precision of a Test Method
1.2 This guide describes methods for expressing test result
E2554Practice for Estimating and Monitoring the Uncer-
uncertainty and relates these to standard statistical methodol-
tainty of Test Results of a Test Method in a Single
ogy. Relationships between uncertainty and concepts of preci-
Laboratory Using a Control Sample Program
sion and bias are described.
2.2 Other Standard:
1.3 This guide also presents concepts needed for a labora-
ISO 17025General Requirements for the Competence of
tory to identify and characterize components of method per-
Testing and Calibration Laboratories
formance. Elements that an ASTM method can include to
provide guidance to the user on estimating uncertainty for the
3. Terminology
method are described.
3.1 Definitions:
1.4 The system of units for this guide is not specified.
3.1.1 AdditionalstatisticaltermsaredefinedinTerminology
Dimensional quantities in the guide are presented only as
E456.
illustrations of calculation methods and are not binding on
3.1.2 accepted reference value, n—a value that serves as an
products or test methods treated.
agreed-upon reference for comparison, and which is derived
1.5 This standard does not purport to address all of the
as: (1) a theoretical or established value, based on scientific
safety concerns, if any, associated with its use. It is the
principles, (2) an assigned or certified value, based on experi-
responsibility of the user of this standard to establish appro-
mental work of some national or international organization, or
priate safety and health practices and determine the applica-
(3) a consensus or certified value, based on collaborative
bility of regulatory limitations prior to use.
experimental work under the auspices of a scientific or
engineering group. E177
2. Referenced Documents
3.1.3 error of result, n—a test result minus the accepted
2.1 ASTM Standards:
reference value of the characteristic.
E29Practice for Using Significant Digits in Test Data to
3.1.4 expanded uncertainty, U, n—uncertainty reported as a
Determine Conformance with Specifications
multiple of the standard uncertainty.
E122PracticeforCalculatingSampleSizetoEstimate,With
3.1.5 random error of result, n—a component of the error
Specified Precision, the Average for a Characteristic of a
that, in the course of a number of test results for the same
Lot or Process
characteristic, varies in an unpredictable way.
3.1.5.1 Discussion—Uncertaintyduetorandomerrorcanbe
1 reduced by averaging multiple test results.
This guide is under the jurisdiction of ASTM Committee E11 on Quality and
Statistics and is the direct responsibility of Subcommittee E11.20 on Test Method
3.1.6 sensitivity coeffıcient, n—differential effect of the
Evaluation and Quality Control.
change in a factor on the test result.
Current edition approved Oct. 1, 2008. Published November 2008. DOI:
10.1520/E2655-08.
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
Standardsvolume information,referto thestandard’sDocumentSummary page on Available fromAmerican National Standards Institute (ANSI), 25 W. 43rd St.,
the ASTM website. 4th Floor, New York, NY 10036, http://www.ansi.org.
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E2655 − 08
3.1.7 standard uncertainty, u, n—uncertaintyreportedasthe ducibility refers to interlaboratory variation. Uncertainty is an
standard deviation of the estimated value of the quantity attribute of the particular test result for a test material. It is an
subject to measurement. estimate of the quality of that particular test result.
3.1.8 systematic error of result, n—acomponentoftheerror
5.3 In the case of a quantity with a definition that does not
that, in the course of a number of test results for the same
dependonthemeasurementortestmethod(e.g.,concentration,
characteristic, remains constant or varies in a predictable way.
pH, modulus, heat content), uncertainty measures how close it
3.1.8.1 Discussion—Systematic errors and their causes may
is believed the measured value comes to the quantity. For
be known or unknown. When causes are known, systematic
results of test methods where the target is only definable
error can sometimes be reduced by incorporating corrections
relative to the test method (e.g., flash points, extractable
into the calculation of the test result.
components,sieveanalysis),uncertaintyofatestresultmustbe
interpreted as a measure of how closely an independent,
3.1.9 uncertainty, n—anindicationofthemagnitudeoferror
equally competent test result would agree with that being
associated with a value that takes into account both systematic
reported.
errors and random errors associated with the measurement or
test process.
5.4 In the simplest cases, uncertainty of a test result is
numerically equivalent to test method precision. That is, if an
3.1.10 uncertainty budget, n—a tabular listing of uncer-
unknownsampleistested,andthetestprecisionisknowntobe
tainty components for a given measurement process giving the
sigma, then uncertainty of the result of test is sigma. The term
magnitudes of contributions to uncertainty of the result from
uncertainty, however, is correct to apply where variation of
those sources.
repeated test results is not relevant, as in the following
3.1.11 uncertainty component, n—a source of error in a test
examples.
result to which is attached a standard uncertainty.
5.4.1 Example—The Newtonian constant of gravitation, G,
-11 -11 3 -1 -2
is 6.6742 × 10 6 0.0010 × 10 m kg s based on 2002
4. Significance and Use
4 -11 3 -1 -2
CODATArecommended values (1). 0.0010 × 10 m kg s
4.1 Part A of the “Blue Book,” Form and Style for ASTM
is the standard uncertainty. The value and the uncertainty
Standards, introduces the statement of measurement uncer-
together represent the state of knowledge of this fundamental
tainty as an optional part of the report given for the result of
physical constant. It is not naturally thought of in terms of
applying a particular test method to a particular material.
variationofrepeatedmeasurements.Both Ganditsuncertainty
4.2 Preparationofuncertaintyestimatesisarequirementfor
are derived from the analysis and comparison of a variety of
laboratoryaccreditationunderISO17025.Thisguidedescribes
measurement data using methods that are an elaboration of
some of the types of data that the laboratory can use as the
those presented in this guide.
basis for reporting uncertainty.
5.4.2 Example—A length is measured but the result only
reported to the nearest inch (for example, a measuring rod
5. Concepts for Reporting Uncertainty of Test Results
graduated in inches was used to obtain the measurement).
5.1 Uncertainty is part of the relationship of a test result to
Precision of the reported value, in the sense of variation of
the property of interest for the material tested. When a test
repeated measurements, is zero when all reported lengths are
procedure is applied to a material, the test result is a value for
the same. In this case it is not possible to detect random
a characteristic of the material. The test result obtained will
variation in the series of repeated measurements. Uncertainty
usually differ from the actual value for that material. Multiple
of the length is primarily composed of the systematic error of
causes can contribute to the error of result. Errors of sampling
60.5 inch due to the resolution of the measurement apparatus.
andeffectsofsamplehandlingmaketheportionactuallytested
5.5 Thegoalinreportinguncertaintyistotakeaccountofall
not identical to the material as a whole. Imperfections in the
potential causes of error in the test result. In many cases,
test apparatus and its calibration, environmental, and human
uncertainty can be related to components of variability due to
factors also affect the result of testing. Nonetheless, after
sampling and to testing. Both of these should be taken into
testinghasbeencompleted,theresultobtainedwillbeusedfor
account for the uncertainty of the measurement when the
further purposes as if it were the actual value. Reporting
purposeoftheresultistoestimatethepropertyfortheentirelot
measurement uncertainty for a test result is an attempt to
of material from which the sample was taken. Uncertainty of
estimate the approximate magnitude of all these sources of
the lot property value based on a single determination is then
error.Incommoncasesthemeasurementwillbereportedinthe
2 2 2
=s 1s 1u where s is an estimate of the sampling standard
1 2 3 1
form x 6 u, in which x represents the test result and u
deviation, s isanestimateofthestandarddeviationofthetest
represents the uncertainty associated with x.
method,and u isstandarduncertaintyduetofactorsthataffect
5.2 Practice E177 describes precision and bias. Uncertainty
all measurements under consideration.
is a closely related but not identical concept. The primary
5.6 A commonly cited definition (2, 3) defines uncertainty
difference between concepts of precision and of uncertainty is
as“aparameter,associatedwiththemeasurementresult,ortest
the object that they address. Precision (repeatability and
result, that characterizes the dispersion of values that could
reproducibility)andbiasareattributesofthetestmethod.They
are estimates of statistical variability of test results for a test
methodappliedtoagivenmaterial.Repeatabilityandinterme-
Theboldfacenumbersinparenthesesrefertothelistofreferencesattheendof
diate precision measure variation within a laboratory. Repro- this standard.
E2655 − 08
reasonablybeattributedtothequantitysubjecttomeasurement the value of t approaches 1.96 as n increases. This is the basis
or characteristic subject to test.” This definition emphasizes for using the factor 2 for expanded uncertainty.
uncertaintyasanattributeoftheparticularresult,asopposedto
5.8.5 Measurement Uncertainty—Measurement uncertainty
statisticalvariationoftestresults.Theuncertaintyparameteris
is uncertainty reported for a test result without taking into
a measure of spread (for example, the standard deviation) of a
account sampling variation or heterogeneity of the material of
probability distribution used to represent the likelihood of
interest. The report of measurement uncertainty then refers
values of the property.
specifically to the particular sample presented for analysis.
5.7 The methodology for uncertainty estimates has been
5.8.6 Reporting Uncertainty with a Bias Component—Good
classified as Type A and Type B as discussed in (4). Type A
measurementpracticerequiresthatbiasesduetoenvironmental
estimates of uncertainty include standard error estimates based
and other factors should be corrected in the reported result
on knowledge of the statistical character of observations, and
when there is a sound basis for correction and the error in the
basedonstatisticalanalysisofreplicatemeasurements.TypeB
correction terms themselves is not greater than the bias. Such
estimates of uncertainty include approximate values derived
corrections are part of the calculation of the result within the
fromexperiencewithmeasurementprocessessimilartotheone
testmethod.Thesymmetricalformofreportingameasurement
being considered, and estimates of standard uncertainty de-
withstandarduncertainty, x 6 u,isadequateformeasurements
rived from the range of possible measurement values for a
where bias is absent or corrected. If the measurement process
given material and an assumed distribution of values within
has a bias for which there is an estimate of magnitude and it is
that range. See Practice E122 for examples (e.g., rectangular,
notcorrectedinthereportedvalue x,aformofreportingshould
triangular, normal) where a standard deviation is derived from
be used making clear both bias and random components. A
a range without data from samples being available. Complex
typical form to highlight the asymmetry caused by bias is
estimatesoftestresultuncertaintyarecalculatedbycombining
x–u/+ u ,where u =bias–standarduncertaintyand u =bias
l h l h
Type A and Type B component standard uncertainties for
+ standard uncertainty.
factors contributing to error (see Section 8).
5.8.7 Bias estimates are often subjective or based on weak
information.Whenbiasispresent,butmagnitudeanddirection
5.8 Forms of Uncertainty Expression:
areunknown,theuncertaintyofthebiasisanimportantpartof
5.8.1 Standard Uncertainty—The uncertainty is reported as
uncertainty as a whole and should be combined with random
the standard deviation of the reported value. The report x 6 u
components. The overall root mean square uncertainty is then
implies that the value should be between x– u and x+ u with
2 2
approximate probability two-thirds, where x is the test result. =
u5 u 1σ .
bias
5.8.2 Relative Standard Uncertainty—The uncertainty is
5.9 The repeatability and reproducibility values published
reported as a fraction of the reported value. For a measured
foranASTMmethodarederivedfromaninterlaboratorystudy
value and a standard uncertainty, x 6 u, the relative standard
following Practice E691 or a similar procedure. Repeatability
uncertainty is u/x. This method of expressing uncertainty may
and reproducibility values given for ASTM test methods are
beusefulwhenstandarduncertaintyisproportionaltothevalue
intendedtoestimatethevariabilityoftestresultsforcompetent
over a wide range. However, for a particular result, reporting
laboratories (see Practice E177). Reproducibility measures
the value and standard uncertainty is preferred.
variabilityoftestresultsonidenticalsamplesderivedind
...