ASTM E2655-14(2020)

This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the
Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
Designation: E2655 − 14 (Reapproved 2020) An American 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 2. Referenced Documents
2.1 ASTM Standards:
1.1 This guide provides concepts necessary for understand-
E29Practice for Using Significant Digits in Test Data to
ing the term “uncertainty” when applied to a quantitative test
Determine Conformance with Specifications
result. Several measures of uncertainty can be applied to a
E122PracticeforCalculatingSampleSizetoEstimate,With
given measurement result; the interpretation of some of the
Specified Precision, the Average for a Characteristic of a
common forms is described.
Lot or Process
1.2 This guide describes methods for expressing test result
E177Practice for Use of the Terms Precision and Bias in
uncertainty and relates these to standard statistical methodol-
ASTM Test Methods
ogy. Relationships between uncertainty and concepts of preci-
E456Terminology Relating to Quality and Statistics
sion and bias are described.
E691Practice for Conducting an Interlaboratory Study to
Determine the Precision of a Test Method
1.3 This guide also presents concepts needed for a labora-
E1402Guide for Sampling Design
tory to identify and characterize components of method per-
E2554Practice for Estimating and Monitoring the Uncer-
formance. Elements that an ASTM method can include to
tainty of Test Results of a Test Method Using Control
provide guidance to the user on estimating uncertainty for the
Chart Techniques
method are described.
E2586Practice for Calculating and Using Basic Statistics
1.4 The system of units for this guide is not specified.
2.2 Other Standard:
Dimensional quantities in the guide are presented only as
ISO/IEC 17025General Requirements for the Competence
illustrations of calculation methods and are not binding on
of Testing and Calibration Laboratories
products or test methods treated.
3. Terminology
1.5 This standard does not purport to address all of the
3.1 Definitions:
safety concerns, if any, associated with its use. It is the
3.1.1 AdditionalstatisticaltermsaredefinedinTerminology
responsibility of the user of this standard to establish appro-
E456.
priate safety, health, and environmental practices and deter-
3.1.2 accepted reference value, n—a value that serves as an
mine the applicability of regulatory limitations prior to use.
agreed-upon reference for comparison, and which is derived
1.6 This international standard was developed in accor-
as: (1) a theoretical or established value, based on scientific
dance with internationally recognized principles on standard-
principles, (2) an assigned or certified value, based on experi-
ization established in the Decision on Principles for the
mental work of some national or international organization, or
Development of International Standards, Guides and Recom-
(3) a consensus or certified value, based on collaborative
mendations issued by the World Trade Organization Technical
experimental work under the auspices of a scientific or
Barriers to Trade (TBT) Committee.
engineering group. E177
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
This guide is under the jurisdiction of ASTM Committee E11 on Quality and contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
Statistics and is the direct responsibility of Subcommittee E11.50 on Metrology. Standards volume information, refer to the standard’s Document Summary page on
Current edition approved Jan. 1, 2020. Published February 2020. Originally the ASTM website.
approved in 2008. Last previous edition approved in 2014 as E2655 – 14. DOI: Available fromAmerican National Standards Institute (ANSI), 25 W. 43rd St.,
10.1520/E2655-14R20. 4th Floor, New York, NY 10036, http://www.ansi.org.
Copyright ©ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA19428-2959. United States
E2655 − 14 (2020)
3.1.3 error of result, n—a test result minus the accepted estimate the approximate magnitude of all these sources of
reference value of the characteristic. error.Incommoncasesthemeasurementwillbereportedinthe
form x 6 u, in which x represents the test result and u
3.1.4 expanded uncertainty, U, n—uncertainty reported as a
represents the uncertainty associated with x.
multiple of the standard uncertainty.
5.2 Practice E177 describes precision and bias. Uncertainty
3.1.5 random error of result, n—a component of the error
is a closely related but not identical concept. The primary
that, in the course of a number of test results for the same
difference between concepts of precision and of uncertainty is
characteristic, varies in an unpredictable way.
the object that they address. Precision (repeatability and
3.1.5.1 Discussion—Uncertaintyduetorandomerrorcanbe
reproducibility)andbiasareattributesofthetestmethod.They
reduced by averaging multiple test results.
are estimates of statistical variability of test results for a test
3.1.6 sensitivity coeffıcient, n—differential effect of the
method applied to a given material. Repeatability and interme-
change in a factor on the test result.
diate precision measure variation within a laboratory. Repro-
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
depend on the measurement or test method (for example,
characteristic, remains constant or varies in a predictable way.
concentration, pH, modulus, heat content), uncertainty mea-
3.1.8.1 Discussion—Systematic errors and their causes may
sures how close it is believed the measured value comes to the
be known or unknown. When causes are known, systematic
quantity. For results of test methods where the target is only
error can sometimes be reduced by incorporating corrections
definable relative to the test method (for example, flash points,
into the calculation of the test result.
extractable components, sieve analysis), uncertainty of a test
3.1.9 uncertainty, n—anindicationofthemagnitudeoferror
result must be interpreted as a measure of how closely an
associated with a value that takes into account both systematic
independent, equally competent test result would agree with
errors and random errors associated with the measurement or
that being reported.
test process.
5.4 In the simplest cases, uncertainty of a test result is
3.1.10 uncertainty budget, n—a tabular listing of uncer-
numerically equivalent to test method precision. That is, if an
tainty components for a given measurement process giving the
unknownsampleistested,andthetestprecisionisknowntobe
magnitudes of contributions to uncertainty of the result from
sigma, then uncertainty of the result of test is sigma. The term
those sources.
uncertainty, however, is correct to apply where variation of
3.1.11 uncertainty component, n—a source of error in a test repeated test results is not relevant, as in the following
examples.
result to which is attached a standard uncertainty.
5.4.1 Example—The Newtonian constant of gravitation, G,
-11 -11 3 -1 -2
4. Significance and Use
is 6.6742 × 10 6 0.0010 × 10 m kg s based on 2002
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
laboratory accreditation under ISO/IEC 17025. This guide
measurement data using methods that are an elaboration of
describes some of the types of data that the laboratory can use
those presented in this guide.
as the 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
testinghasbeencompleted,theresultobtainedwillbeusedfor
further purposes as if it were the actual value. Reporting
Theboldfacenumbersinparenthesesrefertothelistofreferencesattheendof
measurement uncertainty for a test result is an attempt to this standard.
E2655 − 14 (2020)
sampling and to testing. Both of these should be taken into 5.8.4 Confidence Intervals—A confidence interval for a
account for the uncertainty of the measurement when the parameter (the actual value of the material property subject to
purposeoftheresultistoestimatethepropertyfortheentirelot measurement) consists of upper and lower limits generated
of material from which the sample was taken. Uncertainty of from sample data by a method that ensures the limits bracket
the lot property value based on a single determination is then theparametervaluewithastatedprobability1-α,referredtoas
2 2 2
the confidence coefficient.
=s 1s 1u , where s is an estimate of the sampling standard
1 2 3 1
deviation, s is an estimate of the standard deviation of the test 5.8.4.1 From statistical theory, a 95% confidence interval
method,and u isstandarduncertaintyduetofactorsthataffect for the mean of a normal distribution, given n independent
all measurements under consideration. observations x , x ,…, x drawn from the distribution, is xH
1 2 n
6ts/=n wherex¯ isthesamplemean, sisthestandarddeviation
5.6 A commonly cited definition (2, 3) defines uncertainty
of the observations, and t is the 0.975 percentile of the
as“aparameter,associatedwiththemeasurementresult,ortest
Student’s t distribution with n-1 degrees of freedom. Because
result, that characterizes the dispersion of values that could
Student’s t distribution approaches the Normal as n increases,
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
statistical variation of test results.The uncertainty parameter is
5.8.4.2 Practice E2586 defines confidence intervals and
a measure of spread (for example, the standard deviation) of a
provides additional detail on their interpretation.
probability distribution used to represent the likelihood of
5.8.5 Measurement Uncertainty—Measurement uncertainty
values of the property.
is uncertainty reported for a test result without taking into
5.7 The methodology for uncertainty estimates has been
account sampling variation or heterogeneity of the material of
classified as Type A and Type B as discussed in (4). Type A
interest. The report of measurement uncertainty then refers
estimates of uncertainty include standard error estimates based
specifically to the particular sample presented for analysis.
on knowledge of the statistical character of observations, and
5.8.6 Reporting Uncertainty with a Bias Component—Good
basedonstatisticalanalysisofreplicatemeasurements.TypeB
measurementpracticerequiresthatbiasesduetoenvironmental
estimates of uncertainty include approximate values derived
and other factors should be corrected in the reported result
fromexperiencewithmeasurementprocessessimilartotheone
when there is a sound basis for correction and the error in the
being considered, and estimates of standard uncertainty de-
correction terms themselves is not greater than the bias. Such
rived from the range of possible measurement values for a
corrections are part of the calculation of the result within the
given material and an assumed distribution of values within
testmethod.Thesymmetricalformofreportingameasurement
that range. See Practice E122 for examples (for example,
withstandarduncertainty, x 6 u,isadequateformeasurements
rectangular, triangular, normal) where a standard deviation is
where bias is absent or corrected. If the measurement process
derived from a range without data from samples being avail-
has a bias for which there is an estimate of magnitude and it is
able. Complex estimates of test result uncertainty are calcu-
notcorrectedinthereportedvalue x,aformofreportingshould
lated by combining Type A and Type B component standard
be used making clear both bias and random components. A
uncertainties for factors contributing to error (see Section 8).
typical form to highlight the as
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