ASTM D7440-08(2015)e1
(Practice)Standard Practice for Characterizing Uncertainty in Air Quality Measurements
Standard Practice for Characterizing Uncertainty in Air Quality Measurements
SIGNIFICANCE AND USE
6.1 A primary use intended for this practice is for qualifying ASTM International Standards as Standard Test Methods. In the past, a “Precision and Bias” report has been required. However, recently a statement of uncertainty has become an acceptable alternative to D3670 – 91: Guide for Determination of Precision and Bias of Methods of Committee D22. Inclusion of such a statement with a method description simplifies comparison of ASTM Test Methods to analogous ISO and CEN standards, now required to have uncertainty statements.
6.2 Standardizing the characterization of sampling/analytical method performance is expected to be useful in other applications as well. For example, performance details are a necessity for justifying compliance decisions based on experimental air quality assessments (7). Documented uncertainty can form a basis for specific criteria defining acceptable sampling/analytical method performance.
6.3 Furthermore, high quality atmospheric measurements are vital for making decisions as to how hazardous substances are to be controlled. Valid data are required for drawing reasonable epidemiological conclusions, for making sound decisions as to acceptable limits, as well as for determining the efficacy of a hazard control system.
6.4 Finally, because of developing world-wide acceptance of ISO GUM for detailing measurements when statistics are simple, the practice should be useful in comparing ASTM International Test Methods to others’ published methods. The codification of statistical procedures may in fact minimize the difficulty in interpreting a plethora of individual, albeit possibly valid, approaches.
SCOPE
1.1 This practice is for assisting developers and users of air quality methods for sampling concentrations of both airborne and settled materials in characterizing measurements as to uncertainty. Where possible, analysis into uncertainty components as recommended in the ISO Guide to the Expression of Uncertainty in Measurement (ISO GUM, (1)2) is suggested. Aspects of uncertainty estimation particular to air quality measurement are emphasized. For example, air quality assessment is often complicated by: the difficulty of taking replicate measurements owing to the large spatio-temporal variation in concentration values to be measured; systematic error or bias, both corrected and uncorrected; and the (rare) non-normal distribution of errors. This practice operates mainly through example. Background and mathematical development are relegated to appendices for optional reading.
1.2 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory limitations prior to use.
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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.
´1
Designation: D7440 − 08 (Reapproved 2015)
Standard Practice for
Characterizing Uncertainty in Air Quality Measurements
This standard is issued under the fixed designation D7440; 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.
ε NOTE—Editorial corrections were made throughout in July 2015.
1. Scope Weighing Collected Aerosols
2.2 Other International Standards:
1.1 This practice is for assisting developers and users of air
ISO GUMGuide to the Expression of Uncertainty in
quality methods for sampling concentrations of both airborne
Measurement, ISO Guide 98, 1995 (See Ref (1), for an
and settled materials in characterizing measurements as to
additional measurement uncertainty resource.)
uncertainty. Where possible, analysis into uncertainty compo-
ISO7708AirQuality—ParticleSizeFractionDefinitionsfor
nents as recommended in the ISO Guide to the Expression of
Health-Related Sampling
Uncertainty in Measurement (ISO GUM, (1) ) is suggested.
ISO 15767WorkplaceAtmospheres—Controlling and Char-
Aspects of uncertainty estimation particular to air quality
acterizing Errors in Weighing Collected Aerosol
measurement are emphasized. For example, air quality assess-
ISO 16107Workplace Atmospheres—Protocol for Evaluat-
ment is often complicated by: the difficulty of taking replicate
ing the Performance of Diffusive Samplers, 2007
measurements owing to the large spatio-temporal variation in
EN 482Workplace Atmospheres—General Requirements
concentration values to be measured; systematic error or bias,
forthePerformanceofProceduresfortheMeasurementof
both corrected and uncorrected; and the (rare) non-normal
Chemical Agents
distribution of errors. This practice operates mainly through
example. Background and mathematical development are rel-
3. Terminology
egated to appendices for optional reading.
3.1 Definitions—For definitions of terms used in this
1.2 This standard does not purport to address all of the
practice, see Terminology D1356.
safety concerns, if any, associated with its use. It is the
responsibility of the user of this standard to establish appro-
3.2 Other terms defined as follows are taken from ISO GUM
priate safety and health practices and determine the applica-
unless otherwise noted:
bility of regulatory limitations prior to use.
3.2.1 accuracy—closeness of agreement between the result
of a measurement and a true value of the measurand.
2. Referenced Documents
3.2.2 combined standard uncertainty, u —standard uncer-
c
2.1 ASTM Standards:
tainty of the result of a measurement when that result is
D1356Terminology Relating to Sampling and Analysis of
obtainedfromthevaluesofanumberofotherquantities,equal
Atmospheres
to the positive square root of a sum of terms, the terms being
D3670Guide for Determination of Precision and Bias of
the variances or covariances of these other quantities weighted
Methods of Committee D22
according to how the measurement result varies with changes
D6246Practice for Evaluating the Performance of Diffusive
in these quantities.
Samplers
3.2.2.1 Discussion—As within ISO GUM, the “other quan-
D6552Practice for Controlling and Characterizing Errors in
tities” are designated uncertainty components u from source j.
j
The component u is taken as the standard deviation estimate
j
from source j in the case of a source of random variation.
ThispracticeisunderthejurisdictionofASTMCommitteeD22onAirQuality
3.2.3 coverage factor, k—numerical factor used as a multi-
and is the direct responsibility of Subcommittee D22.01 on Quality Control.
CurrenteditionapprovedJuly1,2015.PublishedJuly2015.Originallyapproved plier of the combined standard uncertainty (u ) in order to
c
in 2008. Last previous edition approved in 2008 as D7440 – 08. DOI: 10.1520/
obtain an expanded uncertainty (U).
D7440-08R15E01.
Theboldfacenumbersinparenthesesrefertothelistofreferencesattheendof
this standard.
3 4
For referenced ASTM standards, visit the ASTM website, www.astm.org, or BIPM version available for download from http://www.bipm.org/en/
contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM publications/guides/gum.html. ISO version available from American National
Standards volume information, refer to the standard’s Document Summary page on Standards Institute (ANSI), 25 W. 43rd St., 4th Floor, New York, NY 10036,
the ASTM website. http://www.ansi.org.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
´1
D7440 − 08 (2015)
3.2.3.1 Discussion—The factor k depends on the specific 3.2.14 systematic error (bias)—meanthatwouldresultfrom
meaning attributed to the expanded uncertainty U. However, an infinite number of measurements of the same measurand
for simplicity this practice adopts the now nearly traditional carriedoutunderrepeatabilityconditionsminusatruevalueof
coverage factor as the value 2, determining the specific the measurand.
meaning of the expanded uncertainty U in different circum-
3.2.15 TypeAevaluation (of uncertainty)—methodofevalu-
stances. Other coverage factors if needed are then easily
ation of uncertainty by the statistical analysis of series of
implemented simply by multiplication of the traditional ex-
observations.
panded uncertainty U (see 7.1 – 7.4).
3.2.16 TypeBevaluation(ofuncertainty)—methodofevalu-
3.2.3.2 Discussion—The use of a single coverage factor,
ation of uncertainty by means other than the statistical analysis
often through approximation, avoids the overly conservative
of series of observations.
use of individual component confidence limits rather than root
variance estimates as uncertainty components.
4. Background Information
3.2.4 error (of measurement)—result of a measurement
4.1 Uncertainty in a measurement result can be taken as the
minus a true value of the measurand.
range about an estimate, corrected for bias if known, contain-
ing the true, or mean reference value—in the language of ISO
3.2.5 expanded uncertainty, U—quantity defining an inter-
GUM, the measurand value at given confidence. Uncertainty
val about the result of a measurement that may be expected to
accounts not only for variation in a method’s results at
encompass a large fraction of the distribution of values that
application, but also for incomplete characterization of the
could reasonably be attributed to the measurand.
method when evaluated. In accordance with ISO GUM,
3.2.5.1 Discussion—This definition has the breadth to en-
uncertainty may often usefully be analyzed into individual
compass a wide variety of conceptions.
components.
3.2.5.2 Discussion—The expanded uncertainty U in some
4.2 Thereareseveralaspectsofuncertaintycharacterization
cases is expressed in absolute terms, but sometimes as relative
specific to air quality measurements. One of these aspects
to the measurement result. What is meant is generally clear
concerns known, that is, correctible, systematic error or mean
from the context.
bias of a measurement relative to a true measurand value.
3.2.6 influence quantity—quantity that is not the measurand
Several measurement methods exist with such bias left uncor-
but that affects the result of the measurement.
rectedbecauseofpolicy,tradition,orotherreason. Uncertainty
3.2.7 measurand—particular quantity subject to measure- deals only with what is unknown about a measurement, and as
ment. suchdoesnotincludecorrectible(known)bias.Themagnitude
of the difference between estimate and measurand value is
3.2.8 measurand value—(adapted from ISO GUM), un-
covered by accuracy as defined qualitatively in ISO GUM,
known quantity whose measurement is sought, often called the
rather than uncertainty, particularly when the bias is known,
true value. Examples are the concentration (mg/m)ofa
but uncorrected. Such methods require specification of both
substance in the air at a particular time and place, the
uncertaintyandasmuchasisknownoftheuncorrectedbias,or
time-weighted average of a concentration at a particular
alternatively the adoption of an accuracy measure.
position, or the expected mean concentration estimate as
obtained by a reference method at a specific time and position.
4.3 Oftenbiasisknowntoexist,butwithunknownvalue.In
the case where only limits may be placed on the magnitude of
3.2.9 (population) variance (of a random variable)—the
the bias, ISO GUM generally recommends treating the bias as
expectation of the square of the centered random variable.
uniformly distributed within the known limits. Such a distri-
3.2.10 random error—result of a measurement minus the
bution refers to independent situations, for example,
mean that would result from an infinite number of measure-
calibrations, where bias may arise (see 7.4 and Appendix X2),
ments of the same measurand carried out under the same
rather than variation at the point of method application. Even
(repeatability) conditions of measurement.
though such an equal-likelihood bias distribution may be
3.2.10.1 Discussion—Random error is equal to error minus
unrealistic, nevertheless a standard deviation estimate may be
systematic error.
madethatrevealsthelimitsonthebias.Iftheeven-distribution
approximation is clearly invalid for a relevant set of
3.2.11 (sample) variance—the sum of the squared devia-
measurements, the procedure may be adjusted slightly by
tions of observations from their average divided by one less
adopting an accuracy measure tailored to the assumed limits.
than the number of observations.
4.4 Another issue concerns the distribution of measure-
3.2.11.1 Discussion—The sample variance is an unbiased
ments. ISO GUM deals only with normally distributed first-
estimator of the population variance.
order (that is, “small”) variations relative to measurand values.
3.2.12 standard deviation—positive square root of the vari-
An example to the contrary is afforded by normally distributed
ance.
data confounded by a small number of apparent outliers (3),
3.2.13 symmetric accuracy range A—the range symmetric which may not detract from the method performance (see
about (true) measurand values containing 95% of measure- Appendix X4 for details). Another example is the determina-
ment estimates. A is a specific quantification of accuracy. (2) tion of an aerosol concentration at one location (perhaps at a
ISO 16107 worker’slapel)asanestimateoftheconcentrationataseparate
´1
D7440 − 08 (2015)
TABLE 1 Common Potential Uncertainty Components
point (such as a breathing zone). In this case the variations can
beoftheorderoftheestimateitselfandmayhavethecharacter Sampling
personal sampling pump flow rate: setting the pump and subsequent drift
of a log-normal distribution.
sampling rate of diffusive sampler
sampler dimension (aerosol and diffusive sampling)
4.5 The spatial inhomogeneity alluded to in 4.4 relates to
collection efficiency of a sampler or sampling medium
another point regarding the focus of this practice. The spatio-
(also, see (6))
temporal variations in air quality characteristics are generally
Analytical
aerosol weighing
so large (4) as to preclude evaluation of a method during
recovery (for example, chromatographic or spectroscopic methods)
application through the use of replicate measurements. In this
Poisson counting (for example, in XRD methods)
case, often an initial single method evaluation is undertaken
instrument or sensor variation
operator effects giving inter-lab differences (if data from several labs are to
with the purpose of determining uncertainty present in subse-
be used)
quent applications of the method. Confidence in such an
Sample
evaluation can be specified and relates to the concept of
sample stability
sample preparation (for example, handling silica quasi-suspensions)
prediction-intervals (5) (see 7.2).
sample loss during transport or storage
Evaluation
4.6 A related subject is measurement system control. The
calibration material uncertainty
measurement system must remain in a state of statistical
evaluation chamber concentration uncertainty
control if an introductory evaluation is to characterize later
other bias-correction uncertainty
practical applications of the method. Measurement system Environmental Influence Parameters
temperature (inadequacy of correction, if correction is made as with diffusive
control is evaluated using an ongoing quality control program,
samplers)
testing critical performance aspects for detecting problems
atmospheric pressure
humidity
which may develop in the method.
aerosol size distribution (if not measured by a given aerosol sampling method)
ambient wind velocity
5. Summary of Practice
sampled concentration magnitude itself (for example, sorbent loading)
5.1 The essential idea behind ISO GUM is the analysis to
the fullest extent practical of the elemental sources of what is
unknown in the estimate of a measurand value. This contrasts
with a global or top-down determination of uncertainty, which
error or bias; however, random variation may also fall into this
could for example be done ideally by comparing replicate
category. For example, a common assumption (see, for
estimates to known measurand values over all conditions
example, EN 482) regarding personal sampling in the work-
expected in application of the method. Although a global
place is that the relative standard deviation associated with
uncertaintyevaluationmaysometimesseeminexpensive,there
personal sampling pump variations is <5% at essentially
isadifficultyincoveringessentialcontingenciesofthemethod
100% confidence.
application.
5.4 Intrinsic versus Environmentally Associated Compo-
5.2 Uncertainty component analysis further has several
nents: Influence Quantities:
specific advantages over global analysis. The results may be
5.4.1 Some uncertainties may be intrinsic to a method. For
applicable to a variety of situations. For example, an aerosol
example, estimates from aerosol samplers may depend criti-
sampler might be (globally) evaluated as to particle-size-
cally on sampler dimensions, which if variable leads to
dependent error by side-by-side comparison to a reference
intersampler estimate variation.
sampler in several coal mines. The knowledge obtained may
5.4.2 On the other hand, a sampler’s performance may
not be as easily applied for sampler use in iron mines, for
dependontheenvironment.Forexample,supposeasampleris
example, as more detailed information on how the s
...
NOTICE: This standard has either been superseded and replaced by a new version or withdrawn.
Contact ASTM International (www.astm.org) for the latest information
´1
Designation: D7440 − 08 (Reapproved 2015)
Standard Practice for
Characterizing Uncertainty in Air Quality Measurements
This standard is issued under the fixed designation D7440; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
ε NOTE—Editorial corrections were made throughout in July 2015.
1. Scope Weighing Collected Aerosols
2.2 Other International Standards:
1.1 This practice is for assisting developers and users of air
ISO GUM Guide to the Expression of Uncertainty in
quality methods for sampling concentrations of both airborne
Measurement, ISO Guide 98, 1995 (See Ref (1), for an
and settled materials in characterizing measurements as to
additional measurement uncertainty resource.)
uncertainty. Where possible, analysis into uncertainty compo-
ISO 7708 Air Quality—Particle Size Fraction Definitions for
nents as recommended in the ISO Guide to the Expression of
Health-Related Sampling
Uncertainty in Measurement (ISO GUM, (1) ) is suggested.
ISO 15767 Workplace Atmospheres—Controlling and Char-
Aspects of uncertainty estimation particular to air quality
acterizing Errors in Weighing Collected Aerosol
measurement are emphasized. For example, air quality assess-
ISO 16107 Workplace Atmospheres—Protocol for Evaluat-
ment is often complicated by: the difficulty of taking replicate
ing the Performance of Diffusive Samplers, 2007
measurements owing to the large spatio-temporal variation in
EN 482 Workplace Atmospheres—General Requirements
concentration values to be measured; systematic error or bias,
for the Performance of Procedures for the Measurement of
both corrected and uncorrected; and the (rare) non-normal
Chemical Agents
distribution of errors. This practice operates mainly through
example. Background and mathematical development are rel-
3. Terminology
egated to appendices for optional reading.
3.1 Definitions—For definitions of terms used in this
1.2 This standard does not purport to address all of the
practice, see Terminology D1356.
safety concerns, if any, associated with its use. It is the
responsibility of the user of this standard to establish appro-
3.2 Other terms defined as follows are taken from ISO GUM
priate safety and health practices and determine the applica-
unless otherwise noted:
bility of regulatory limitations prior to use.
3.2.1 accuracy—closeness of agreement between the result
of a measurement and a true value of the measurand.
2. Referenced Documents
3.2.2 combined standard uncertainty, u —standard uncer-
c
2.1 ASTM Standards:
tainty of the result of a measurement when that result is
D1356 Terminology Relating to Sampling and Analysis of
obtained from the values of a number of other quantities, equal
Atmospheres
to the positive square root of a sum of terms, the terms being
D3670 Guide for Determination of Precision and Bias of
the variances or covariances of these other quantities weighted
Methods of Committee D22
according to how the measurement result varies with changes
D6246 Practice for Evaluating the Performance of Diffusive
in these quantities.
Samplers
3.2.2.1 Discussion—As within ISO GUM, the “other quan-
D6552 Practice for Controlling and Characterizing Errors in
tities” are designated uncertainty components u from source j.
j
The component u is taken as the standard deviation estimate
j
from source j in the case of a source of random variation.
This practice is under the jurisdiction of ASTM Committee D22 on Air Quality
3.2.3 coverage factor, k—numerical factor used as a multi-
and is the direct responsibility of Subcommittee D22.01 on Quality Control.
plier of the combined standard uncertainty (u ) in order to
Current edition approved July 1, 2015. Published July 2015. Originally approved
c
in 2008. Last previous edition approved in 2008 as D7440 – 08. DOI: 10.1520/
obtain an expanded uncertainty (U).
D7440-08R15E01.
The boldface numbers in parentheses refer to the list of references at the end of
this standard.
3 4
For referenced ASTM standards, visit the ASTM website, www.astm.org, or BIPM version available for download from http://www.bipm.org/en/
contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM publications/guides/gum.html. ISO version available from American National
Standards volume information, refer to the standard’s Document Summary page on Standards Institute (ANSI), 25 W. 43rd St., 4th Floor, New York, NY 10036,
the ASTM website. http://www.ansi.org.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
´1
D7440 − 08 (2015)
3.2.3.1 Discussion—The factor k depends on the specific 3.2.14 systematic error (bias)—mean that would result from
meaning attributed to the expanded uncertainty U. However, an infinite number of measurements of the same measurand
for simplicity this practice adopts the now nearly traditional carried out under repeatability conditions minus a true value of
coverage factor as the value 2, determining the specific the measurand.
meaning of the expanded uncertainty U in different circum-
3.2.15 Type A evaluation (of uncertainty)—method of evalu-
stances. Other coverage factors if needed are then easily
ation of uncertainty by the statistical analysis of series of
implemented simply by multiplication of the traditional ex-
observations.
panded uncertainty U (see 7.1 – 7.4).
3.2.16 Type B evaluation (of uncertainty)—method of evalu-
3.2.3.2 Discussion—The use of a single coverage factor,
ation of uncertainty by means other than the statistical analysis
often through approximation, avoids the overly conservative
of series of observations.
use of individual component confidence limits rather than root
variance estimates as uncertainty components.
4. Background Information
3.2.4 error (of measurement)—result of a measurement
4.1 Uncertainty in a measurement result can be taken as the
minus a true value of the measurand.
range about an estimate, corrected for bias if known, contain-
ing the true, or mean reference value—in the language of ISO
3.2.5 expanded uncertainty, U—quantity defining an inter-
GUM, the measurand value at given confidence. Uncertainty
val about the result of a measurement that may be expected to
accounts not only for variation in a method’s results at
encompass a large fraction of the distribution of values that
application, but also for incomplete characterization of the
could reasonably be attributed to the measurand.
method when evaluated. In accordance with ISO GUM,
3.2.5.1 Discussion—This definition has the breadth to en-
uncertainty may often usefully be analyzed into individual
compass a wide variety of conceptions.
components.
3.2.5.2 Discussion—The expanded uncertainty U in some
4.2 There are several aspects of uncertainty characterization
cases is expressed in absolute terms, but sometimes as relative
specific to air quality measurements. One of these aspects
to the measurement result. What is meant is generally clear
concerns known, that is, correctible, systematic error or mean
from the context.
bias of a measurement relative to a true measurand value.
3.2.6 influence quantity—quantity that is not the measurand
Several measurement methods exist with such bias left uncor-
but that affects the result of the measurement.
rected because of policy, tradition, or other reason. Uncertainty
3.2.7 measurand—particular quantity subject to measure- deals only with what is unknown about a measurement, and as
ment. such does not include correctible (known) bias. The magnitude
of the difference between estimate and measurand value is
3.2.8 measurand value—(adapted from ISO GUM), un-
covered by accuracy as defined qualitatively in ISO GUM,
known quantity whose measurement is sought, often called the
rather than uncertainty, particularly when the bias is known,
true value. Examples are the concentration (mg/m ) of a
but uncorrected. Such methods require specification of both
substance in the air at a particular time and place, the
uncertainty and as much as is known of the uncorrected bias, or
time-weighted average of a concentration at a particular
alternatively the adoption of an accuracy measure.
position, or the expected mean concentration estimate as
obtained by a reference method at a specific time and position.
4.3 Often bias is known to exist, but with unknown value. In
the case where only limits may be placed on the magnitude of
3.2.9 (population) variance (of a random variable)—the
the bias, ISO GUM generally recommends treating the bias as
expectation of the square of the centered random variable.
uniformly distributed within the known limits. Such a distri-
3.2.10 random error—result of a measurement minus the
bution refers to independent situations, for example,
mean that would result from an infinite number of measure-
calibrations, where bias may arise (see 7.4 and Appendix X2),
ments of the same measurand carried out under the same
rather than variation at the point of method application. Even
(repeatability) conditions of measurement.
though such an equal-likelihood bias distribution may be
3.2.10.1 Discussion—Random error is equal to error minus
unrealistic, nevertheless a standard deviation estimate may be
systematic error.
made that reveals the limits on the bias. If the even-distribution
approximation is clearly invalid for a relevant set of
3.2.11 (sample) variance—the sum of the squared devia-
measurements, the procedure may be adjusted slightly by
tions of observations from their average divided by one less
adopting an accuracy measure tailored to the assumed limits.
than the number of observations.
4.4 Another issue concerns the distribution of measure-
3.2.11.1 Discussion—The sample variance is an unbiased
ments. ISO GUM deals only with normally distributed first-
estimator of the population variance.
order (that is, “small”) variations relative to measurand values.
3.2.12 standard deviation—positive square root of the vari-
An example to the contrary is afforded by normally distributed
ance.
data confounded by a small number of apparent outliers (3),
3.2.13 symmetric accuracy range A—the range symmetric which may not detract from the method performance (see
about (true) measurand values containing 95 % of measure- Appendix X4 for details). Another example is the determina-
ment estimates. A is a specific quantification of accuracy. (2) tion of an aerosol concentration at one location (perhaps at a
ISO 16107 worker’s lapel) as an estimate of the concentration at a separate
´1
D7440 − 08 (2015)
TABLE 1 Common Potential Uncertainty Components
point (such as a breathing zone). In this case the variations can
be of the order of the estimate itself and may have the character Sampling
personal sampling pump flow rate: setting the pump and subsequent drift
of a log-normal distribution.
sampling rate of diffusive sampler
sampler dimension (aerosol and diffusive sampling)
4.5 The spatial inhomogeneity alluded to in 4.4 relates to
collection efficiency of a sampler or sampling medium
another point regarding the focus of this practice. The spatio-
(also, see (6))
temporal variations in air quality characteristics are generally
Analytical
aerosol weighing
so large (4) as to preclude evaluation of a method during
recovery (for example, chromatographic or spectroscopic methods)
application through the use of replicate measurements. In this
Poisson counting (for example, in XRD methods)
case, often an initial single method evaluation is undertaken
instrument or sensor variation
operator effects giving inter-lab differences (if data from several labs are to
with the purpose of determining uncertainty present in subse-
be used)
quent applications of the method. Confidence in such an
Sample
evaluation can be specified and relates to the concept of
sample stability
sample preparation (for example, handling silica quasi-suspensions)
prediction-intervals (5) (see 7.2).
sample loss during transport or storage
4.6 A related subject is measurement system control. The Evaluation
calibration material uncertainty
measurement system must remain in a state of statistical
evaluation chamber concentration uncertainty
control if an introductory evaluation is to characterize later
other bias-correction uncertainty
Environmental Influence Parameters
practical applications of the method. Measurement system
temperature (inadequacy of correction, if correction is made as with diffusive
control is evaluated using an ongoing quality control program,
samplers)
testing critical performance aspects for detecting problems
atmospheric pressure
humidity
which may develop in the method.
aerosol size distribution (if not measured by a given aerosol sampling method)
ambient wind velocity
5. Summary of Practice
sampled concentration magnitude itself (for example, sorbent loading)
5.1 The essential idea behind ISO GUM is the analysis to
the fullest extent practical of the elemental sources of what is
unknown in the estimate of a measurand value. This contrasts
with a global or top-down determination of uncertainty, which
error or bias; however, random variation may also fall into this
could for example be done ideally by comparing replicate
category. For example, a common assumption (see, for
estimates to known measurand values over all conditions
example, EN 482) regarding personal sampling in the work-
expected in application of the method. Although a global
place is that the relative standard deviation associated with
uncertainty evaluation may sometimes seem inexpensive, there
personal sampling pump variations is <5 % at essentially
is a difficulty in covering essential contingencies of the method
100 % confidence.
application.
5.4 Intrinsic versus Environmentally Associated Compo-
5.2 Uncertainty component analysis further has several
nents: Influence Quantities:
specific advantages over global analysis. The results may be
5.4.1 Some uncertainties may be intrinsic to a method. For
applicable to a variety of situations. For example, an aerosol
example, estimates from aerosol samplers may depend criti-
sampler might be (globally) evaluated as to particle-size-
cally on sampler dimensions, which if variable leads to
dependent error by side-by-side comparison to a reference
intersampler estimate variation.
sampler in several coal mines. The knowledge obtained may
5.4.2 On the other hand, a sampler’s performance may
not be as easily applied for sampler use in iron mines, for
depend on the environment. For example
...
This document is not an ASTM standard and is intended only to provide the user of an ASTM standard an indication of what changes have been made to the previous version. Because
it 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 version
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Designation: D7440 − 08 D7440 − 08 (Reapproved 2015)
Standard Practice for
Characterizing Uncertainty in Air Quality Measurements
This standard is issued under the fixed designation D7440; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
ε NOTE—Editorial corrections were made throughout in July 2015.
1. Scope
1.1 This practice is for assisting developers and users of air quality methods for sampling concentrations of both airborne and
settled materials in characterizing measurements as to uncertainty. Where possible, analysis into uncertainty components as
recommended in the ISO Guide to the Expression of Uncertainty in Measurement ((ISO GUM, (1,) ISO GUM) ) is suggested.
Aspects of uncertainty estimation particular to air quality measurement are emphasized. For example, air quality assessment is
often complicated by: the difficulty of taking replicate measurements owing to the large spatio-temporal variation in concentration
values to be measured; systematic error or bias, both corrected and uncorrected; and the (rare) non-normal distribution of errors.
This practice operates mainly through example. Background and mathematical development are relegated to appendices for
optional reading.
1.2 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility
of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory
limitations prior to use.
2. Referenced Documents
2.1 ASTM Standards:
D1356 Terminology Relating to Sampling and Analysis of Atmospheres
D3670 Guide for Determination of Precision and Bias of Methods of Committee D22
D6061 Practice for Evaluating the Performance of Respirable Aerosol Samplers
D6246 Practice for Evaluating the Performance of Diffusive Samplers
D6552 Practice for Controlling and Characterizing Errors in Weighing Collected Aerosols
E691 Practice for Conducting an Interlaboratory Study to Determine the Precision of a Test Method
2.2 Other International Standards:
ISO GUM Guide to the Expression of Uncertainty in Measurement, ISO Guide 98, 1995 (See Ref (1), giving initial
publication.)for an additional measurement uncertainty resource.)
ISO 7708 Air Quality—Particle Size Fraction Definitions for Health-Related Sampling
ISO 15767 Workplace Atmospheres—Controlling and Characterizing Errors in Weighing Collected Aerosol
ISO 16107 Workplace Atmospheres—Protocol for Evaluating the Performance of Diffusive Samplers, 2007
EN 482 Workplace Atmospheres—General Requirements for the Performance of Procedures for the Measurement of Chemical
Agents
3. Terminology
3.1 Definitions—For definitions of terms used in this practice, see Terminology D1356.
3.2 Other terms defined as follows are taken from ISO GUM unless otherwise noted:
3.2.1 accuracy—closeness of agreement between the result of a measurement and a true value of the measurand.
This practice is under the jurisdiction of ASTM Committee D22 on Air Quality and is the direct responsibility of Subcommittee D22.01 on Quality Control.
Current edition approved April 1, 2008July 1, 2015. Published May 2008July 2015. Originally approved in 2008. Last previous edition approved in 2008 as D7440 – 08.
DOI: 10.1520/D7440-08.10.1520/D7440-08R15E01.
The boldface numbers in parentheses refer to the list of references at the end of this standard.
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 Standards
volume information, refer to the standard’s Document Summary page on the ASTM website.
Available from BIPM version available for download from http://www.bipm.org/en/publications/guides/gum.html. ISO version available from American National
Standards Institute (ANSI), 25 W. 43rd St., 4th Floor, New York, NY 10036, http://www.ansi.org.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
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D7440 − 08 (2015)
3.2.2 combined standard uncertainty, u —standard uncertainty of the result of a measurement when that result is obtained from
c
the values of a number of other quantities, equal to the positive square root of a sum of terms, the terms being the variances or
covariances of these other quantities weighted according to how the measurement result varies with changes in these quantities.
3.2.2.1 Discussion—
As within ISO GUM, the “other quantities” are designated uncertainty components u from source j. The component u is taken
j j
as the standard deviation estimate from source j in the case of a source of random variation.
3.2.3 coverage factor, k—numerical factor used as a multiplier of the combined standard uncertainty (u ) in order to obtain an
c
expanded uncertainty (U).
3.2.3.1 Discussion—
The factor k depends on the specific meaning attributed to the expanded uncertainty U. However, for simplicity this practice adopts
the now nearly traditional coverage factor as the value 2, determining the specific meaning of the expanded uncertainty U in
different circumstances. Other coverage factors if needed are then easily implemented simply by multiplication of the traditional
expanded uncertainty U (see 7.1 – 7.4).
3.2.3.2 Discussion—
The use of a single coverage factor, often through approximation, avoids the overly conservative use of individual component
confidence limits rather than root variance estimates as uncertainty components.
3.2.4 error (of measurement)—result of a measurement minus a true value of the measurand.
3.2.5 expanded uncertainty, U—quantity defining an interval about the result of a measurement that may be expected to
encompass a large fraction of the distribution of values that could reasonably be attributed to the measurand.
3.2.5.1 Discussion—
This definition has the breadth to encompass a wide variety of conceptions.
3.2.5.2 Discussion—
The expanded uncertainty U in some cases is expressed in absolute terms, but sometimes as relative to the measurement result.
What is meant is generally clear from the context.
3.2.6 influence quantity—quantity that is not the measurand but that affects the result of the measurement.
3.2.7 measurand—particular quantity subject to measurement.
3.2.8 measurand value—(adapted from ISO GUM), unknown quantity whose measurement is sought, often called the true
value. Examples are the concentration (mg/m ) of a substance in the air at a particular time and place, the time-weighted average
of a concentration at a particular position, or the expected mean concentration estimate as obtained by a reference method at a
specific time and position.
3.2.9 (population) variance (of a random variable)—the expectation of the square of the centered random variable.
3.2.10 random error—result of a measurement minus the mean that would result from an infinite number of measurements of
the same measurand carried out under the same (repeatability) conditions of measurement.
3.2.10.1 Discussion—
Random error is equal to error minus systematic error.
3.2.11 (sample) variance—the sum of the squared deviations of observations from their average divided by one less than the
number of observations.
3.2.11.1 Discussion—
The sample variance is an unbiased estimator of the population variance.
3.2.12 standard deviation—positive square root of the variance.
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D7440 − 08 (2015)
3.2.13 symmetric accuracy range A—the range symmetric about (true) measurand values containing 95 % of measurement
estimates. A is a specific quantification of accuracy.(2) ISO 16107
3.2.14 systematic error (bias)—mean that would result from an infinite number of measurements of the same measurand carried
out under repeatability conditions minus a true value of the measurand.
3.2.15 Type A evaluation (of uncertainty)—method of evaluation of uncertainty by the statistical analysis of series of
observations.
3.2.16 Type B evaluation (of uncertainty)—method of evaluation of uncertainty by means other than the statistical analysis of
series of observations.
4. Background Information
4.1 Uncertainty in a measurement result can be taken as the range about an estimate, corrected for bias if known, containing
the true, or mean reference value—in the language of ISO GUM, the measurand value at given confidence. Uncertainty accounts
not only for variation in a method’s results at application, but also for incomplete characterization of the method when evaluated.
Per In accordance with ISO GUM, uncertainty may often usefully be analyzed into individual components.
4.2 There are several aspects of uncertainty characterization specific to air quality measurements. One of these aspects concerns
known, that is, correctible, systematic error or mean bias of a measurement relative to a true measurand value. Several
measurement methods exist with such bias left uncorrected because of policy, tradition, or other reason. Uncertainty deals only
with what is unknown about a measurement, and as such does not include correctible (known) bias. The magnitude of the
difference between estimate and measurand value is covered by accuracy as defined qualitatively in ISO GUM, rather than
uncertainty, particularly when the bias is known, but uncorrected. Such methods require specification of both uncertainty and as
much as is known of the uncorrected bias, or alternatively the adoption of an accuracy measure.
4.3 Often bias is known to exist, but with unknown value. In the case where only limits may be placed on the magnitude of
the bias, ISO GUM generally recommends treating the bias as uniformly distributed within the known limits. Such a distribution
refers to independent situations, for example, calibrations, where bias may arise (see 7.4 and Appendix X2), rather than variation
at the point of method application. Even though such an equal-likelihood bias distribution may be unrealistic, nevertheless a
standard deviation estimate may be made that reveals the limits on the bias. If the even-distribution approximation is clearly invalid
for a relevant set of measurements, the procedure may be adjusted slightly by adopting an accuracy measure tailored to the assumed
limits.
4.4 Another issue concerns the distribution of measurements. ISO GUM deals only with normally distributed first-order (that
is, “small”) variations relative to measurand values. An example to the contrary is afforded by normally distributed data
confounded by a small number of apparent outliers (3), which may not detract from the method performance (see Appendix X4
for details). Another example is the determination of an aerosol concentration at one location (perhaps at a worker’s lapel) as an
estimate of the concentration at a separate point (such as a breathing zone). In this case the variations can be of the order of the
estimate itself and may have the character of a log-normal distribution.
4.5 The spatial inhomogeneity alluded to in 4.4 relates to another point regarding the focus of this practice. The spatio-temporal
variations in air quality characteristics are generally so large (4) as to preclude evaluation of a method during application through
the use of replicate measurements. In this case, often an initial single method evaluation is undertaken with the purpose of
determining uncertainty present in subsequent applications of the method. Confidence in such an evaluation can be specified and
relates to the concept of prediction-intervals (5) (see 7.2).
4.6 A related subject is measurement system control. The measurement system must remain in a state of statistical control if
an introductory evaluation is to characterize later practical applications of the method. Measurement system control is evaluated
using an ongoing quality control program, testing critical performance aspects for detecting problems which may develop in the
method.
5. Summary of Practice
5.1 The essential idea behind ISO GUM is the analysis to the fullest extent practical of the elemental sources of what is
unknown in the estimate of a measurand value. This contrasts with a global or top-down determination of uncertainty, which could
for example be done ideally by comparing replicate estimates to known measurand values over all conditions expected in
application of the method. Although a global uncertainty evaluation may sometimes seem inexpensive, there is a difficulty in
covering essential contingencies of the method application.
5.2 Uncertainty component analysis further has several specific advantages over global analysis. The results may be applicable
to a variety of situations. For example, an aerosol sampler might be (globally) evaluated as to particle-size-dependent error by
side-by-side comparison to a reference sampler in several coal mines. The knowledge obtained may not be as easily applied for
sampler use in iron mines, for example, as more detailed information on how the sampler performs over given dust size
distributions may be needed. Furthermore, specific problem areas of a given method may be pinpointed. The detailed itemization
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D7440 − 08 (2015)
of uncertainty sources leads to a transparency in covering the essential problems of a measurement method. Examples of
potentially significant uncertainty components are listed in Table 1.
5.3 Type A and B Uncertainty Components:
5.3.1 Components that have been statistically evaluated during method application may be classified as Type A. (See Section
7 for specific examples.)
5.3.2 Some components are often statistically evaluated during an initial method evaluation, rather than at application. Also
acknowledged is a common situation that components may not have been characterized in a statistically valid manner and therefore
may require professional judgment for itemizing. Such components are termed Type B uncertainties. Type B uncertainties are often
associated with unknown systematic error or bias; however, random variation may also fall into this category. For example, a
common assumption (see, for example, EN 482) regarding personal sampling in the workplace is that the relative standard
deviation associated with personal sampl
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