1、Designation: D 7440 08Standard Practice forCharacterizing Uncertainty in Air Quality Measurements1This standard is issued under the fixed designation D 7440; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of last revision
2、. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon (e) indicates an editorial change since the last revision or reapproval.1. Scope1.1 This practice is for assisting developers and users of airquality methods for sampling concentrations of both airborneand settled
3、materials in characterizing measurements as touncertainty. Where possible, analysis into uncertainty compo-nents as recommended in the ISO Guide to the Expression ofUncertainty in Measurement (1,2ISO GUM) is suggested.Aspects of uncertainty estimation particular to air qualitymeasurement are emphasi
4、zed. For example, air quality assess-ment is often complicated by: the difficulty of taking replicatemeasurements owing to the large spatio-temporal variation inconcentration values to be measured; systematic error or bias,both corrected and uncorrected; and the (rare) non-normaldistribution of erro
5、rs. This practice operates mainly throughexample. Background and mathematical development are rel-egated to appendices for optional reading.1.2 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard t
6、o establish appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:3D 1356 Terminology Relating to Sampling and Analysis ofAtmospheresD 3670 Guide for Determination of Precision and Bias ofMethods of
7、Committee D22D 6061 Practice for Evaluating the Performance of Respi-rable Aerosol SamplersD 6246 Practice for Evaluating the Performance of Diffu-sive SamplersD 6552 Practice for Controlling and Characterizing Errorsin Weighing Collected AerosolsE 691 Practice for Conducting an Interlaboratory Stud
8、y toDetermine the Precision of a Test Method2.2 Other International Standards:ISO GUM Guide to the Expression of Uncertainty inMeasurement, ISO Guide 98, 1995 (See Ref (1), givinginitial publication.)4ISO 7708 Air QualityParticle Size Fraction Definitionsfor Health-Related Sampling4ISO 15767 Workpla
9、ce AtmospheresControlling andCharacterizing Errors in Weighing Collected Aerosol4ISO 16107 Workplace AtmospheresProtocol for Evaluat-ing the Performance of Diffusive Samplers, 20074EN 482 Workplace AtmospheresGeneral Requirementsfor the Performance of Procedures for the Measurement ofChemical Agents
10、43. Terminology3.1 DefinitionsFor definitions of terms used in this prac-tice, see Terminology D 1356.3.2 Other terms defined as follows are taken from ISOGUM unless otherwise noted:3.2.1 accuracycloseness of agreement between the resultof a measurement and a true value of the measurand.3.2.2 combin
11、ed standard uncertainty, ucstandard uncer-tainty of the result of a measurement when that result isobtained from the values of a number of other quantities, equalto the positive square root of a sum of terms, the terms beingthe variances or covariances of these other quantities weightedaccording to
12、how the measurement result varies with changesin these quantities.3.2.2.1 DiscussionAs within ISO GUM, the “other quan-tities” are designated uncertainty components ujfrom source j.The component ujis taken as the standard deviation estimatefrom source j in the case of a source of random variation.3.
13、2.3 coverage factor, knumerical factor used as a multi-plier of the combined standard uncertainty (uc) in order toobtain an expanded uncertainty (U).3.2.3.1 DiscussionThe factor k depends on the specificmeaning attributed to the expanded uncertainty U. However,for simplicity this practice adopts the
14、 now nearly traditional1This practice is under the jurisdiction ofASTM Committee D22 onAir Qualityand is the direct responsibility of Subcommittee D22.01 on Quality Control.Current edition approved April 1, 2008. Published May 2008.2The boldface numbers in parentheses refer to the list of references
15、 at the end ofthis standard.3For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStandards volume information, refer to the standards Document Summary page onthe ASTM website.4Available from American National
16、 Standards Institute (ANSI), 25 W. 43rd St.,4th Floor, New York, NY 10036, http:/www.ansi.org.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.coverage factor as the value 2, determining the specificmeaning of the expanded uncertainty
17、 U in different circum-stances. Other coverage factors if needed are then easilyimplemented simply by multiplication of the traditional ex-panded uncertainty U (see 7.1-7.4).3.2.3.2 DiscussionThe use of a single coverage factor,often through approximation, avoids the overly conservativeuse of indivi
18、dual component confidence limits rather than rootvariance estimates as uncertainty components.3.2.4 error (of measurement)result of a measurementminus a true value of the measurand.3.2.5 expanded uncertainty, Uquantity defining an inter-val about the result of a measurement that may be expected toen
19、compass a large fraction of the distribution of values thatcould reasonably be attributed to the measurand.3.2.5.1 DiscussionThis definition has the breadth to en-compass a wide variety of conceptions.3.2.5.2 DiscussionThe expanded uncertainty U in somecases is expressed in absolute terms, but somet
20、imes as relativeto the measurement result. What is meant is generally clearfrom the context.3.2.6 influence quantityquantity that is not the measurandbut that affects the result of the measurement.3.2.7 measurandparticular quantity subject to measure-ment.3.2.8 measurand value(adapted from ISO GUM),
21、 un-known quantity whose measurement is sought, often called thetrue value. Examples are the concentration (mg/m3)ofasubstance in the air at a particular time and place, thetime-weighted average of a concentration at a particularposition, or the expected mean concentration estimate asobtained by a r
22、eference method at a specific time and position.3.2.9 (population) variance (of a random variable)theexpectation of the square of the centered random variable.3.2.10 random errorresult of a measurement minus themean that would result from an infinite number of measure-ments of the same measurand car
23、ried out under the same(repeatability) conditions of measurement.3.2.10.1 DiscussionRandom error is equal to error minussystematic error.3.2.11 (sample) variancethe sum of the squared devia-tions of observations from their average divided by one lessthan the number of observations.3.2.11.1 Discussio
24、nThe sample variance is an unbiasedestimator of the population variance.3.2.12 standard deviationpositive square root of the vari-ance.3.2.13 symmetric accuracy range Athe range symmetricabout (true) measurand values containing 95 % of measure-ment estimates. A is a specific quantification of accura
25、cy. (2)ISO 161073.2.14 systematic error (bias)mean that would result froman infinite number of measurements of the same measurandcarried out under repeatability conditions minus a true value ofthe measurand.3.2.15 Type A evaluation (of uncertainty)method ofevaluation of uncertainty by the statistica
26、l analysis of series ofobservations.3.2.16 Type B evaluation (of uncertainty)method ofevaluation of uncertainty by means other than the statisticalanalysis of series of observations.4. Background Information4.1 Uncertainty in a measurement result can be taken as therange about an estimate, corrected
27、 for bias if known, contain-ing the true, or mean reference valuein the language of ISOGUM, the measurand value at given confidence. Uncertaintyaccounts not only for variation in a methods results atapplication, but also for incomplete characterization of themethod when evaluated. Per ISO GUM, uncer
28、tainty may oftenusefully be analyzed into individual components.4.2 There are several aspects of uncertainty characterizationspecific to air quality measurements. One of these aspectsconcerns known, that is, correctible, systematic error or meanbias of a measurement relative to a true measurand valu
29、e.Several measurement methods exist with such bias left uncor-rected because of policy, tradition, or other reason. Uncertaintydeals only with what is unknown about a measurement, and assuch does not include correctible (known) bias. The magnitudeof the difference between estimate and measurand valu
30、e iscovered by accuracy as defined qualitatively in ISO GUM,rather than uncertainty, particularly when the bias is known,but uncorrected. Such methods require specification of bothuncertainty and as much as is known of the uncorrected bias, oralternatively the adoption of an accuracy measure.4.3 Oft
31、en bias is known to exist, but with unknown value. Inthe case where only limits may be placed on the magnitude ofthe bias, ISO GUM generally recommends treating the bias asuniformly distributed within the known limits. Such a distri-bution refers to independent situations, for example, calibra-tions
32、, where bias may arise (see 7.4 and Appendix X2), ratherthan variation at the point of method application. Even thoughsuch an equal-likelihood bias distribution may be unrealistic,nevertheless a standard deviation estimate may be made thatreveals the limits on the bias. If the even-distribution appr
33、oxi-mation is clearly invalid for a relevant set of measurements, theprocedure may be adjusted slightly by adopting an accuracymeasure tailored to the assumed limits.4.4 Another issue concerns the distribution of measure-ments. ISO GUM deals only with normally distributed first-order (that is, “smal
34、l”) variations relative to measurand values.An example to the contrary is afforded by normally distributeddata confounded by a small number of apparent outliers (3),which may not detract from the method performance (seeAppendix X4 for details). Another example is the determina-tion of an aerosol con
35、centration at one location (perhaps at aworkers lapel) as an estimate of the concentration at a separatepoint (such as a breathing zone). In this case the variations canbe of the order of the estimate itself and may have the characterof a log-normal distribution.4.5 The spatial inhomogeneity alluded
36、 to in 4.4 relates toanother point regarding the focus of this practice. The spatio-temporal variations in air quality characteristics are generallyso large (4) as to preclude evaluation of a method duringapplication through the use of replicate measurements. In thiscase, often an initial single met
37、hod evaluation is undertakenD7440082with the purpose of determining uncertainty present in subse-quent applications of the method. Confidence in such anevaluation can be specified and relates to the concept ofprediction-intervals (5) (see 7.2).4.6 A related subject is measurement system control. The
38、measurement system must remain in a state of statisticalcontrol if an introductory evaluation is to characterize laterpractical applications of the method. Measurement systemcontrol is evaluated using an ongoing quality control program,testing critical performance aspects for detecting problemswhich
39、 may develop in the method.5. Significance and Use5.1 Aprimary use intended for this practice is for qualifyingASTM International Standards as Standard Test Methods. Inthe past, a “Precision and Bias” report has been required.However, recently a statement of uncertainty has become anacceptable alter
40、native to D367091: Guide for Determinationof Precision and Bias of Methods of Committee D-22. Inclu-sion of such a statement with a method description simplifiescomparison of ASTM Test Methods to analogous ISO andCEN standards, now required to have uncertainty statements.5.2 Standardizing the charac
41、terization of sampling/analytical method performance is expected to be useful in otherapplications as well. For example, performance details are anecessity for justifying compliance decisions based on experi-mental air quality assessments (6). Documented uncertaintycan form a basis for specific crit
42、eria defining acceptablesampling/analytical method performance.5.3 Furthermore, high quality atmospheric measurementsare vital for making decisions as to how hazardous substancesare to be controlled. Valid data are required for drawingreasonable epidemiological conclusions, for making sounddecisions
43、 as to acceptable limits, as well as for determining theefficacy of a hazard control system.5.4 Finally, because of developing world-wide acceptanceof ISO GUM for detailing measurements when statistics aresimple, the practice should be useful in comparing ASTMInternational Test Methods to others pub
44、lished methods. Thecodification of statistical procedures may in fact minimize thedifficulty in interpreting a plethora of individual, albeit possi-bly valid, approaches.6. Summary of Practice6.1 The essential idea behind ISO GUM is the analysis tothe fullest extent practical of the elemental source
45、s of what isunknown in the estimate of a measurand value. This contrastswith a global or top-down determination of uncertainty, whichcould for example be done ideally by comparing replicateestimates to known measurand values over all conditionsexpected in application of the method. Although a global
46、uncertainty evaluation may sometimes seem inexpensive, thereis a difficulty in covering essential contingencies of the methodapplication.6.2 Uncertainty component analysis further has severalspecific advantages over global analysis. The results may beapplicable to a variety of situations. For exampl
47、e, an aerosolsampler might be (globally) evaluated as to particle-size-dependent error by side-by-side comparison to a referencesampler in several coal mines. The knowledge obtained maynot be as easily applied for sampler use in iron mines, forexample, as more detailed information on how the sampler
48、performs over given dust size distributions may be needed.Furthermore, specific problem areas of a given method may bepinpointed. The detailed itemization of uncertainty sourcesleads to a transparency in covering the essential problems of ameasurement method. Examples of potentially significant un-c
49、ertainty components are listed in Table 1.6.3 Type A and B Uncertainty Components:6.3.1 Components that have been statistically evaluatedduring method application may be classified as Type A. (SeeSection 7 for specific examples.)6.3.2 Some components are often statistically evaluatedduring an initial method evaluation, rather than at application.Also acknowledged is a common situation that componentsmay not have been characterized in a statistically valid mannerand therefore may require professional judgment for itemizing.Such components are termed Type
