1、Designation: D7729 12 (Reapproved 2018)1Standard Practice forDetermining and Expressing Precision of MeasurementResults, in the Analysis of Water, as Relative StandardDeviation, Utilizing DQCALC Software1This standard is issued under the fixed designation D7729; the number immediately following the
2、designation indicates the year oforiginal adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon () indicates an editorial change since the last revision or reapproval.1NOTEThe Keywords section was added ed
3、itorially in August 2018.1. Scope1.1 This practice describes a procedure for developing agraphical model of relative standard deviation versus concen-tration for analytical methods used in the analysis of water(methods that are subject to non-additive random errors) for thepurpose of assigning a sta
4、tement of noise or randomness toanalytical results (commonly referred to as a precisionstatement), in either a manual or an automated fashion.1.2 Data analysis and modeling is done with CommitteeD19 Adjunct DQCALC2(a Microsoft Excel3-based tool).1.3 The values stated in SI units are to be regarded a
5、sstandard. No other units of measurement are included in thisstandard.1.4 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 to establish appro-priate safety, health, and environmental practices a
6、nd deter-mine the applicability of regulatory limitations prior to use.1.5 This international standard was developed in accor-dance with internationally recognized principles on standard-ization established in the Decision on Principles for theDevelopment of International Standards, Guides and Recom
7、-mendations issued by the World Trade Organization TechnicalBarriers to Trade (TBT) Committee.2. Introduction2.1 An understanding of the uncertainty associated withmeasurement results is necessary for evaluating the utility ofthose results. Without a reported uncertainty estimate, users ofmeasuremen
8、t results are unable to determine if the data aresufficiently precise for any specific data use.2.2 Measurement uncertainty (MU) is most generally un-derstood to be “a parameter characterizing the dispersion of thequantity values being attributed to a measurand” (from VIM2.26). This definition can b
9、e implemented as an expression(“uncertainty statement”) associated with an reported measure-ment that represents the statistically based (Type A estimate)dispersion of experimental results around a reported value.2.3 There is no universally agreed upon format or nomen-clature for uncertainty stateme
10、nts. The literature offers sugges-tions ranging from simple expressions of standard deviation or“fractional uncertainty” (standard deviation divided by re-ported result) to confidence intervals to detailed “uncertaintyreports.”2.4 In addition to the “random” errors encompassed in theideas expressed
11、in 1.1 and 1.2, there are also “systematic”errors, biases, that can be considered as part of uncertainty. Theliterature is not consistent on how unknown bias is consideredin an uncertainty statement. For purposes of this practice, biasis assumed to have been corrected for or insignificant in therepo
12、rted results, and bias is not specifically incorporated in theproposed uncertainty statement.2.5 For purposes of this practice, the terms MU, uncertaintystatement,ormeasurement uncertainty will be used synony-mously to designate the expression accompanying measure-ment results for the purpose of ass
13、essing the utility of thoseresults.2.6 This practice proposes the use of fractional uncertaintyor relative standard deviation (RSD) as the expression of MU.2.7 Traditionally, in the generation and publication of datarelated to the analysis of water, a continuous function (model)describing the relati
14、onship of uncertainty (as standard devia-tion) to concentration is not available. To compensate for thislack, discrete points bounding certain levels of uncertainty arecalculated, for example, “detection limits” (typically around33 % RSD) and “quantitation limits” (often around 10 %1This practice is
15、 under the jurisdiction of ASTM Committee D19 on Water andis the direct responsibility of Subcommittee D19.02 on Quality Systems,Specification, and Statistics.Current edition approved Aug. 1, 2018. Published September 2018. Originallyapproved in 2012. Last previous edition approved in 2012 as D7729
16、12. DOI:10.1520/D7729-12R18E01.2Available from ASTM International Headquarters. Order Adjunct No. ADJDQ-CALC. Original adjunct produced in 2007.3Microsoft Excel is a trademark of the Microsoft Corporation, Redmond, WA.Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocke
17、n, PA 19428-2959. United StatesThis international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for theDevelopment of International Standards, Guides and Recommendations issued by the World Trade Organizat
18、ion Technical Barriers to Trade (TBT) Committee.1RSD). Results are flagged to indicate their relationship to oneof these limits. Alternatively, this practice directs the creationof a model of uncertainty (RSD versus concentration) whichallows assignment of a discrete uncertainty estimate to anyresul
19、t value measured within the range of modeled data.2.8 This practice is based on the use of the DQCALCsoftware that was developed to simplify the calculation of theinter-laboratory quantitation estimate (IQE) (Practice D6512).This practice is restricted to the development of an uncertaintymodel for t
20、he reporting of MU within a single laboratory. Inaddition to providing an estimate of single-laboratory measure-ment uncertainty, the DQCALC software automatically calcu-lates LC from Curie, equivalent to the United States Envi-ronmental Protection Agency (EPA)s method detection limit(MDL), and the
21、ASTM detection estimate for a single lab (thisutilizes a “3 sigma” tolerance interval rather than the standardconfidence interval).2.9 This practice provides the tools to allow a laboratory toembed the RSD versus concentration relationship into asufficiently powerful laboratory information managemen
22、t sys-tem (LIMS) resulting in the ability to automatically report MUwith all data reported out of the LIMS for modeled parameters.2.10 The DQCALC software is available from ASTM (seePractice D7510 and Adjunct DQCALC2).2.11 In addition, this practice discusses the variables thatshould be considered f
23、or inclusion in the uncertainty modelingstudy.3. Referenced Documents3.1 ASTM Standards:4D1129 Terminology Relating to WaterD6512 Practice for Interlaboratory Quantitation EstimateD7510 Practice for Performing Detection and QuantitationEstimation and Data Assessment Utilizing DQCALCSoftware, based o
24、n ASTM Practices D6091 and D6512 ofCommittee D19 on Water3.2 Other Documents:5VIM International Vocabulary of Metrology, Basic and Gen-eral Concepts and Associated Terms, 3rd edition, JCGM200:20084. Terminology4.1 Definitions:4.1.1 For definitions of terms used in this standard, refer toTerminology
25、D1129.4.2 Definitions of Terms Specific to This Standard:4.2.1 measurement uncertainty, nin the analysis of water,a value representing the precision of a reported determination.4.2.2 water analysis measurement uncertainty, nin theanalysis of water, a value representing the precision of areported det
26、ermination, expressed as the relative standarddeviation of typical measurements of the same form.4.3 Symbols:4.3.1 IQEInter-Laboratory Quantitation Estimate4.3.2 LIMSLaboratory Information Management System4.3.3 MUMeasurement Uncertainty4.3.4 RSDRelative Standard Deviation5. Summary of Practice5.1 T
27、he relationship between relative standard deviation andconcentration is modeled using a multi-replicate and multi-level design and utilizing the curve fitting tools in the DQ-CALC software. The DQCALC software will return thecoefficients for the selected function/model of standard devia-tion against
28、 concentration. The general equations are given inthis practice. From the equation, the appropriate standarddeviation for any concentration in the range represented in themodel study can be calculated. This can then be converted intoRSD, the recommended reporting format.5.2 Practice D6512, the IQE p
29、ractice that forms the basis forthis practice, has the feature of correcting for recovery.Therefore, for purposes of this practice, true concentrations,that is, concentrations that have been “corrected” for recoverybias are used. Where a laboratory in use of its methods oftesting does not correct re
30、sultant values, the calculated RSDwill be marginally higher or lower, depending on the magni-tude of the uncorrected bias in the reported data. Whereuncorrected bias is less than 10 % of the magnitude of theresult, the error in the RSD estimate may be consideredinsignificant.6. Sources of Imprecisio
31、n6.1 When utilizing the result of a measurement to make abinary decision (yes/no, pass/fail, etc.) there is a risk of makinga false positive determination (saying a condition exists whenit does not) or a false negative determination (saying acondition does not exist when it does). The more precise t
32、heestimate of the measurement uncertainty of the result (thesmaller the relative standard deviation), the less chance there isof making such incorrect assessments.6.2 The most precise possible estimate of a results MUwould be obtained through replicate measurements done at thesame time as the initia
33、l measurement. (This would, of course,also give a more precise estimate of the measurement result a mean with n 1). The greater the number of replicatesperformed, the better the estimate of MU. In practice, this levelof analytical work is rarely performed, unless there are direconsequences associate
34、d with the result.6.3 Under typical circumstances in analytical laboratories,uncertainty is not determined from replicates of real-worldsamples. An assumption (rarely tested) is made that theuncertainty of the measurements of standards of known (trace-able) concentration is comparable to the uncerta
35、inty of mea-surements on real world samples. It is well known that differentmatrices, especially matrices with suspended matter containingthe analyte, have much different measurement uncertainties4For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at
36、 serviceastm.org. For Annual Book of ASTMStandards volume information, refer to the standards Document Summary page onthe ASTM website.5Available from Bureau International des Poids et Mesures (BIMP), Pavillon deBreteuil F-92312 Svres Cedex, France, http:/www.bipm.org.D7729 12 (2018)12and they are t
37、ypically greater than that of measurements ontraceable standard solutions, but for pragmatic reasons this isoften ignored. This means uncertainty estimates determinedfrom standards run in replicate with the real world samplemeasurement, are estimates of uncertainty that are typicallymuch smaller (im
38、plying much better precision) than is war-ranted and are estimates of the method performance on idealsamples.6.4 But, again, under typical circumstances, replicate stan-dard determinations are not performed with each particular realworld sample measurement. They are typically performedacross differe
39、nt batches, different days, different operators, andeven across different laboratories. Each of these elements orvariables batch, day, etc. adds an extra component of“noise,” each increasing the magnitude of the uncertaintyestimate.6.5 Within each prescribed set of variables (given batch,day, operat
40、or, etc.), the replicate precision obtained is oftencomparable. But, due to varying “conditions” (usually un-known and undeterminable) the mean result under each con-dition differs. This difference between mean results underdifferent conditions is what adds additional variability extranoise and incr
41、eases the magnitude of the measurementuncertainty estimate. Essentially, as each new variable is addedto the uncertainty determination, biases become incorporatedas random noise.6.6 The net result of these assumptions and non-idealconditions of test during MU estimation is that the MU valueobtained
42、and reported is itself uncertain, and the magnitude oferror in the MU estimate is difficult or impossible to determine.6.7 As a matter of practicality, even with the use ofstandards rather than real-world sample replicates and theinclusion of “extra” sources of noise, the MU estimates obtainusually
43、bear a useful relationship to the analytical results theyare reported with, and provide a reasonable ballpark ofuncertainty for the data users.6.8 In utilizing this practice to obtain MU estimates to bereported with real-world sample results, the user is cautioned tobe cognizant of these caveats in
44、choosing what sources ofvariability temporal, procedural, material, etc. are to beincluded in the MU study design. Users will need to recognizethat estimates of MU that incorporate sources of variabilityinappropriate to the data use or exclude sources that areappropriate to the data use may produce
45、uncertainties that aretypically smaller than would be most appropriate to the datause.7. Relative Standard Deviation Versus ConcentrationModels7.1 As explained in Practice D6512 (IQE), the D19 ap-proach to establishing a relationship between standard devia-tion and concentration involves generating
46、independent mea-surements at predetermined concentrations over the analyticalrange of interest, including down to zero concentration or theblank, where of interest.7.2 The standard deviations (and means) from the indepen-dent measurements at each concentration are calculated. Theseresults are correc
47、ted for bias. Four models of the function ofstandard deviation to true concentration are fitted. The modelwith the best fit is determined. The relationship of measuredconcentration to true concentration is established throughlinear regression. Least squares is used where the standarddeviation model
48、selected was any model other than constant,for the other three models, the linear regression of true versusmeasured concentration is established using weighted leastsquares.7.3 The four models used for fitting standard deviationversus true concentration are: constant, exponential, straight-line, and
49、 hybrid. Multiple statistical tools and graphs arepresented to help the user decide which model is the best fit.7.4 It is the responsibility of the user to make the mostappropriate choice between models. The simplest model thatadequately represents the data over the range of interest for theintended use should be selected.8. Procedure8.1 Carry out a precision analysis study designed as de-scribed in Practice D6512 (IQE). The study must have thefollowing characteristics:8.1.1 The study should have a minimum of five levels andfive replicates at each level.
