1、BRITISH STANDARD BS ISO 11843-2:2000 Incorporating corrigendum October 2007 Capability of detection Part 2: Methodology in the linear calibration case ICS 03.120.30; 17.020 BS ISO 11843-2:2000 This British Standard was published under the authority of the Standards Committee and comes into effect on
2、 15 June 2000 BSI 2008 ISBN 978 0 580 60989 3 National foreword This British Standard is the UK implementation of ISO 11843-2:2000, incorporating corrigendum October 2007, which should be read in conjunction with BS ISO 11843-1:2000. The start and finish of text introduced or altered by corrigendum
3、is indicated in the text by tags. Text altered by ISO corrigendum October 2007 is indicated in the text by . The UK participation in its preparation was entrusted to Technical Committee SS/6, Precision of test methods. A list of organizations represented on this committee can be obtained on request
4、to its secretary. This publication does not purport to include all the necessary provisions of a contract. Users are responsible for its correct application. Compliance with a British Standard cannot confer immunity from legal obligations. Amendments/corrigenda issued since publication Date Comments
5、 31 March 2008 Implementation of ISO corrigendum October 2007Referencenumber ISO11843-2:2000(E) INTERNATIONAL STANDARD ISO 11843-2 Firstedition 2000-05-01 Capabilityofdetection Part2: Methodologyinthelinearcalibrationcase Capacit de dtection Partie 2: Mthodologie de ltalonnage linaire BS ISO 11843-2
6、:2000ii iii Contents Foreword.iv Introduction.v 1 Scope1 2 Normativereferences1 3 Termsanddefinitions.2 4 Experimentaldesign2 4.1 General2 4.2 Choiceofreferencestates2 4.3 Choiceofthenumberofreferencestates,I,andthe(numbersof)replicationsofprocedure,J, KandL3 5 Thecriticalvaluesy c andx c andthemini
7、mumdetectablevaluex d ofameasurementseries.3 5.1 Basicassumptions3 5.2 Case1Constantstandarddeviation.4 5.3 Case2Standarddeviationlinearlydependentonthenetstatevariable6 6 Minimumdetectablevalueofthemeasurementmethod9 7 Reportinganduseofresults10 7.1 Criticalvalues.10 7.2 Minimumdetectablevalues10 A
8、nnexA(normative)Symbolsandabbreviations.11 AnnexB(informative)Derivationofformulae14 AnnexC(informative)Examples.20 Bibliography24 BS ISO 11843-2:2000iv Foreword ISO(theInternationalOrganizationforStandardization)isaworldwidefederationofnationalstandardsbodies(ISO memberbodies).TheworkofpreparingInt
9、ernationalStandardsisnormallycarriedoutthroughISOtechnical committees.Eachmemberbodyinterestedinasubjectforwhichatechnicalcommitteehasbeenestablishedhas therighttoberepresentedonthatcommittee.Internationalorganizations,governmentalandnon-governmental,in liaisonwithISO,alsotakepartinthework.ISOcollab
10、oratescloselywiththeInternationalElectrotechnical Commission(IEC)onallmattersofelectrotechnicalstandardization. InternationalStandardsaredraftedinaccordancewiththerulesgivenintheISO/IECDirectives,Part3. DraftInternationalStandardsadoptedbythetechnicalcommitteesarecirculatedtothememberbodiesforvoting
11、. PublicationasanInternationalStandardrequiresapprovalbyatleast75%ofthememberbodiescastingavote. AttentionisdrawntothepossibilitythatsomeoftheelementsofthispartofISO11843maybethesubjectof patentrights.ISOshallnotbeheldresponsibleforidentifyinganyorallsuchpatentrights. InternationalStandardISO11843-2
12、waspreparedbyTechnicalCommitteeISO/TC69, Applications of statistical methods, Subcommittee SC 6, Measurement methods and results. ISO11843consistsofthefollowingparts,underthegeneraltitle Capability of detection: Part 1: Terms and definitions Part 2: Methodology in the linear calibration case AnnexAf
13、ormsanormativepartofthispartofISO11843.AnnexesBandCareforinformationonly. data are used Part 4: Methodology for comparing the minimum detectable value with a given value Part 5: Methodology in the linear and non-linear calibration cases Part 3: Methodology for determination of the critical value for
14、 the response variable when no calibration BS ISO 11843-2:2000 v Introduction Anidealrequirementforthecapabilityofdetectionwithrespecttoaselectedstatevariablewouldbethattheactual stateofeveryobservedsystemcanbeclassifiedwithcertaintyaseitherequaltoordifferentfromitsbasicstate. However,duetosystemati
15、candrandomdistortions,thisidealrequirementcannotbesatisfiedbecause: inrealityallreferencestates,includingthebasicstate,areneverknownintermsofthestatevariable.Hence, allstatescanonlybecorrectlycharacterizedintermsofdifferencesfrombasicstate,i.e.intermsofthenet statevariable. Inpractice,referencestate
16、sareveryoftenassumedtobeknownwithrespecttothestatevariable.Inother words,thevalueofthestatevariableforthebasicstateissettozero;forinstanceinanalyticalchemistry,the unknownconcentrationortheamountofanalyteintheblankmaterialusuallyisassumedtobezeroand valuesofthenetconcentrationoramountarereportedinte
17、rmsofsupposedconcentrationsoramounts.In chemicaltraceanalysisespecially,itisonlypossibletoestimateconcentrationoramountdifferenceswith respecttoavailableblankmaterial.Inordertopreventerroneousdecisions,itisgenerallyrecommendedto reportdifferencesfromthebasicstateonly,i.e.dataintermsofthenetstatevari
18、able; NOTE IntheISOGuide30andinISO11095nodistinctionismadebetweenthestatevariableandthenetstate variable.Asaconsequence,inthesetwodocumentsreferencestatesare,withoutjustification,assumedtobeknownwith respecttothestatevariable. thecalibrationandtheprocessesofsamplingandpreparationaddrandomvariationto
19、themeasurement results. InthispartofISO11843,thefollowingtworequirementswerechosen: theprobabilityis ofdetecting(erroneously)thatasystemisnotinthebasicstatewhenitisinthebasic state; theprobabilityis of(erroneously)notdetectingthatasystem,forwhichthevalueofthenetstatevariableis equaltotheminimumdetec
20、tablevalue(x d ),isnotinthebasicstate. BS ISO 11843-2:2000blank 1 Capabilityofdetection Part2: Methodologyinthelinearcalibrationcase 1 Scope ThispartofISO11843specifiesbasicmethodsto: designexperimentsfortheestimationofthecriticalvalueofthenetstatevariable,thecriticalvalueofthe responsevariableandth
21、eminimumdetectablevalueofthenetstatevariable, estimatethesecharacteristicsfromexperimentaldataforthecasesinwhichthecalibrationfunctionislinear andthestandarddeviationiseitherconstantorlinearlyrelatedtothenetstatevariable. ThemethodsdescribedinthispartofISO11843areapplicabletovarioussituationssuchasc
22、heckingthe existenceofacertainsubstanceinamaterial,theemissionofenergyfromsamplesorplants,orthegeometric changeinstaticsystemsunderdistortion. Criticalvaluescanbederivedfromanactualmeasurementseriessoastoassesstheunknownstatesofsystems includedintheseries,whereastheminimumdetectablevalueofthenetstat
23、evariableasacharacteristicofthe measurementmethodservesfortheselectionofappropriatemeasurementprocesses.Inordertocharacterizea measurementprocess,alaboratoryorthemeasurementmethod,theminimumdetectablevaluecanbestatedif appropriatedataareavailableforeachrelevantlevel,i.e.ameasurementseries,ameasureme
24、ntprocess,a laboratoryorameasurementmethod.Theminimumdetectablevaluesmaybedifferentforameasurementseries, ameasurementprocess,alaboratoryorthemeasurementmethod. ISO11843isapplicabletoquantitiesmeasuredonscalesthatarefundamentallycontinuous.Itisapplicableto measurementprocessesandtypesofmeasurementeq
25、uipmentwherethefunctionalrelationshipbetweenthe expectedvalueoftheresponsevariableandthevalueofthestatevariableisdescribedbyacalibrationfunction.If theresponsevariableorthestatevariableisavectorialquantitythemethodsofISO11843areapplicable separatelytothecomponentsofthevectorsorfunctionsofthecomponen
26、ts. 2 Normativereferences Thefollowingnormativedocumentscontainprovisionswhich,throughreferenceinthistext,constituteprovisionsof thispartofISO11843.Fordatedreferences,subsequentamendmentsto,orrevisionsof,anyofthesepublications donotapply.However,partiestoagreementsbasedonthispartofISO11843areencoura
27、gedtoinvestigatethe possibilityofapplyingthemostrecenteditionsofthenormativedocumentsindicatedbelow.Forundated references,thelatesteditionofthenormativedocumentreferredtoapplies.MembersofISOandIECmaintain registersofcurrentlyvalidInternationalStandards. ISO3534-3:1999, Statistics Vocabulary and symb
28、ols Part 3: Design of experiments. ISO 3534-1, Statistics Vocabulary and symbols Part 1: General statistical terms and terms used in probability ISO 3534-2, Statistics Vocabulary and symbols Part 2: Applied statistics BS ISO 11843-2:20002 ISO11095:1996, Linear calibration using reference materials.
29、ISO11843-1:1997, Capability of detection Part 1: Terms and definitions. ISOGuide30:1992, Terms and definitions used in connection with reference materials. 3 Termsanddefinitions ForthepurposesofthispartofISO11843,thetermsanddefinitionsofISO3534(allparts),ISOGuide30, ISO11095andISO11843-1apply. 4 Exp
30、erimentaldesign 4.1 General Theprocedurefordeterminingvaluesofanunknownactualstateincludessampling,preparationandthe measurementitself.Aseverystepofthisproceduremayproducedistortion,itisessentialtoapplythesame procedureforcharacterizing,foruseinthepreparationanddeterminationofthevaluesoftheunknownac
31、tual state,forallreferencestatesandforthebasicstateusedforcalibration. Forthepurposeofdeterminingdifferencesbetweenthevaluescharacterizingoneormoreunknownactualstates andthebasicstate,itisnecessarytochooseanexperimentaldesignsuitedforcomparison.Theexperimentalunits ofsuchanexperimentareobtainedfromt
32、heactualstatestobemeasuredandallreferencestatesusedfor calibration.Anidealdesignwouldkeepconstantallfactorsknowntoinfluencetheoutcomeandcontrolofunknown factorsbyprovidingarandomizedordertoprepareandperformthemeasurements. Inrealityitmaybedifficulttoproceedinsuchaway,asthepreparationsanddeterminatio
33、nofthevaluesofthe statesinvolvedareperformedconsecutivelyoveraperiodoftime.However,inordertodetectmajorbiases changingwithtime,itisstronglyrecommendedtoperformonehalfofthecalibrationbeforeandonehalfafterthe measurementoftheunknownstates.However,thisisonlypossibleifthesizeofthemeasurementseriesisknow
34、n inadvanceandifthereissufficienttimetofollowthisapproach.Ifitisnotpossibletocontrolallinfluencingfactors, conditionalstatementscontainingallunprovenassumptionsshallbepresented. Manymeasurementmethodsrequireachemicalorphysicaltreatmentofthesamplepriortothemeasurement itself.Bothofthesestepsofthemeas
35、urementprocedureaddvariationtothemeasurementresults.Ifitisrequired torepeatmeasurementstherepetitionconsistsinafullrepetitionofthepreparationandthemeasurement. However,inmanysituationsthemeasurementprocedureisnotrepeatedfully,inparticularnotallofthe preparationalstepsarerepeatedforeachmeasurement;se
36、enotein5.2.1. 4.2 Choiceofreferencestates Therangeofvaluesofthenetstatevariablespannedbythereferencestatesshouldinclude thevaluezeroofthenetstatevariable,i.e.inanalyticalchemistryasampleoftheblankmaterial,and atleastonevalueclosetothatsuggestedbyaprioriinformationontheminimumdetectablevalue;ifthis r
37、equirementisnotfulfilled,thecalibrationexperimentshouldberepeatedwithothervaluesofthenetstate variable,asappropriate. Thereferencestatesshouldbechosensothatthevaluesofthenetstatevariable(includinglog-scaledvalues)are approximatelyequidistantintherangebetweenthesmallestandlargestvalue. Incasesinwhich
38、thereferencestatesarerepresentedbypreparationsofreferencematerialstheircomposition shouldbeascloseaspossibletothecompositionofthematerialtobemeasured. BS ISO 11843-2:2000 3 4.3 Choiceofthenumberofreferencestates,I,andthe(numbersof)replicationsofprocedure, J,KandL Thechoiceofreferencestates,numberofp
39、reparationsandreplicatemeasurementsshallbeasfollows: thenumberofreferencestatesIusedinthecalibrationexperimentshallbeatleast3;however,I=5is recommended; thenumberofpreparationsforeachreferencestateJ(includingthebasicstate)shouldbeidentical;atleast twopreparations(J=2)arerecommended; thenumberofprepa
40、rationsfortheactualstateKshouldbeidenticaltothenumberJofpreparationsforeach referencestate; thenumberofrepeatedmeasurementsperformedperpreparationLshallbeidentical;atleasttworepeated measurements(L=2)arerecommended. NOTE Theformulaeforthecriticalvaluesandtheminimumdetectablevalueinclause5areonlyvali
41、dunderthe assumptionthatthenumberofrepeatedmeasurementsperpreparationisidenticalforallmeasurementsofreferencestates andactualstates. Asthevariationsandcostduetothepreparationusuallywillbemuchhigherthanthoseduetothemeasurement, theoptimalchoiceofJ, K and L may be derived from an optimization of const
42、raints regarding variation and costs. 5 Thecriticalvaluesy c andx c andtheminimumdetectablevaluex d ofameasurement series 5.1 Basicassumptions Thefollowingproceduresforthecomputationofthecriticalvaluesandtheminimumdetectablevaluearebasedon theassumptionsofISO11095.ThemethodsofISO11095areusedwithoneg
43、eneralization;see5.3. BasicassumptionsofISO11095arethat thecalibrationfunctionislinear, measurementsoftheresponsevariableofallpreparationsandreferencestatesareassumedtobe independentandnormallydistributedwithstandarddeviationreferredtoas“residualstandarddeviation“, theresidualstandarddeviationiseith
44、eraconstant,i.e.itdoesnotdependonthevaluesofthenetstate variablecase1,oritformsalinearfunctionofthevaluesofthenetstatevariablecase2. ThedecisionregardingtheapplicabilityofthispartofISO11843andthechoiceofoneofthesetwocasesshould bebasedonpriorknowledgeandavisualexaminationofthedata. BS ISO 11843-2:20
45、004 5.2 Case1Constantstandarddeviation 5.2.1 Model Thefollowingmodelisbasedonassumptionsoflinearityofthecalibrationfunctionandofconstantstandard deviationandisgivenby: Yabx ij i ij (1) where x i isthesymbolforthenetstatevariableinstatei; ij arerandomvariableswhichdescribetherandomcomponentofsampling
46、,preparationandmeasurement error. Itisassumedthatthe ij areindependentandnormallydistributedwithexpectationzeroandthetheoretical residualstandarddeviation :; ij N0 2 ej .Therefore,valuesY ij oftheresponsevariablearerandomvariables withtheexpectationEY abx ij i di andthevarianceVY ij di ,notdepending
47、onx i . NOTE InthecasesinwhichJsamplesarepreparedformeasurementandeachofthemismeasuredLtimessothatJ L measurementsareperformedaltogetherforreferencestatei,thenY ij referstotheaverageoftheLmeasurementsobtainedon thepreparedsample. 5.2.2 Estimationofthecalibrationfunctionandtheresidualstandarddeviatio
48、n InaccordancewithISO11095,estimates(seenote)fora,band 2 aregivenby: b (2) aybx (3) 2 2 11 1 2 IJ yabx ij i j J i I ej (4) ThesymbolsusedhereandelsewhereinthispartofISO11843aredefinedinannexA. NOTE Estimatesaredenotedbyasymboltodifferentiatethemfromtheparametersthemselveswhichareunknown. 5.2.3 Computationofcriticalvalues Thecriticalvalueoftheresponsevariableisgivenby: yat KIJ x s xx c () ,095 2 11 (5) 11 () () IJ ii j ij xx xxyy s = BS ISO 11843-2:2000 5 Thecriticalvalueofthenetstatevariableisgivenby: xt b KIJ x s xx c 095 2 11 , () (6) t 095, afisthe95%-quantileofthet-distributionwith IJ2deg
