SIST EN ISO 6974-2:2002

2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.LQVNRErdgas - Bestimmung der Zusammensetzung mit definierter Unsicherheit durch Gaschromatographie - Teil 2: Messsystem charakteristiken und Statistiken für die Datenverarbeitung (ISO 6974-2:2001)Gaz naturel - Détermination de la composition avec une incertitude définie par chromatographie en phase gazeuse - Partie 2: Caractéristiques du systeme de mesure et statistiques pour le traitement des données (ISO 6974-2:2001)Natural gas - Determination of composition with defined uncertainty by gas chromatography - Part 2: Measuring-system characteristics and statistics for processing of data (ISO 6974-2:2001)75.060Zemeljski plinNatural gasICS:Ta slovenski standard je istoveten z:EN ISO 6974-2:2002SIST EN ISO 6974-2:2002en01-september-2002SIST EN ISO 6974-2:2002SLOVENSKI
STANDARD



SIST EN ISO 6974-2:2002



EUROPEAN STANDARDNORME EUROPÉENNEEUROPÄISCHE NORMEN ISO 6974-2March 2002ICS 75.060English versionNatural gas - Determination of composition with defineduncertainty by gas chromatography - Part 2: Measuring-systemcharacteristics and statistics for processing of data (ISO 6974-2:2001)Gaz naturel - Détermination de la composition avec uneincertitude définie par chromatographie en phase gazeuse -Partie 2: Caractéristiques du système de mesure etstatistiques pour le traitement des données (ISO 6974-2:2001)Erdgas - Bestimmung der Zusammensetzung mitdefinierter Unsicherheit durch Gaschromatographie - Teil 2:Messsystem charakteristiken und Statistiken für dieDatenverarbeitung (ISO 6974-2:2001)This European Standard was approved by CEN on 5 January 2002.CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this EuropeanStandard the status of a national standard without any alteration. Up-to-date lists and bibliographical references concerning such nationalstandards may be obtained on application to the Management Centre or to any CEN member.This European Standard exists in three official versions (English, French, German). A version in any other language made by translationunder the responsibility of a CEN member into its own language and notified to the Management Centre has the same status as the officialversions.CEN members are the national standards bodies of Austria, Belgium, Czech Republic, Denmark, Finland, France, Germany, Greece,Iceland, Ireland, Italy, Luxembourg, Malta, Netherlands, Norway, Portugal, Spain, Sweden, Switzerland and United Kingdom.EUROPEAN COMMITTEE FOR STANDARDIZATIONCOMITÉ EUROPÉEN DE NORMALISATIONEUROPÄISCHES KOMITEE FÜR NORMUNGManagement Centre: rue de Stassart, 36
B-1050 Brussels© 2002 CENAll rights of exploitation in any form and by any means reservedworldwide for CEN national Members.Ref. No. EN ISO 6974-2:2002 ESIST EN ISO 6974-2:2002



EN ISO 6974-2:2002 (E)2CORRECTED
2002-04-24ForewordThe text of the International Standard from Technical Committee ISO/TC 193 "Natural gas" ofthe International Organization for Standardization (ISO) has been taken over as a EuropeanStandard by the Technical Board of CEN.This European Standard shall be given the status of a national standard, either by publication ofan identical text or by endorsement, at the latest by September 2002, and conflicting nationalstandards shall be withdrawn at the latest by September 2002.According to the CEN/CENELEC Internal Regulations, the national standards organizations ofthe following countries are bound to implement this European Standard: Austria, Belgium, CzechRepublic, Denmark, Finland, France, Germany, Greece, Iceland, Ireland, Italy, Luxembourg,Malta, Netherlands, Norway, Portugal, Spain, Sweden, Switzerland and the United Kingdom.Endorsement noticeThe text of the International Standard ISO 6974-2:2001 has been approved by CEN as aEuropean Standard without any modifications.NOTE
Normative references to International Standards are listed in annex ZA (normative).SIST EN ISO 6974-2:2002



EN ISO 6974-2:2002 (E)3Annex ZA(normative)Normative references to international publicationswith their relevant European publicationsThis European Standard incorporates by dated or undated reference, provisions from otherpublications. These normative references are cited at the appropriate places in the text and thepublications are listed hereafter. For dated references, subsequent amendments to or revisions ofany of these publications apply to this European Standard only when incorporated in it byamendment or revision. For undated references the latest edition of the publication referred toapplies (including amendments).NOTE Where an International Publication has been modified by common modifications, indicatedby (mod.), the relevant EN/HD applies.PublicationYearTitleENYearISO 6974-12000Natural gas - Determination ofcomposition with defineduncertainty by gas chromatography- Part 1: Guidelines for tailoredanalysisEN ISO 6974-12001SIST EN ISO 6974-2:2002



SIST EN ISO 6974-2:2002



ReferencenumberISO6974-2:2001(E)©ISO2001INTERNATIONALSTANDARDISO6974-2Firstedition2001-02-01Naturalgas—Determinationofcompositionwithdefineduncertaintybygaschromatography—Part2:Measuring-systemcharacteristicsandstatisticsforprocessingofdataGaznaturel—Déterminationdelacompositionavecuneincertitudedéfinieparchromatographieenphasegazeuse—Partie2:CaractéristiquesdusystèmedemesureetstatistiquespourletraitementdesdonnéesSIST EN ISO 6974-2:2002



ISO6974-2:2001(E)PDFdisclaimerThisPDFfilemaycontainembeddedtypefaces.InaccordancewithAdobe'slicensingpolicy,thisfilemaybeprintedorviewedbutshallnotbeeditedunlessthetypefaceswhichareembeddedarelicensedtoandinstalledonthecomputerperformingtheediting.Indownloadingthisfile,partiesacceptthereintheresponsibilityofnotinfringingAdobe'slicensingpolicy.TheISOCentralSecretariatacceptsnoliabilityinthisarea.AdobeisatrademarkofAdobeSystemsIncorporated.DetailsofthesoftwareproductsusedtocreatethisPDFfilecanbefoundintheGeneralInforelativetothefile;thePDF-creationparameterswereoptimizedforprinting.EverycarehasbeentakentoensurethatthefileissuitableforusebyISOmemberbodies.Intheunlikelyeventthataproblemrelatingtoitisfound,pleaseinformtheCentralSecretariatattheaddressgivenbelow.©ISO2001Allrightsreserved.Unlessotherwisespecified,nopartofthispublicationmaybereproducedorutilizedinanyformorbyanymeans,electronicormechanical,includingphotocopyingandmicrofilm,withoutpermissioninwritingfromeitherISOattheaddressbeloworISO'smemberbodyinthecountryoftherequester.ISOcopyrightofficeCasepostale56CH-1211Geneva20Tel.+41227490111Fax+41227490947E-mailcopyright@iso.chWebwww.iso.chPrintedinSwitzerlandii©ISO2001–AllrightsreservedSIST EN ISO 6974-2:2002



ISO6974-2:2001(E)©ISO2001–AllrightsreservediiiContentsPageForeword.ivIntroduction.v1Scope.12Normativereferences.13Termsanddefinitions.14Symbolsandsubscripts.24.1Symbols.24.2Subscripts.35Procedure.45.1Step1:Determinationoftheoptimalresponsefunctions.45.2Step2:Selectionoftheresponsefunctionstobeusedinpractice.85.3Step3:Routinecalibrationwithaworking-referencegasmixture.105.4Step4:Calculationofnon-normalizedcomponentmolefractions.105.5Step5:Calculationofnon-normalizedcomponentstandarddeviations.105.6Step6:Calculationofnormalizedcomponentmolefractions.125.7Step7:Calculationofnormalizedcomponentstandarddeviations.125.8Step8:Calculationofuncertaintyandrepeatabilityoftheresults.135.9RelationshipbetweenISO6974-2andISO6976.13AnnexA(informative)Criticalvaluesoft.14AnnexB(informative)Example.15AnnexC(informative)Relativeresponsefactors(K).23Bibliography.24SIST EN ISO 6974-2:2002



ISO6974-2:2001(E)iv©ISO2001–AllrightsreservedForewordISO(theInternationalOrganizationforStandardization)isaworldwidefederationofnationalstandardsbodies(ISOmemberbodies).TheworkofpreparingInternationalStandardsisnormallycarriedoutthroughISOtechnicalcommittees.Eachmemberbodyinterestedinasubjectforwhichatechnicalcommitteehasbeenestablishedhastherighttoberepresentedonthatcommittee.Internationalorganizations,governmentalandnon-governmental,inliaisonwithISO,alsotakepartinthework.ISOcollaboratescloselywiththeInternationalElectrotechnicalCommission(IEC)onallmattersofelectrotechnicalstandardization.InternationalStandardsaredraftedinaccordancewiththerulesgivenintheISO/IECDirectives,Part3.DraftInternationalStandardsadoptedbythetechnicalcommitteesarecirculatedtothememberbodiesforvoting.PublicationasanInternationalStandardrequiresapprovalbyatleast75%ofthememberbodiescastingavote.AttentionisdrawntothepossibilitythatsomeoftheelementsofthispartofISO6974maybethesubjectofpatentrights.ISOshallnotbeheldresponsibleforidentifyinganyorallsuchpatentrights.InternationalStandardISO6974-2waspreparedbyTechnicalCommitteeISO/TC193,Naturalgas,SubcommitteeSC1,Analysisofnaturalgas.ThispartaswellastheotherfivepartsofISO6974cancelandreplaceISO6974:1984whichspecifiedonlyonemethod.ISO6974consistsofthefollowingparts,underthegeneraltitleNaturalgas—Determinationofcompositionwithdefineduncertaintybygaschromatography:—Part1:Guidelinesfortailoredanalysis—Part2:Measuring-systemcharacteristicsandstatisticsforprocessingofdata—Part3:Determinationofhydrogen,helium,oxygen,nitrogen,carbondioxideandhydrocarbonsuptoC8usingtwopackedcolumns—Part4:Determinationofnitrogen,carbondioxideandC1toC5andC6+hydrocarbonsforalaboratoryandon-linemeasuringsystemusingtwocolumns—Part5:Determinationofnitrogen,carbondioxideandC1toC5andC6+hydrocarbonsforalaboratoryandon-lineprocessapplicationusingthreecolumns—Part6:Determinationofhydrogen,helium,oxygen,nitrogen,carbondioxideandhydrocarbonsuptoC8usingthreecapillarycolumnsAnnexesA,BandCofthispartofISO6974areforinformationonly.SIST EN ISO 6974-2:2002



ISO6974-2:2001(E)©ISO2001–AllrightsreservedvIntroductionThispartofISO6974describesthedataprocessingforthe“tailored”analysisofnaturalgas.Thispartistobeusedinconjunctionwithpart1ofISO6974whichgivestheguidelinesfor“tailored”analysis.Anymethodofanalysis,eitheroneofthoseinpart3ofISO6974andsubsequentpartsoranothermethodofchoicecanonlybeappliedinconjunctionwithparts1and2ofISO6974.Thecalculationofthecompositionofthegasusingresponsecurves,aworking-referencegasmixtureandrelativeresponsefactorsaredescribedinpart1ofISO6974,whiletheelaborationoftheseformulaeisdescribedinthispartofISO6974.Theworking-referencegasmixtureandthegassampleareanalysedwiththesameanalyticalsystemunderthesamesetofconditions.Componentsnotmeasuredbythismethodwillinfluencetheaccuracyofthemethodandshouldthereforebeknown.Ifnoworking-referencegasmixtureisusedfortheregularcalibrationoftheanalyticalsystem,anumberofequationsgiveninthispartofISO6974willchange.Suchchangesareindicatedforeachoftheseequations.Oncetheworkingrangesofthecomponentshavebeendefined,anevaluationiscarriedouttodeterminewhethercomponentsaretobeconsideredas:maincomponentsorgroupsofcomponentstobeanalysedusingdirectmeasurement(directlymeasuredcomponents);componentsorgroupsofcomponentstobeanalysedusingindirectmeasurement,asafunctionofadifferent,referencecomponentinthecalibrationgas(indirectlymeasuredcomponents);componentsthatarenotmeasuredandwhosemolefractioncanbeassumedtobeconstant(componentsnotmeasured).Thesumofthemolefractionsofthemaincomponents,theindirectcomponentsandthefixedcomponentsisequalto1.SIST EN ISO 6974-2:2002



SIST EN ISO 6974-2:2002



INTERNATIONALSTANDARDISO6974-2:2001(E)©ISO2001–Allrightsreserved1Naturalgas—Determinationofcompositionwithdefineduncertaintybygaschromatography—Part2:Measuring-systemcharacteristicsandstatisticsforprocessingofdata1ScopeThispartofISO6974describesthedataprocessingforthetailoredanalysisofnaturalgas.Itincludesthedeterminationofthemeasuringsystemcharacteristicsandthestatisticalapproachtodatahandlinganderrorcalculationwiththeaimofdefiningtheuncertaintyinthemolefractionsofthecomponentmeasured.ThispartofISO6974isonlyapplicableinconjunctionwithpart1ofISO6974.2NormativereferencesThefollowingnormativedocumentscontainprovisionswhich,throughreferenceinthistext,constituteprovisionsofthispartofISO6974.Fordatedreferences,subsequentamendmentsto,orrevisionsof,anyofthesepublicationsdonotapply.However,partiestoagreementsbasedonthispartofISO6974areencouragedtoinvestigatethepossibilityofapplyingthemostrecenteditionsofthenormativedocumentsindicatedbelow.Forundatedreferences,thelatesteditionofthenormativedocumentreferredtoapplies.MembersofISOandIECmaintainregistersofcurrentlyvalidInternationalStandards.ISO6974-1,Naturalgas—Determinationofcompositionwithdefineduncertaintybygaschromatography—Part1:Guidelinesfortailoredanalysis.ISO6976,Naturalgas—Calculationofcalorificvalues,density,relativedensityandWobbeindexfromcomposition.3TermsanddefinitionsForthepurposesofthispartofISO6974,thefollowingtermsanddefinitionsapply.3.1responseoutputsignalofthemeasuringsystemforacomponentthatismeasuredaspeakareaorpeakheightNOTEResponseisexpressedincounts.3.2uncertaintyestimateattachedtoameasurementresultwhichcharacterizestherangeofvalueswithinwhichthetruevalueisassertedtolieNOTEIngeneral,theuncertaintyofmeasurementscomprisesmanycomponents.Someofthesecomponentsmaybeestimatedonthebasisofstatisticaldistributionoftheresultsofseriesofmeasurementsandcanbecharacterizedbyexperimentalstandarddeviation.Theestimatesofothercomponentscanonlybebasedonexperienceorotherinformation.SIST EN ISO 6974-2:2002



ISO6974-2:2001(E)2©ISO2001–Allrightsreserved3.3certified-referencegasmixtureCRMmixturewhichisusedforthedeterminationoftheresponsecurvesofthemeasuringsystemNOTECertified-referencegasmixturesmaybepreparedgravimetricallyinaccordancewithISO6142[1]orISO13275[2]orcertifiedandvalidatedbycomparisonwithprimarystandardgasmixturesofcloselyrelatedcompositioninaccordancewithISO6143[3](seeISO14111[4]).3.4working-referencegasmixtureWRMmixturewhichisusedasaworkingstandardforregularcalibrationofthemeasuringsystemNOTEWorking-referencegasmixturesmaybepreparedbyagravimetricmethodinaccordancewithISO6142[1]orcertifiedandvalidatedbycomparisonwithCRMofcloselyrelatedcompositioninaccordancewithISO6143[3].3.5directmeasurementmeasurementbywhichindividualcomponentsand/orgroupsofcomponentsaredeterminedbycomparisonwithidenticalcomponentsintheworking-referencegasmixture3.6indirectmeasurementmeasurementbywhichindividualcomponentsand/orgroupsofcomponentswhicharethemselvesnotpresentintheworking-referencegasmixturearedeterminedusingrelativeresponsefactorstoareferencecomponentintheworking-referencegasmixture4Symbolsandsubscripts4.1Symbolsai,bi,ci,dipolynomialcoefficientsofthecomponentiamc,bmc,etc.polynomialcoefficientsofthecomponentsorgroupsofcomponentstobeanalysedusingdirectmeasurementasafunctionofidenticalcomponentsorgroupsinthecalibrationgashsnumberofreplicatesofthesamplehwrmnumberofreplicatesoftheworking-referencegasmixtureKrelativeresponsefactorwithrespecttothereferencecomponentmorderoftheresponsefunctionfittedntotalnumberofanalysesusedintheregressionqnumberofdirectcomponentsplusnumberofindirectcomponentsRinstrumentresponse,expressedasrawdata,e.g.areacountsorpeakheightRfresponsefactor(basedonasinglepointcalibration)sMSEresidualmeansquare(MSE)sMSRmeansquareduetoregression(MSR)SIST EN ISO 6974-2:2002



ISO6974-2:2001(E)©ISO2001–Allrightsreserved32SSEsresidualsumofsquares(SSE)2SSRssumofsquaresduetoregression(SSR)ˆ()sxstandarddeviationofthepredictedvalues(x)standarddeviationofanormalizedmolefractions(x)standarddeviationofanon-normalizedmolefractions(xc,WRC)standarddeviationofamolefractionintheWRM(fromthecertificateofWRM)s(R)standarddeviationoftheresponsesatonemolefractionlevelTithedifferenceinslopebetweenthetangentoftheoptimalresponsefunctioninRwr,iandcalibrationlinebasedonthesinglepointmethodoftheWRMonlytreducedvariableofthet-distributionxc,wrmmolefractionoftheWRM(givenonthecertificate)ˆxpredictedvalueofthemolefractionaccordingtoaresponsefunctionxnon-normalizedmolefractionxnormalizedmolefractionxL,wrlowestmolefractionintheworkingrangexU,wrhighestmolefractionintheworkingrangenumberofdegreesoffreedom4.2SubscriptsccertifiedicomponentijmolefractionleveljhnumberofreplicateshLlowestmcmaincomponentsorgroupsofcomponentstobeanalysedusingdirectmeasurementasafunctionofidenticalcomponentsorgroupsinthecalibrationgasMSEresidualmeansquareMSRmeansquareduetoregressionocothercomponentsthatarenotmeasuredand/orcanberegardedasbeingpresentataconstantmolefractionSIST EN ISO 6974-2:2002



ISO6974-2:2001(E)4©ISO2001–AllrightsreservedrrfcomponentsorgroupsofcomponentstobeanalysedusingindirectmeasurementasafunctionofadifferentreferencecomponentinthecalibrationgasrefreferencecomponentSSEresidualsumofsquaresSSRsumofsquaresduetoregressionssampleUhighest(upperlimit)wrworkingrangewrmworking-referencegasmixture5Procedure5.1Step1:Determinationoftheoptimalresponsefunctions5.1.1GeneralremarksDetectorresponsefunctionsaredeterminedusingcertifiedreferencegasmixtures(CRMs).Foreachofthedirectcomponents,selectthemostoptimaldetectorresponsefunctionwhichgivesthebestrelationshipbetweenresponsesignalandcomponentquantityoftheCRM.Carryoutthisstepinthefollowingcases:initialinstallationofthesystembythesupplier;returntooperationafteramaintenanceofthesystem;returntooperationafterreplacementofamajorpartofthesystem,e.g.injectionvalve,column,detector;returntooperationafterfailuretopassaroutinecheckofthesystemusingtestgas(es).NOTEItmaybenecessarytodeterminethebeststatisticalcurvefitoftheresults.Althoughquadraticandcubiccurvesmaygiveabetterfittothedata,foraseriesofgasesthismaynotbefeasible.Itismoreimportanttoobtainconsistentresultsforthedifferentgases.Inpractice,thisconsistencycanoftenbeobtainedbysimplydrawingtherelative-response(=absoluteresponse/molefraction)versusmole-fractioncurves.5.1.2SelectionofreferencegasesTodefinetheresponsefunctions,differentmolefractionlevelsofthedirectcomponentsareanalysed.Thenumberoflevelsneededdependsontheorderoftheresponsecurvethathastobefitted.Theminimumnumberoflevelsneededisthesameasthenumberofpolynomialcoefficients(seebelow)intheequationtobefitted.Howeveritisrecommendedtouseafewmoremolefractionlevelsthannecessary.Inmostcases,theorderoftheresponsecurveisunknownbeforehandbutbyincreasingthenumberofdatapoints,theresponsecurveislessinfluencedbymeasurementerror.Therefore,aminimumofsevenlevelsisrecommendedalthoughanothernumberofmolefractionlevelsmaybesufficienttoobtainagoodcurvefit.Choosetheselevelssoastospreadthemuniformlyacrossthespecifiedworkingrangeofeachcomponentandtocoverarangewhichisslightlylargerthantheanticipatedmolefractionrange.Thiscanbemadepossiblebyusingasetofmulti-componentmixtures,eachcontainingdifferentmolefractionsofallthedirectcomponents.NOTE1Thecomponentscanpossiblybetestedasbinarymixturesinmethane.However,thiswouldgreatlylengthenthetestingprocess,asaseparatesetofcylinderswouldbeneededforeachnon-methanecomponent.SIST EN ISO 6974-2:2002



ISO6974-2:2001(E)©ISO2001–Allrightsreserved5NOTE2Itisobviouslynotpossibletomakeamixturewitheverycomponentatthehighestlevelrequired,oratthelowest,somostofthemulti-componentreferencegasmixtureswillhavecompositionswhicharequitedifferentfromnormalnaturalgases.Providedthatthemixturesareshowntobestableinstorageanduse,thiswillnotcreateaproblem.NOTE3PriortotheuseofaWRMitisnecessarytoprovethatthereisnocontradictionbetweenthemulti-pointcalibration,madebyCRMs,andthemolefractionvaluesoftheWRM.5.1.3MeasurementprocedureAnalyseeachoftheCRMs,containingthedirectcomponents,atleasttwice(preferably5to10times)usingthegaschromatograph.TabulatethedatafortheindividualresponsesRijhofeachcomponenti,ateachmolefractionjandforeachreplicateh.Beforeproceeding,inspectthedataforoutliers.InspecttheresultsofeachgroupbycomponentandlevelfromonecalibrationintervalforoutliersorstragglersusingGrubb'stestorsomeothersuitableoutliertest.Rejectthepossibledeterminedoutliers.NOTEInanysetofdata,individualresultsmaybefoundwhicharenotconsistentwiththeotherdataofthatset.Theseareregardedasoutliersorstragglersandshall,underthecorrectcircumstances,beeliminatedfromthesetofdata.Possiblecausesofoutlierscanbeidentified,forexampletranscriptionerrorsorcarryoverfromthepreviousCRMwhichwasnotfullypurgedfromthesystembeforetheresultsfromthenewCRMwererecorded.5.1.4Selectionoftheresponsefunction5.1.4.1IntroductionTheresponsefunctionshallbeselectedfromthefollowingpolynomialfunctions.Ifamorecomplexfunctionisneeded,thismeansthatthemethodisunsuitableforthisapplication.()iiiixabRfirstorder(1)2()iiiiiixabRcRsecondorder(2)23()iiiiiiiixabRcRdRthirdorder(3)Theaiterm(intercept)isplacedbetweenbracketsbecausetheinterceptistestedindependentlyoftheorderofthemodel,soeachoftheabovelistedresponsefunctionsmayalsoappearwithouttheinterceptterm.Choosetheresponsefunctionwiththefollowingassumptionsinmind:themostlikelyresponseisastraightlinethroughtheorigin;azerointercept,implyingnoresponsetoacomponentinitsabsence,islikelyformostcomponents;curvatureoftheresponsefunctioncanbedescribedbyasecondordertermpossiblybyathirdorderterm;itisunlikelythatahigherordertermwillhavegreatersignificancethanalowerorderterminthesameequation;thepresenceofamaximumoraminimumintheplotofcalculatedmolefractionsversusresponsewithintheworkingrangeisnotacceptable.5.1.4.2RegressionanalysisForthedataobtainedin5.1.3,carryoutregressionanalysisusingacomputerprogramcapableof:performingaleastsquaresregressionofcomponentmolefractions,xi,asthedependentvariableasafunctionoftheindividualresponses,Rijh,astheindependentvariable;performingaleastsquaresregressionofxiasafunctionofRijhand2ijhR;SIST EN ISO 6974-2:2002



ISO6974-2:2001(E)6©ISO2001–AllrightsreservedperformingaleastsquaresregressionofxiasafunctionofRijh,2ijhRand3ijhR;producingoutputforeachofthefittedresponsefunctionsofthe:confidenceintervalforeachcoefficients;sumofsquaresduetoregression(SSR),2SSRs;residualsumofsquares(SSE),2SSEs;meansquareduetoregression(MSR),sMSR;residualmeansquare(MSE),sMSE;numberofdegreesoffreedom()associatedwithsMSRandsMSE;predictedvaluesofthecomponentmolefractionsˆix;standarddeviationsofthepredictedvaluesˆisx.5.1.4.3CalculationCalculatethesignificanceofeachoftheresponsefunctionsforeachofthecomponentsusingthefollowingprocedure(seereference[5]intheBibliography).Calculatethevalueoft(criticalvaluesoftaregiveninTableA.1ofannexA)forthefirstorderregressiont(1),relatingtobi,asSSR2MSE(1)(1)(1)st=s(4)Theorderoftheregression,giveninparenthesesisasfollows:(1)referstodatafromthefirstorderregression;(2)referstodatafromthesecondorderregression;(3)referstodatafromthethirdorderregression;(4)referstodatafromthefourthorderregression.Fromthefirstandsecondorderdata,calculatet(2),relatingtoci,as22SSRSSRMSE(2)(1)(2)(2)sst=s(5)Fromthesecondandthirdorderdata,calculatet(3),relatingtodi,as22SSRSSRMSE(3)(2)(3)(3)sst=s(6)SIST EN ISO 6974-2:2002



ISO6974-2:2001(E)©ISO2001–Allrightsreserved7Intheacceptanceoftheinstrumentcarryoutatestforthedeterminationofthethirdorderdatausingasignificancetestbetweenthirdandfourthorder:22SSRSSRMSE(4)(3)(4)(4)sstsIfthefourthorderissignificant,thesystemisunsuitablefortheapplication.NOTETheuncertaintyoftherelativeresponsefactorK,comparedtotheuncertaintyofthereferencecomponent,isconsiderednegligible.[Seeequations(13)and(15)](KicomparedtoRrrf,i).5.1.4.4ComparisonCompareeachcalculatedvalueoftwiththecriticalvalues(annexA)atitsassociatednumberofdegreesoffreedom.Calculatethenumberofdegreesoffreedomusingthefollowingequation:=n(m1)NOTEForexamplewithsevenCRMseachanalysed5times,n=57=35,fort(1)=35(11)=33,fort(2)=35(21)=32,fort(3)=31.Ifthecalculatedvalueoftislessthanthecriticalvalue(withthesame),thecoefficientisnotsignificant(atasignificancelevelof95%).Ifthecalculatedvalueoftisgreaterthanthecriticalvalue,thecoefficientissignificant(atasignificancelevelof95%).Selectthemostappropriateorderwhichincludesanintercepttermasfollows:ift(3)issignificant,selectthethirdorderresponsefunction;ift(3)isnotsignificantandt(2)issignificant,selectthesecondorderresponsefunction;ift(3)andt(2)arenotsignificantandt(1)issignificant,selectthefirstorderresponsefunction;ift(3),t(2)andt(1)arenotsignificant,donotcontinuewiththisprocedureasthereisnosuitablerelationshipbetweenthemolefractionandtheresponse.Atthisstage,considerthesignificanceoftheinterceptterm.Fromtheselectedresponsefunction,checkthe95%confidenceintervaloftheintercept.Ifthisintervalincludeszero,thentheinterceptcanbesettozeroandremovedfromtheresponsefunction.Repeattheregressionanalysisfortheselectedorderandforanylowerorders.Usethesameprocedureasdescribedabovewithouttheintercept(ai=0).Thecoefficientscalculatedbythisprocessareidentifiedasb0i,c0iandd0i.Calculatet0(1),relatingtob0i,withtheappropriate2SSR,0s(sumofsquaresduetozerointerceptregression)andsMSE,0(residualmeansquareduetozerointercept),usingthefollowingequations:2SSR,00MSE,0(1)(1)(1)s=ts(7)Ifahigherorderresponsefunctionhasbeenselectedwithazerointercept,thenusethezerointerceptdatatocalculatet0(2)[andt0(3)].Compareeachcalculatedvalueoftwiththecriticalvalues(annexA)atitsassociatednumberofdegreesoffreedom.Thenumberofdegreesoffreedomiscalculatedasfollows:=nmSelectthemostappropriateorderwithzerointercepttermasfollows:ift0(3)issignificant,selectthethirdorderresponsefunction;ift0(3)isnotsignificantandt0(2)issignificant,selectthesecondorderresponsefunction;SIST EN ISO 6974-2:2002



ISO6974-2:2001(E)8©ISO2001–Allrightsreservedift0(3)andt0(2)arenotsignificantandt0(1)issignificant,selectthefirstorderresponsefunction;ift0(3),t0(2)andt0(1)arenotsignificant,donotcontinuewiththisprocedureasthereisnosuitablerelationshipbetweenthemolefractionandtheresponse.5.2Step2:Selectionoftheresponsefunctionstobeusedinpractice5.2.1GeneralremarksTheresponsefunctionsselectedinstep1(see5.1)aretheoptimalrelationshipsbetweenmolefractionandresponse.However,itmaybenecessarytoselectanotherresponsefunctionwhenthecomputerprogramofthegaschromatographisnotcapableofhandlingthirdorderfunctionsorfunctionswithanintercept.Inthiscase,afirstorderequationwithoutanintercepthastobeused.Thisapproachisusuallycalledthesinglepointcalibrationmethod.Whenthereisadifferencebetweentheoptimalfunctionandthefirstorderequationwithoutaninterceptfunction,itisobviousthatadditionaluncertaintymaybeintroduced.Thetwomethods,namelymethodAusingtheoptimalfunctionandmethodBusingsinglepointcalibration,aredifferentintermsofcalculationoftheuncertaintyandinthewaycalibrationsaredealtwithbythegaschromatograph.AnnexBdescribeshowdatafromatypicaltestresultarehandledusingmethodAandmethodB.5.2.2MethodACalculatethedesiredresponsefunctionsusingCRMsandthecoefficientsoftheresponsefunctions.Theroutinecalibration,usingaWRM,updatestheresponsefunctioncoefficients.Possibleadditionaluncertainty(resultingfromotherresponsefunctionsthantheoptimalones)shallbetakenintoaccountinthestandardcalculations.Itissufficienttocalculatetheresponsefunctionswhichareneededinpractice.5.2.3MethodB5.2.3.1GeneralassumptionsCalibratethegaschromatographusingaWRM.Thisimpliestheuseofalinearcalibration(firstorderregression)withoutanintercept.ThisproceduredoesnotupdateacalibrationbasedonCRMsbutstandsonitsown;anadditionalcalculationstepisneededtotakeintoaccountthepossibleadditionaluncertainty(swrm,i).Forthiscalculationthefollowingassumptionsaremade:theoptimalresponsefunctionshavealreadybeencalculatedusingstep1(see5.1);themolefractionsofthecomponentsintheWRMarewithintheworkingrangeofthecomponentsintheprocessgas(centreoftherange,ifpossible);theresponseontheWRMisknown(Rwrm,i);theworkingrangesofthecomponentsintheprocessgasarewithintheapplicationrangeoftherespectivepartofISO6974;themolefractionsofthecomponentsintheprocessgashaveamoreorlessnormaldistributionwiththemolefractionoftheWRMastheaverage.5.2.3.2CalculationsCalculatethederivativeoftheoptimalresponsefunctionstowardstheresponseofthegaschromatograph(Ri)asfollows:a)optimalresponsefunctiondeterminedbymethodAis:23iiiiiiiixabRcRdRSIST EN ISO 6974-2:2002



ISO6974-2:2001(E)©ISO2001–Allrightsreserved9b)usingsinglepointcalibration,differentiatetheoptimalresponsefunctionusingthefollowingequation:223iiiiiixbcRdRc)calcu
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