1、AMERICAN NATIONAL STANDARDOCTOBER 2013ANSI/ASQ Z1.92003 (R2013)SAMPLING PROCEDURES AND TABLES FOR INSPECTION BY VARIABLES FOR PERCENT NONCONFORMINGThis standard is a reaffirmation of ANSI/ASQ Z1.9-2003 (R2008)AMERICANNATIONALSTANDARDSampling Procedures and Tables forInspectionby Variables forPercent
2、 NonconformingPreparedbyTheStatisticsSubcommitteeoftheAccreditedStandardsCommitteeZ1onQuality,Environment,DependabilityandStatisticsANSI-AccreditedStandardsDeveloper(ASD)AmericanSocietyforQualityANSI/ASQZ1.9-2003(R2013)ABSTRACTSamplingProceduresandTablesforInspectionbyVariablesforPercentNonconformin
3、gisanacceptancesamplingsystemtobeusedonacontinuingstreamoflotsforAQLspecified.Itprovidestightened,normal,andreducedplanstobeusedonmeasurementswhicharenormallydistributed.Variationmaybemeasuredbysamplestandarddeviation,samplerange,orknownstandarddeviation.Itisapplicableonlywhenthenormalityofthemeasur
4、ementsisassured.AMERICAN NATIONAL STANDARD:AnAmericanNationalStandardimpliesaconsensusofthosesubstantiallycon-cernedwithitsscopeandprovisions.AnAmericanNationalStandardisintendedasaguidetoaidthemanufacturer,theconsumer,andthegeneralpublic.TheexistenceofanAmericanNationalStandarddoesnotinanyrespectpr
5、ecludeany-one,whetherhehasapprovedthestandardornot,frommanufacturing,marketing,purchasing,orusingproducts,process-es,orproceduresnotconformingtothestandard.AmericanNationalStandardsaresubjecttoperiodicreviewandusersarecautionedtoobtainthelatestedition.CAUTION NOTICE:ThisAmericanNationalStandardmaybe
6、revisedorwithdrawnatanytime.TheproceduresoftheAmericanNationalStandardsInstituterequirethatactionbetakentoreaffirm,revise,orwithdrawthisstandardnolaterthanfiveyearsfromthedateofpublication.PurchasersofAmericanNationalStandardsmayreceivecurrentinformationonallstandardsbycallingorwritingtheAmericanNat
7、ionalStandardsInstitute.2013byASQCopyright protection notice for the ANSI/ASQ Z1.9-2003 (R2013) Standard.ThisStandardissubjecttocopyrightclaimsofANSI,andASQ.Notforresale.Nopartofthispublicationmaybereproducedinanyform,includinganelectronicretrievalsystem,withoutthepriorwrittenpermissionofASQ.Allrequ
8、estspertainingtotheANSI/ASQZ1.9-2003(R2013)StandardshouldbesubmittedtoASQ.ASQwillconsiderrequestsforchangeandinformationonthesubmittalofsuchrequestsregardingthisStandard.AllrequestsshouldbeinwritingtotheattentionoftheStandardsAdministratorattheaddressbelow.ASQ Mission:TheAmericanSocietyforQualityadv
9、ancesindividualandorganizationalperformanceexcellenceworldwidebyprovidingopportunitiesforlearning,qualityimprovement,andknowledgeexchange.Publishedby:ANSI/ASQZ1.9-2003(R2013)ANSI/ASQZ1.9-2003(R2013)isaveryminorrevisionofANSI/ASQZ1.9-2003(R2008),alsoreferredtoasANSI/ASQZ1.9-2008.ANSI/ASQ Z1.9-2003 (R
10、2013) continues to allow complete interchangeability of the tabulatedplanswithISO3951-1,whichprovidedagraphicalmeansforimplementationoftheplans.ANSI/ASQZ1.9-2003(R2013)isalsoroughlymatchedtoANSI/ASQZ1.4-2003(R2013),whichcorresponds directly to the old military standard MIL-STD-105E. The matching is
11、sufficient toallowinspectionundereitherstandardforstatedAQLsandinspectionlevelswithreasonablyequiv-alent protection. Tables are given in Section EAppendix that show differences in protectionbetweenANSI/ASQZ1.9-2003(R2013)andANSI/ASQZ1.4-2003(R2013).Theseareforuseincriticalapplicationstodeterminewhet
12、hermovingfromonestandardtotheotherisappropriate.Change:TableB-2StandardDeviationMethodMasterTableforReducedInspectionforPlansBasedonVariabilityUnknown(SingleSpecificationLimitForm1)InrowN,changedSampleSizefrom30to50.Suggestionsforimprovementofthisstandardarewelcomed.Sendyourcommentstothesponsor,ASQS
13、tandards,600NorthPlankintonAvenue,Milwaukee,WI53203.iiiFOREWARD(This page intentionally left blank)CONTENTSPageINTRODUCTION viiFigure1 FlowchartforuseofANSI/ASQZ1.9ixSECTIONA GENERALDESCRIPTIONOFSAMPLINGPLANS .1Tables:TableA-1 AQLConversionTable5TableA-2 SampleSizeCodeLetters6TableA-3 OperatingChara
14、cteristicCurvesforSamplingPlansofSectionsB,C,andD(GraphsforSampleSizeCodeLettersBthroughP).6SECTIONB VARIABILITYUNKNOWNSTANDARDDEVIATIONMETHOD.32PartI SINGLESPECIFICATIONLIMIT32Examples:ExampleB-1 ExampleofCalculations:SingleSpecificationLimitForm1 .34ExampleB-2 ExampleofCalculations:SingleSpecifica
15、tionLimitForm2 .35Tables:TableB-1 MasterTableforNormalandTightenedInspection(SingleSpecificationLimitForm1).36TableB-2 MasterTableforReducedInspection(SingleSpecificationLimitForm1) 37PartII DOUBLESPECIFICATIONLIMIT.38Examples:ExampleB-3 ExampleofCalculations:DoubleSpecificationLimitOneAQLValueforBo
16、thUpperandLowerSpecificationLimitCombined40ExampleB-4 ExampleofCalculations:DoubleSpecificationLimitDifferentAQLValuesforUpperandLowerSpecificationLimits41Tables:TableB-3 MasterTableforNormalandTightenedInspection(DoubleSpecificationLimitandForm2SingleSpecificationLimit) 42TableB-4 MasterTableforRed
17、ucedInspection(DoubleSpecificationLimitandForm2SingleSpecificationLimit) .43TableB-5 TableforEstimatingtheLotPercentNonconforming.44TableB-6 ValuesofFforMaximumStandardDeviation(MSD) 53AppendixB Definitions.54SECTIONC VARIABILITYUNKNOWNRANGEMETHOD55PartI SINGLESPECIFICATIONLIMIT55Examples:ExampleC-1
18、 ExampleofCalculations:SingleSpecificationLimitFormI58ExampleC-2 ExampleofCalculations:SingleSpecificationLimitForm2 .59Tables:TableC-1 MasterTableforNormalandTightenedInspection(SingleSpecificationLimitFormI) .60TableC-2 MasterTableforReducedInspection(SingleSpecificationLimitFormI).61PartII DOUBLE
19、SPECIFICATIONLIMIT 62ANSI/ASQZ1.9-2003(R2013)vviPageExamples:ExampleC-3 ExampleofCalculations:DoubleSpecificationLimitOneAQLValueforBothUpperandLowerSpecificationLimitCombined65ExampleC-4 ExampleofCalculations:DoubleSpecificationLimitDifferentAQLValueforUpperandLowerSpecificationLimits 66Tables:Tabl
20、eC-3 MasterTableforNormalandTightenedInspection(DoubleSpecificationLimitandForm2SingleSpecificationLimit) 67TableC-4 MasterTableforReducedInspection(DoubleSpecificationLimitandForm2SingleSpecificationLimit) .68TableC-5 TableforEstimatingtheLotPercentNonconforming.69TableC-6 ValuesoffforMaximumAverag
21、eRange(MAR)78AppendixC Definitions 79SECTIOND VARIABILITYKNOWN.80PartI SINGLESPECIFICATIONLIMIT80Examples:ExampleD-1 ExampleofCalculations:SingleSpecificationLimitForm1 .82ExampleD-2 ExampleofCalculations:SingleSpecificationLimitForm2 .83Tables:TableD-1 MasterTableforNormalandTightenedInspection(Sin
22、gleSpecificationLimitForm1).84TableD-2 MasterTableforReducedInspection(SingleSpecificationLimitForm1) 86PartII DOUBLESPECIFICATIONLIMIT.88Examples:ExampleD-3A ExampleofCalculations:DoubleSpecificationLimitOneAQLValueforBothUpperandLowerSpecificationLimitCombined90ExampleD-3B ExampleofCalculations:Do
23、ubleSpecificationLimitOneAQLValueforBothUpperandLowerSpecificationLimitCombined91ExampleD-4 ExampleofCalculations:DoubleSpecificationLimitDifferentAQLValuesforUpperandLowerSpecificationLimits .92Tables:TableD-3 MasterTableforNormalandTightenedInspection(DoubleSpecificationLimitandForm2SingleSpecific
24、ationLimit) 93TableD-4 MasterTableforReducedInspection(DoubleSpecificationLimitandForm2SingleSpecificationLimit) 95TableD-5 TableforEstimatingtheLotPercentageNonconforming97TableD-6 ValueofFforMaximumProcessStandardDeviation.98AppendixD Definitions.99SECTIONE APPENDIXMATCHWITHANSI/ASQZ1.4 100Tables:
25、1 MatchingCodeLettersandANSI/ASQZ1.9SampleSize. . . 1012 ANSI/ASQZ1.9PercentagePointsinTermsofPercentNonconforming. . 1023 ANSI/ASQZ1.4(MIL-STD-105)PercentagePointsinTermsofPercentNonconforming.1034 DifferenceinPercentagePointsANSI/ASQZ1.9MinusANSI/ASQZ1.4(MIL-STD-105).104ANSI/ASQZ1.9-2003(R2013)ANS
26、I/ASQZ1.9-2003(R2013)viiINTRODUCTIONThisstandardwaspreparedtomeetaneedfortheuseofstandardsamplingplansforinspectionbyvariablesinprocure-ment,supplyandstorage,andmaintenanceinspectionoperations.Thevariablessamplingplansapplytoasinglequalitycharacteristicwhichcanbemeasuredonacontinuousscale,andforwhic
27、hqualityisexpressedintermsofpercentnon-conforming.Thetheoryunderlyingthedevelopmentofthevariablessamplingplans,includingtheoperatingcharacteris-ticcurves,assumesthatmeasurementsofthequalitycharacteristicsareindependent,identicallynormallydistributedran-domvariables.It is important to note that varia
28、bles sampling plans are not to be used indiscriminately, simply because it is possible toobtain variables measurement data. The users are advised to consult their technical agency to determine the feasibility ofapplication in considering applications where the normality orindependence assumptions ma
29、y be questioned.Incomparisonwithattributessamplingplans,variablessamplingplanshavetheadvantageofusuallyresultinginconsid-erablesavingsinsamplesizeforcomparableassuranceastothecorrectnessofdecisionsinjudgingasinglequalitychar-acteristic,orforthesamesamplesize,greaterassuranceisobtainedusingvariablesp
30、lans.Attributessamplingplanshavetheadvantageofgreatersimplicity,ofbeingapplicabletoeithersingleormultiplequalitycharacteristics,andofrequiringnoknowledgeaboutthedistributionofthecontinuousmeasurementsofanyofthequalitycharacteristics.Thisstandardisdividedintofoursections.SectionAdescribesgeneralproce
31、duresofthesamplingplans.SectionsBandCdescribespecificproceduresandapplicationsofthesamplingplanswhenvariabilityisunknown.InSectionBthestan-darddeviationisusedasthebasisforanestimateoftheunknownvariability,andinSectionCtheaveragerangeofthesam-pleisused.SectionDdescribestheplanswhenvariabilityisknown.
32、EachofSectionsB,C,andDisdividedintotwoparts:(I)SamplingPlansfortheSingleSpecificationLimitCase,and(II)SamplingPlansfortheDoubleSpecificationLimitCase.Forthesinglespecificationlimitcase,theacceptabilitycriterionisgivenintwoforms:Form1andForm2.Eitheroftheformsmaybeused,sincetheyareidenticalastosamples
33、izeanddecisionforlotacceptabilityorrejectability.IndecidingwhethertouseForm1orForm2,thefollowingpointsshouldbeborneinmind.Form1providesthelotacceptabilitycriterionwithoutestimatinglotpercentnonconforming.TheForm2lotacceptabilitycriterionrequiresestimatesoflotpercentnonconforming.Operatingcharacteris
34、ticcurvesinTableA-3arefortheNormalInspectionsamplingplansandshowtherelationshipbetweenqualityandpercentoflotsexpectedtobeacceptedforthequalitycharacteristicinspected.Asstated,theseoperatingchar-acteristiccurvesarebasedontheassumptionthatmeasurementsareselectedatrandomfromanormaldistribution.Thecorre
35、spondingsamplingplansinSectionsB,C,andDwerematchedascloselyaspossibleunderasystemoffixedsamplesizewithrespecttotheiroperatingcharacteristiccurves.OperatingcharacteristiccurvesinTableA-3havebeencomputedforthesamplingplansbasedonthestandarddeviationestimateofunknownvariability.Theyareequallyappli-cabl
36、eforsamplingplansbasedontheaveragerangeofthesampleandthosebasedonknownvariability.CertaincharacteristicsconcerningthesamplingplansinSectionBandCandthoseinSectionDshouldbenoted.Plansbasedontheestimateofunknownvariabilityrequirefewersampleunitsforcomparableassurancewhenthestandarddevi-ationisusedthanw
37、hentheaveragerangeofthesampleisused.Ontheotherhand,plansusingtheaveragerangeofthesamplerequiresimplercomputationsandmaybebetterunderstoodbyoperatingpersonnel.Plansusingknownvariabilityrequireconsiderablyfewersampleunitsforcomparableassurancethaneitheroftheplansofunknownvariability;however,therequire
38、mentofknownvariabilityisastringentone.Theuseriswelladvisedtoconsultastatisticianbeforeapplyingsamplingplansusingknownvariability.TableB-6providesvaluesofthefactorFtocomputethemaximumstandarddeviation:MSD.TheMSDservesasaguideforthemaximumallowablemagnitudeoftheestimateoflotstandarddeviationwhenusingp
39、lansforthedoublespecifica-tionlimitcase,basedonthestandarddeviation.SimilarlyTableC-6providesvaluesofthefactorftocomputethemaxi-mumaveragerange:MAR.TheMARservesasaguideforthemaximumallowablemagnitudeoftheaveragerangeofthesamplewhenusingplansforthedoublespecificationlimitcase,basedontheaveragerange.T
40、heestimateoflotstandarddeviationoraveragerangeofthesample,ifitislessthantheMSDorMAR,respectively,helpstoensure,butdoesnotguar-antee,lotacceptability.Allsymbolsandtheirdefinitionsaregivenintheappendixoftheapplicablesection.Anillustrationofthecomputationsandproceduresusedinthesamplingplansisgiveninthe
41、examplesinPartsIandIIoftheapplicablesection.Thecomputationsinvolvesimplearithmeticoperationssuchasaddition,subtraction,multiplication,anddivisionofnumbers,oratmost,thetakingofasquarerootofanumber.TheusershouldbecomefamiliarwiththegeneralproceduresofSectionA,andrefertotheapplicablesectionfordetailedi
42、nstructionsregardingspecificprocedures,computations,andtablesforthesamplingplans.SectionEAppendixprovidesinformationaboutthematchbetweenthisvariablesstandard,ANSI/ASQZ1.9,andthecorrespondingattributesstandard,ANSI/ASQZ1.4.TheflowchartinFigure1showsthebasicprocedureforusingthestandard.ANSI/ASQZ1.9-20
43、03(R2013)viiiANSI/ASQZ1.9-2003(R2013)ixSTARTDetermine code letter from tables A-1 and A-2Process known?Obtain information1. Lot size (N)2. Level (Z1.9II)3. AQLSpec. limit Spec. limitRangemethod?Spec. limitForm?sMSD?M and n fromB-3 and B-4Computek and n fromB-1 or B-2ComputeM and n fromB-3 and B-4Com
44、puteM, c, and n fromC-3 and C-4ComputeM, v, and n fromD-3 and D-4Computek and n fromC-1 or C-2ComputeM, c, and n fromC-3 and C-4Computek and n fromD-1 or D-2ComputeM, v, and n fromD-3 and D-4ComputeForm?RMAR?Form?MPSD?IsPLor PU M?IsP M?IsPLor PU M?IsP M?IsP M?IsPLor PU M?Isor k?Isor k?(X L) s(U X)sI
45、sor k?(X L) (U X)NoNoSingleTwo Two TwoYe sRRRYe s Ye sOne One OneNo No NoStd. dev. methodStd. dev. method Range method Sigma methodStd. dev. method Range method Range method Sigma method Sigma methodDouble Single Double Single DoubleMSD = F(U L)F from B-6MAR = f(U L)f from C-6MPSD = F(U L)F from D-6
46、YesYesRAYe sNoRAYe sNoRAYe sNoRAYe sNoRAYe sNoRAYe sNoRAYe sNoRAYe sNoRAYe sNo1) X2) s3)XLsorUXs1) X2) R3)XLorUX1) X2)X LorU X1) X2) s4) Obtain PUand PLfrom B-55) P = PU+ PL3) QL= , andXLsUXsQU=1) X4) Obtain PUand PLfrom D-55) P = PU+ PL2) QL= ,and(X L)v(U X)vQU=R R4) Obtain PUand PLfrom C-55) P = P
47、U+ PL3) QL= , and(X L)c(U X)cQU=1) X2) RRR1) X2) s4) Obtain PUand PLfrom B-53) QL= , andXLsUXsRR1) X3) Obtain PUand PLfrom D-52) QL= , and(X L)v(U X)v(X L) R(U X)RQU=1) X2) R4) Obtain PUand PLfrom C-53) QL= , and(X L)c(U X)cQU=QU=Figure 1 Flowchart foruse of ANSI/ASQ Z1.9(This page intentionally lef
48、t blank)A1. SCOPEA1.1 Purpose. This standard establishes sampling plansand procedures for inspection by variables for use in pro-curement, supply and storage, and maintenance inspectionoperations. When applicable this standard shall be refer-enced in the specification, contract, or inspection instru
49、c-tions,andtheprovisionssetforthherein shall govern.Theseacceptancesamplingplansforvariablesaregiveninterms of the percent or proportion of product in a lot orbatchthatdepartfromsomerequirement.Thegeneralter-minologyusedwithinthedocumentwillbegivenintermsof percent of nonconforming units or number of noncon-formities,sincethesetermsarelikelytoconstitutethemostwidelyusedcriteriaforacceptancesampling.A2. DEFINITIONSANDTERMINOLOGYFor the purpose of this American National Standard, thedefinitio
