工程能力课件

17四月2024工程能力ContentsDefinitionObjectiveDesignforPCSPopulationandSampleHowtoperformaPCSHowtointerpretaPCSDefinitionMachineCapability:

Variationcausedbythemachineandnotthevariationcausedbyotherpartsoftheprocess.ProcessCapability:

Variationcausedbyallthesourcesofvariation-themachine,thematerialused,themethodsemployed,theoperators,involved,andtheenvironmentasitaffectstheproducts.DefinitionInclude:Changesinincomingshipmentsofmaterials,Shiftsintemperatures,Toolwear,Useofdifferentoperators,SmallchangesinmethodsWhenyouestimatetheprocesscapability,ObjectiveOldProcessesNewProcessesNewMaterialEvaluationProductSpecificationsProcessManagementProductDesignProblemSolvingUSES:DesignforPCSTerminology:

SubgroupWindow⇒TimeBetweenSubgroups⇒Specimen⇒Sample⇒

SampleSize⇒Thedurationofeach‘sampling’periodThedurationofeach‘nosampling’periodAnindividualunitofproductThecollectionofSpecimensgatheredduringasubgroupwindowThenumberofspecimensinthesampleDesignforPCSHowtotakesample:SamplingNoSamplingSamplingNoSamplingTime“NoSampling”intervalsshouldbeofvaryinglength-randomlyDesignforPCSStandardDeviations:

Sigma(σ)isusedtorepresentstandarddeviation

σs:Specimen–to-specimenstandarddeviation

σw:Window–to-windowstandarddeviation

σh:

HistoricalstandarddeviationDesignforPCSProcessVariation:ThetotalamountofprocessVariation(σh)isacombinationofσsandσw.σh=√

σ²s+σ²wPopulationandSamplePopulation(母集團)Sample(標本)RemarkSizeMean(平均)Variance(分散)StandardDeviation(標準扁差)

N

μσ²σ

nx

s²

s

E

(X)=μE(S²)=σ²PopulationandSampleObjectivePopulationSampleDataActiononaproductionprocess:ProcesscontrolProcessanalysisActiononalot:InspectionEstimationofqualityProcessLotSampleLotSampleDataDataSamplingActionMeasurementSamplingActionMeasurementHowtoperformaPCSDefiningtheObjectiveofthePCSExaminationofprocessstabilityLookingforaCPKvalueEstimationofthesteady-stateprocessvariationMaintainingcontrolchartsafterthePCS……?HowtoperformaPCS2.

SettingOperatingConditionsTheconditionswillvaryfromstudytostudydependingontheobjectives.Machineadjustments?Operatingcrewschange?Rawmaterialslotchange?Linespeedchange?HowtoperformaPCS3.DesigningthePCSSubgroupwindowThedecisiononhowlargetomakethesubgroupwindowdependsontheobjectiveofthePCS.Ex)Iftheobjectiveistostudytheextremeshorttermvariationoftheprocess,thesubgroupwindowwouldbechosentobeassmallaspossible.Thespecimensgatheredduringeachsubgroupwindowmustbedrawnatrandom

HowtoperformaPCS3.DesigningthePCS2)SampleSizeAlargesamplesizeprovidesmoresensitivityfordetectingshiftsinmeanandstandarddeviation.Samplesizedeterminationisastatisticalandeconomicissue.Reasonablesamplesize:4-5HowtoperformaPCS3.DesigningthePCSNumberofSubgroupsTheremustbeenoughsubgroupstoproperlyestimatethecontrolchartparameters.Minimumsubgroups:20ThenumberofsubgroupstogetherwiththesubgroupwindowdeterminesthelengthofthePCS.HowtoperformaPCS3.DesigningthePCSTimeBetweenSubgroupsThetimesbetweensubgroupsshouldbeofvaryinglengthtoavoidpossiblecoincidencewithaprocesscycle.

T-WST=WS+(S-1)BB=S-1

T:ThetotaldurationofthePCS

W:Thesubgroupwindow

S:ThenumberofsubgroupsB:ThetimebetweensubgroupsHowtoperformaPCSHowtoperformaPCS4.PerformingthePCS1)ThemeasurementofeachspecimenEachspecimengatheredduringthePCSismeasuredforaspecificsetofproperties.EachspecimenmustretainitsidentitythroughoutthePCS.SpecimensshouldbetestedinrandomorderVariationofrecalibration,differentinstrumentsand/ortechnicians…HowtoperformaPCS4.PerformingthePCS2)ProcessCapability=6σ

Processcapabilityisameasurablepropertyoftheprocess.Theresultingmeasureisexpressedintermsof6σofvariation.σ=thestandarddeviationoftheprocessunderastateofstatisticalcontrol.Thestandarddeviation

measuresthedistanceonthehorizontalscaleassociatedwiththe68.26%,95.46%,and99.7%.HowtoperformaPCSFigure:AreasunderthenormaldistributionX~N(μ,σ²)

Xisnormallydistributedwithmeanμandvarianceσ²HowtoperformaPCS4.PerformingthePCS3)ProcessCapabilityMeasurementOneofmethodsformeasuringprocesscapabilityisthecontrolchartmethod.X-Rcontrolchartsforvariablessuchaslengthorwidth,temperatureandvolume.Theprocesscapabilityiscomputedas6σ,whichincludes99.73%ofthedata.

HowtoperformaPCS4.PerformingthePCS4)StatisticalBasisoftheChartsIfx₁,x₂,…,xnisasampleofsizen,thentheaverageofthissampleisx₁+x₂+…+xnx=nTheprocessaverageisthegrandaveragex₁+x₂+…+xmx=m

xwouldbeusedasthecenterlineonthexchart

HowtoperformaPCSXisnormallydistributedwithmeanμ

andstandarddeviationσx=σ／√nSubgroupn=9n=4n=1μHowtoperformaPCS4.PerformingthePCS4)StatisticalBasisoftheChartsIfx₁,x₂,…,xnisasampleofsizen,thentherangeofthesampleisthedifferencebetweenthelargestandsmallestobservations;R=xmax–xmin

LetR₁,R₂,…,Rmbetherangeofthemsamples,

R₁+R₂+…+Rm

R=m

HowtoperformaPCS4.PerformingthePCS4)StatisticalBasisoftheChartsControlLimitsforthexchart

UCL=x+A₂RCL=xLCL=x-A₂RTheconstantA₂istabulatedforvarioussamplesizesinTableVIHowtoperformaPCS4.PerformingthePCS4)StatisticalBasisoftheChartsControlLimitsfortheRchart

UCL=D₄RCL=RLCL=D₃RTheconstantD₃andD₄aretabulatedforvariousvaluesofninTableVIHowtoperformaPCS4.PerformingthePCS4)StatisticalBasisoftheChartsThepurposeofacontrolchartistodeterminewhetherornotaprocessisinastateofstatisticalcontrol,andifnot,Discardthedata,trytoeliminatethecauseoftheout-of–controlcondition,andrepeatthePCS.Acceptthecomputationasagoodapproximationofprocesscapability.HowtoperformaPCS4.PerformingthePCS3)ProcessCapabilityMeasurement-MethodⅡ

R

6σ=6S=6―d²

S:Thecalculated

standarddeviationofthesampleR:Theaveragerangeofthesubgroupsd²:Theconstantforconvertingrangesintostandarddeviations,fortheparticularsubgroupsizeValuesofd²forvarioussamplesizesaregiveninTableVIHowtoperformaPCS4.PerformingthePCS5)ProcessCapabilityMeasurement-MethodⅡPreparationAssureyourselfthattheprocessyouwanttostudyisinDesignState,useNormalMaterialsandNormalOperators.TakeasmuchtimeasthePCS’sclientwillpermit.PerformanceCollect50pairsofsamplesovertheallottedtimeperiodandmeasuretheproductvariableofinterest(pairmeansconsecutivesamples).HowtoperformaPCS4.PerformingthePCS5)ProcessCapabilityMeasurement-MethodⅡUseoftheRangetoestimateσc

Thedifference

inthemeasurementbetweeneachpairgivesavaluecalledRange(R).CalculatetheaverageRange(R)ofthe50pairs.Estimatethestandarddeviationoftheprocess’scapability(σc)as:

RRσc=―=d₂1.128HowtoperformaPCS4.PerformingthePCS5)ProcessCapabilityMeasurement-MethodⅡUseoftheRangetoestimateσcAssurethateachRcollectedwasincontrol.DothisbycalculatinganduppercontrollimitontheindividualR’sbyUCL=D₄R=3.268RIfanyrangevalueisgreaterthan3.268R,discardthisvalue,recalculateRandrepeatprocedure.HowtoperformaPCS4.PerformingthePCS5)ProcessCapabilityMeasurement-MethodⅡx

andσhObtainthe

average(x)andthestandarddeviation(σh)oftheprocess’shistorybyusingalltheindividualmeasurementsandcalculatingtheaverageandthestandarddeviationintheconventionalmanner.HowtoperformaPCS4.PerformingthePCS5)ProcessCapabilityMeasurement-MethodⅡσh-Calculation

S=√∑(x–x)²orS=√n∑(x²)–(∑x)²n–1n(n–1)

S:samplestandarddeviation∑:sumofx:observedvaluesx:arithmeticmeann:numberofobservationsHowtointerpretaPCS1.DrawingConclusions1)InterpretingtheresultsofaPCSProcessCapability

()

x

()currentcapability

x±3σc

x±3σhtypicalhistoryProductARequirementCapable

Bmostlikelycapital$Notcapablerequired

CNotcapablebutmaybeifmaterialoroperationpracticechangedHowtointerpretaPCS1.DrawingConclusions2)ApplyingPCSresultstotheproductspecificationSpecificationRequirementCurrentCapabilityHistoryRevised6-15-03AgreementFuture(Who/When)EndSealStrengthTar.136orgreaterDefectiveislessthan100gmsTar.507gmsMin.281gmsMax.733gmsTar.507gmsMin.210gmsMax.804gmsAgreePadWeightTar.3.43-3.66gmsNodefectdefinitionTar.3.57gmsMin.3.42gmsMax.3.72gmsTar.3.57gmsMin.3.29gmsMax.3.85gmsNo.Targetrequiredtootight.

?HowtointerpretaPCS1.DrawingConclusions3)DefiningProcessCapabilityIndexOneformofcapabilityindex(Cp)is