SPC-抽样教程.ppt

SPCPartII SamplingPlansforX chart LearningObjectives RevisionofSPCFundamentals SPC原理校正MisconceptionsofSPC SPC误解ProcessControlModel 制程控制模型TwoBasicCausesofVariability 2种基本变异原因ReviewofX RChartandX sChart 均值极差及单值控制图回顾ReviewofAttributesControlCharts属性控制图回顾DesigningtheX chart均值控制图的设计SamplingRisks aandb 抽样风险ARL0andARL1DeterminingSamplingInterval决定抽样时间间隔DeterminingSampleSize决定样本大小 MisconceptionsofSPC Let scheckourunderstandingbylookingatthemostcommoncontrolchart X chart 通过回顾基本的均值控制图 检阅我们对SPC的了解 MoremythsandmisconceptionsontheX chart 对均值控制图的误解 MisconceptionsofSPC MoremythsandmisconceptionsoftheX chart 对均值控制图的误解 MisconceptionsofSPC MythNo 5 WeknowA2R 3s Butwhichs sx sx swithin soverall ProcessControlModelforQualityControl RawMaterial Components Sub Assemblies原材料 零件及半成品 Process Product Observation观察 DataCollection数据收集Evaluation评估 DataAnalysis数据分析Diagnosis诊断 FaultDiscovery错误发现Decision决策 FormulateAction阐明行动Implementation推行 TakeAction采取行动 UncontrollableInputs不可控的输入 ControllableInputs可控的输入 StatisticalProcessControl Theprocesscontrolmodelshiftsfocustothehomefront i e themanufacturingprocess takingapreventiveinsteadofreactivemode 制程控制模型具有前瞻性 如 制造制程 是采取预防措施而非直接解决问题Italsohassomethingwhichtheoldconceptofproductcontrollacked statistics Thisallowsuseofsamplestounderstandtheentireprocess 较早时期产品控制缺乏统计这一让我们明白整个制程的概念Thenewemphasishadtohaveaname StatisticalProcessControl SPC 新的产品控制观念强调了SPCWeowetheapplicationofstatisticsasatoolformanufacturingtoDrWalterA Shewhart 统计在制造中的应用应归功于修哈特博士 TwoBasicCausesofVariability ChanceCausesofVariation变异的偶因Duetothecumulativeeffectofmanysmallunavoidablesourcesofvariation 许多不可避免的小的变异源的累积Alsoknownas commonvariation普通变异randomvariation随机变异inherentvariation内在变异naturalvariation自然变异Aprocessoperatingwithonlychancecausesofvariationissaidtobe instatisticalcontrol 仅有偶因变异的制程处于统计控制 TwoBasicCausesofVariability Assignable orSpecial CausesofVariation变异的异因Variationinaprocessthatisdifferentfromfromchancevariation disturbsaprocesssothatwhatitproducesseemsunnatural 这种变异明显异常于偶因引起的变异 制程受到明显的影响 显得不自然 Examplesofsuchcausesofvariationare异因引起的变异的例子 improperlyadjustedmachine不正常的调机excessivetoolwear过多使用工具defectiverawmaterial使用有缺陷的原材料Aprocessoperatinginthepresenceofassignablecausesofvariationissaidtobe out of control 异因引起的变异的制程处于不受控 ObjectivesofSPCCharts Allcontrolchartshaveoneprimarypurpose 所有控制图均有一个基本的目的Todetectassignablecausesofvariation探测严重引起制程变异的异因 因此 thatcausesignificantprocessshift sothat investigationandcorrectiveactionmaybeundertakentoridtheprocessoftheassignablecausesofvariationbeforetoomanynon conformingunitsareproduced 大量不合格品产生前 必须调查研究并采取改善行动 以消除起制程变异的异因inotherwords tokeeptheprocessinstatisticalcontrol 换句话说 使得制程处于统计控制 ObjectivesofSPCCharts Thefollowingaresecondaryobjectivesordirectbenefitsoftheprimaryobjective 以下是采用控制图的好处Toreducevariabilityinaprocess 减少制程的变异Tohelpestimatetheparametersofaprocessandestablishitsprocesscapability 帮助估计制程参数 建立制程能力 ProcessControl制程控制 Meansthatchancecausesaretheonlysourceofvariationpresent 偶因是制程变异的唯一因数Refersto voiceoftheprocess i e weonlyneeddatafromtheprocesstodetermineifaprocessisincontrol控制图反映制程的声音 我们仅需要制程的数据来决定制程是否受控 Qualitycharacteristicismonitoredtoverifyifitformsastabledistributionovertime withcontrollimitscomputedfromtheprocessdataonly通过监控质量特性 由制程数据计算制程的控制范围 检验制程是否形成在一定控制范围内的稳定的分布 Justbecauseaprocessisincontroldoesnotnecessarilymeanitisacapableprocess仅仅因为制程受控不能够确定制程是有能力 The goodness ofaprocessismeasuredbyitsprocesscapability制程的好会是由它的能力来量度的 Compares voiceoftheprocess with voiceofthecustomer whichisgivenintermsofcustomerspecs orrequirements比较制程的声音和客户的声音 客户的声音即由客户给定规格或要求 Measureshowwellastabledistribution processincontrol meetscustomerrequirementsbytheproportionofproductswithinoroutofcustomerspecs衡量一个稳定的制程如何满足客户的需要是看它的产品在客户规格范围内的分布情况来确定 ProcessCapability制程能力 ControlLimitsvsSpec Limits SpecificationLimits USL LSL 规格极限determinedbydesignconsiderations由设计来决定representthetolerablelimitsofindividualvaluesofaproduct产品的个别值代表偏差usuallyexternaltovariabilityoftheprocess通常外在环境影响制程的变异ControlLimits UCL LCL 控制极限derivedbasedonvariabilityoftheprocess来源于制程的变异usuallyapplytosamplestatisticssuchassubgroupaverageorrange ratherthanindividualvalues通常应用于抽样统计 如子组平均或极差 而非个别值 Spec limitsshouldnotbeplacedoncontrolchartsforsubgroups规格极限不应放在控制图上 Spec limitsinvolveindividualvaluesofthequalitycharacteristic whilecontrollimitsinvolvesamplestatisticsofthequalitycharacteristic规格极限包括质量特性的个别值 控制极限仅包括质量特性的抽样统计值 Spec limitsareimposedbyexternaldemands thusdonothelpidentifyassignablecauses规格极限被应用于外部 不能识别异因 Pointsplottedwithinthecontrollimitsdonotindicatedirectlythatpartsaremeetingcustomerspecs orCpkrequirements点在控制线内不代表产品满足客户规格或Cpk要求 Spec LimitshasNoBusinessinControlCharts ShewhartControlCharts Overview 变量 属性 缺陷 有缺陷的 ReviewofX RCharts均值极差图回顾 CentralLimitTheoremandNormalDistribution Shewhartvariablescontrolchartsforsubgroupsworkbecauseoftwoimportantprinciples修哈特控制图应用于子组 因为以下2个重要原理 CentralLimitTheorem中心极限定律NormalDistribution正态分布Shewhartfoundthatwhentheaveragesofsubgroupsfromaconstant causesystemareplottedintheformofahistogram thenormaldistributionappears修哈特发现当把常量系统的子组平均值作成一个直方图时 就出现了常态分布 ConstructionofX RCharts TheX Rchartisthemostversatileofcontrolcharts andisusedinmostapplications 均值极差控制图是个通用控制图Chartingofaveragesandchartingofrangesareusedtocheckifaconstant causesystemexists均值图和极差图用于检验常量系统是否存在 X chartmeasuresvariabilitybetweensamples均值图测量2个样本间的差异 R chartmeasuresvariabilitywithinsamples极差图测量样本内的差异 TheCenterLineandControlLimitsofaX chart TheCenterLineandControlLimitsofaR chart ConstructionofX RCharts Forsamplesizen 10 RlosesitsefficiencyinestimatingprocesssigmaandR chartmaynotbeappropriate 样本数大于10时 极差不能用于估算制程标准差 极差图不适用 ConstructionofX RCharts ShewhartConstants修哈特常数 HowdowebegintosetupanX Rchartfromscratch 如何建立均值极差控制图 ImplementingtheControlChart控制图的推行 ImplementingtheControlChart 1 PreparationofSampling抽样准备2 DataCollection数据收集3 ConstructtheControlChart组建控制图4 Analysis Interpretation分析5 UsetheControlChartasaProcessMonitoringTool使用控制图作为制程监控工具 IndicatorsofInstability制程不稳定判断 PrimaryIndicators主要判断依据anypointoutsideofacontrollimit任意点出界SecondaryIndicators次要判断依据anynon randompatternofpointsonacontrolchart任意规律的点shiftorrun交替性Trend一定趋势Stratification分层Mixture混合性Periodicity周期性 MiniTab sTestsforInstability SecondaryIndicators PrimaryIndicator WarningLimits警告线 The3 controllimitsarealsocalledactionlimits i e investigationandcorrectiveactionarerequiredwhenapointplotsoutsideoftheselimits 3 控制线又叫行动线 如果点在这些线以外 必须采取行动 Sometimes 2 warninglimitsaremarkedonacontrolcharttoincreasethesensitivityofthecontrolchart 有时2 警告线也标示在图上 以增加控制图的敏锐性 SowhatdoyoudoifapointisabovetheWarningLimit 点在警告线以上如何办 Animportantideaincontrolcharttheoryisthewaywepullspecimenstoformasubgroupofdata控制图原理的一个重要概念是我们将样本组成数据子组的方法 ThisshouldfollowwhatShewhartcalledtherationalsubgroupconcept这必须依据修哈特的合理子组概念 Therationalsubgroupconceptrequiresthatpartsarepulledconsecutivelyfromtheprocesswhenformingasubgroup修哈特的合理子组概念要求组成子组的样本必须连续地从制程抽取 RationalSubgroups合理子组 Thus therationalsubgroupconceptimpliesthatsubgroupsshouldbeselectedsothatifassignablecausesarepresent合理子组概念意味着选择子组时 展示异因 theprobabilityfordifferencesbetweensubgroupswillbemaximized 应最大化2个子组的差异whiletheprobabilityfordifferenceswithinasubgroupwillbeminimized同时应最小化子组内的差异 RationalSubgroups合理子组 ConstructionofSubgroups子组构建Preferredmethod首选方法 Takeconsecutiveunitsofproduction选取连续生产产品Becausethespecimensarecollectedwithinashorttime frame thisminimizesthechanceofvariabilityduetoanassignablecausetoappearwithinasampleonly因样本在一短时间内收集 可以最小化异因在一个样本内出现的机会 Itmaximizesthechanceofvariabilityduetoanassignablecausetoappearbetweensamples可以最大化异因在不同样本内出现的机会 Goodfordetectingprocessshifts能很好地探测制程偏移 RationalSubgroups合理子组 X SCharts TheCenterLineandControlLimitsofaXChartareTheCenterLineandControlLimitsofaSChartare ShewhartConstants Forn 25 AttributesControlCharts属性控制图 43 pChart FractionNon Conforming少数不合格RejectRate DefectiveRate拒收率 缺陷率PercentFallout Theunderlyingprinciplesofthepchartarebasedonthebinomialdistribution P图的原理基于二项分布 Themeanandvarianceofthedistributionofp sarecomputedfromthebinomialequation giving P图分布的均值和偏差由二项分布公式计算而来 pChart pChart FollowingShewhart sprinciple theCenterLineandControlLimitsofapchartare根据休哈特原理 中心线和控制线分别是 Thepchartalsoassumesasymmetricalbell shapedistribution withsymmetricalcontrollimitsoneachsideofthecenterline P图呈对称铃型分布 控制线对称地分布在中心线的两侧 Thisimpliesthatthebinomialdistributionisapproximatelyclosetotheshapeofthenormaldistribution whichcanhappenundercertainconditionsofpandn这说名在p n一定的条件下 二项分布接近正态分布 p 1 2andn 10implyingnp 5Forothervaluesofp thegeneralguidelineistohavenp 10togetasatisfactoryapproximationofthenormaltothebinomial 如果P不等于1 2 通则是使np 10 这样就可以使二项分布得到满意的正态型 pChart Ifthesamplesizeisnotconstant thentheControlLimitsofapchartmaybecomputedbyeithermethod如果样本大小不为常数 控制线可以用以下任意一放法得到 a VariableControlLimits变量控制线whereniistheactualsamplesizeofeachsamplingi这里n是每次抽样的实际数b ControlLimitsBasedonAverageSampleSize控制线基于平均样本数wherenistheaverage ortypical samplesizeofallthesamples这里n是所有样本数的平均值 pChart WhentoUseControlLimitsBasedonAverageSampleSizeinsteadofVariableControlLimits当使用基于样本平均大小的控制线时Smallestsubgroupsize nmin isatleast30 ofthelargestsubgroupsize nmax 最小样本大小至少是最大样本大小的30 Futuresamplesizeswillnotdiffergreatlyfromthosepreviouslyobserved 后来的样本大小与目前样本大小无较大区别WhenusingControlLimitsBasedonAverageSampleSize theexactcontrollimitsofapointshouldbedeterminedandexaminedrelativetothatvalueif当使用基于样本平均大小的控制线时 每一点的控制线由于那一点的值来决定如果 Thereisanunusuallylargevariationinthesizeofaparticularsample某一特别的样本的大小有明显的变化Thereisapointwhichisnearthecontrollimits 有一点接近控制线 pChart AverageSampleSize npChart Ifthesamplesizeisconstant itispossibletobaseacontrolchartonthenumbernonconforming np ratherthanthefractionnonconforming p 如果样本大小是常数 可以基于控制图的不合格品数 而非部分不合格品数TheCenterLineandControlLimitsofannpchartare SampleSizeforpandnpCharts SampleSizeisdeterminedbasedonthe2criteria样本大小基于2个标准来决定 AssumptiontoapproximateBinomialDistributiontoaNormalDistribution假定二项分布近似正态分布ToensurethattheLCLisgreaterthanzero 确保下控制线大于0 cChart DefectsperUnit DPU 单位缺陷ErrorRate DefectRate缺陷率DefectsperOpportunity cChart Ifthenumberofnonconformities defects perinspectionunitisdenotedbyc then如果每个检查单元的缺陷数为c 则 TheCenterLineandControlLimitsofacchartare uChart Incaseswherethenumberofinspectionunitsisnotconstant theuchartmaybeusedinstead with如果检查单元的数量不为常数 则用u图 Iftheaveragenumberofdefectsperinspectionunitisdenotedbyu then如果每个检查单元的平均缺陷数用u表示 则 Whereciisthecountofthenumberofdefectsinnumberofinspectionunits ai这里ci是数量为ai的检查单元的缺陷数 uChart TheCenterLineandControlLimitsofauchartare SamplingPlansforXChart均值图抽样计划 Samplingfrequency 抽样频率Samplesize 样本大小Widthofcontrollimits 控制线宽度 SamplingFrequency抽样频率Themostdesirablesituationwithregardstodetectingshiftswouldbetotakelargesamplesveryfrequently探测变化最理想的做法是频繁地抽取大的样本 Butthisisusuallynoteconomicallyfeasible andtheproblemisoneofresourceallocation 由于资源分配的问题 这在经济上不可行Shouldwetakesmallersamplesatshortintervals Orlargersamplesatlongerintervals 可以在较短时间内抽取小样本吗 或在较长时间间隔内抽取较大样本吗Currentindustrypracticetendstofavoursmaller morefrequentsamples目前业界的共识是频繁地抽去小样本 DesigninganX RChart SamplingFrequency ARL抽样频率 平均运转周期Agoodwayistostartevaluatingsamplingfrequencyistodeterminetherequiredsamplingfrequencystatistically一个好的方法是评估抽样频率 统计地决定需要的抽样频率 WeusetheAverageRunLength ARL todothis我们使用平均运转周期来决定Thenfinallyweighthecomputedresultswithsoundpracticaljudgement最后根据计算结果和惯例来决定 DesigninganX RChart ControlCharts SamplingRisks Ifthereisnochangeintheprocess thereisstillachanceofgettingapointoutofthe3scontrollimits Whatistheimplication 如果制程没有改变 但有一点在3s控制线外 它表示什么呢 ControlCharts SamplingRisks TypeIError一类错误Concludingthattheprocessisoutofcontrolwhenitisreallyincontrol制程受控 但却认为已经失控 probabilityofmakingTypeIerror范此类错误的可能性 commonlyknownastheproducer srisk制造商的风险 totalof0 27 forcontrollimitsof 3s对于 3s控制线 范此类错误的可能性为0 27 ControlCharts SamplingRisks TypeIErrorandTampering一类错误及干预Iftheprocessisreallyincontrol andprocessadjustmentismadebecauseofTypeIerror itiscalledtamperingwiththeprocess 制程受控但由于范一类错误而调整制程 这叫干预制程Tamperinghasbeenshowntoactuallyincreasethevariabilityoftheprocess 干预制程实际是给制程增加变异 ControlCharts SamplingRisks TypeIIError二类错误Concludingthattheprocessisincontrolwhenitisreallyoutofcontrol制程不受控但却认为它受控 probabilityofmakingTypeIIerror范此类错误的可能性 commonlyknownastheconsumer srisk客户的风险 0 135 0 135 AverageRunLength ARL ARLreferstotheaveragenumberofsamples orpoints plottedtoseeanout of controlsignalForaprocessthatisin control Foraprocessthatisout of control ARLsareusedtohelpevaluatedecisionsonsamplesizeandsamplingfrequency平均运转周期用来帮助决定抽样大小和频率 SamplingFrequency In ControlARL ARL0 受控平均运转周期FortheX chartwith3slimits a 0 0027Therefore in controlARL 1 0 0027 370 Thismeansthatiftheprocessremainsunchanged oneout of controlsignalwillbegeneratedevery370samples制程不变条件下 每370个样本可能产生一个失控信号 Ifthesamplingintervalis1hr onefalsealarmwillbeseenevery370hrstypically 如果取样间隔为1小时 则每370小时就会看到1个错误报警 DesigninganX RChart SamplingFrequency Out of ControlARL ARL1 失控平均运转周期Nowsupposetheprocesshasdriftedby3s 现假定制程偏移3sProbabilityofXstillwithinthe3slimits 0 5均值在3s线内的可能性为0 5Thus out of controlARL 1 1 0 5 2 Thismeansfromthetimetheprocessshifted thechartneeds2samplestodetecttheshift 这意味着从制程开始发生偏移时 控制图需要2个样本才能探测得到这种偏移Ifthesamplingintervalis1hr AverageTimetoSignal ATS orexposureis2hrstypically 如果抽样间隔是1小时 则这种变化要2小时才能知道 DesigninganX RChart SampleSize样本大小Whataboutsamplesize Howdowecomputetheadequatesamplesizestatistically 如何计算足够的样本大小RecallthatthesamplesizehelpstocontrolorlimittheamountofTypeIIerror b 样本大小帮组控制或限制二类错误Recallalsothatsamplesizeisafunctionofseveralparameters 样本大小是几个参数的函数n f a b D s Hence eachparameterneedstobeestablishedbeforewecancomputesamplesize因此 计算样本大小前 需要先建立各个参数 DesigninganX RChart SamplingInterval SampleSizeProcedure抽样间隔和样本大小选择程序Using 3slimits a 0 27 ARL0 1 a 370Definetherequiredfalsealarmrate确定需要的错误报警率 F A rate Ave ofproductionhrstoget1falsealarm得到一个错误报警生产的平均时间Fromaboveinformation determinetherequiredsamplinginterval S I usingfollowingequation根据上面的资料 用以下等式确定抽样间隔 ARL0 xS I F A rateRoundupS I hrs tonexthigherconvenientnumber四舍五入抽样间隔时间到最佳Definetherequiredexposurerate 决定需要的发生率Exp rate Ave ofproductionhrsbeforedetectingshift探测到变异前的平均生产时间 DesigninganX RChart SamplingInterval SampleSizeProcedure抽样间隔和样本大小选择程序BringS I Exp rateintofollowingequationtocomputetherequiredARL1抽样间隔和发生率代入下列公式计算ARL1 ARL1xS I Exp rateFromcomputedARL1 establishtherequiredb or 1 b usingARL1 1 1 b 计算b or 1 b Atthisjuncture samplingintervalisalreadyestablished someparametersalreadyestablishedforsamplesizecalculation到现在已经有了计算样本大小的一些参数 n f a b D s DesigninganX RChart SamplingInterval SampleSizeProcedure抽样间隔和样本大小选择程序Basedonengineeringjudgment defineD max allowableprocessdriftinmthatmustbedetected根据工程判断 决定允许制程在m内漂移的最大值DEstablishprocesssxfromhistoricaldata orifnotavailable collectsomepartstogetaroughestimate根据历史数据建立制程 如果不可能 建立一个大概Alternatively D sxratio k canbederivedfromprocesscapabilityconsiderationsusingfollowingequation 比例k可以通过下列公式而得到k D sx 3 Ppkcurrent Ppkmin Withthat allparametersforcomputingnarefound这样 所有计算n的参数已经建立 n可以确定了 n f a b D s DesigninganX RChart DesigninganX RChart Thischartisfora 0 27 only k 1 b SamplingInterval SampleSizeProcedure抽样间隔和样本大小选择程序Insteadofusingabovegraph followingequationcanbeusedtocalculaten下列等式也可以计算n值 Alternatively aboveformulaisalsoavailableinMinitab Use Stat PowerandSampleSize 1 sampleZ这个公式也可以在Minitab中找到 DesigninganX RChart Example1 DesigninganX RChart Yourmanagementhasthefollowingconcernswithregardstoimplementingcontrolchartsattheshopfloor在推行控制图时 管理层很关心下列问题 FalseAlarm 错误报警Notmorethan1falsealarmforevery500hrsofproduction每500小时的生产不超过1个错误报警 Exposure 暴露Notmorethan3hrsexposureifprocesshasshifted如果制程偏移 不超过3小时暴露 AllowableShift允许偏移 Fromhistoricaldata Ppk 2 2 Mincustomerrequirement Ppk 1 6DesignanappropriateXbar Rcharttomeettheaboveconstraints 设计一个均值极差图满足上列条件要求 Aftersometime thefactorydecidestoswitchto14hrsofproductionperday 一段时间后 工厂决定每天14小时生产Tolerablefalsealarm 极限错误报警Average1falsealarmpermonth 30days 每月平均1个错误报警WhatchangesdoyouneedtomaketothechartsyouhavedesignedinExample1 照此条件 对所设计的例子1的控制图有何改变 Example2 DesigninganX RChart WheretoUseSPCCharts Whenamistake proofingdeviceisnotfeasible当过失防治设施不可行时IdentifyprocesseswithhighRPNsfromFMEA从FMEA中识别高风险度的制程Evaluatethe CurrentControls columntodetermine gaps inthecontrolplan DoesSPCmakesense 评估现行控制程序 确定控制计划的差距IdentifycriticalvariablesbasedonDOE根据DOE识别关键变量Customerrequirements客户需求Managementcommitments管理层允诺 EndofTopicWhatquestiondoyouhave ReadingReference IntroductiontoStatisticalQualityControl DouglasC Montgomery JohnWiley Sons ISBN0 471 30353 4 1 PreparationofSamplingChoosethequalitycharacteristictobemeasuredmeasurementstakenonthefinalproductmeasurementstakenonthein processproductmeasurementstakenontheprocessvariablesDeterminethebasis sizeandfrequency ImplementingtheControlChart 2 DataCollectionStartcollectingdatainsubgroupsaccordingtotheestablishedsubgroupsizeandsamplingintervalCalculatetherelevantstatistics mean range foreachsubgroupPlotthesubgroupstatisticsonacontrolchart Atthistime thesubgroupmeansandrangesareplottedwithoutanycontrollimits ImplementingtheControlChart 3 ConstructtheControlChartCalculatethetrialcenterlineandthetrialcontrollimitswhenenoughdatahavecollectedPlotthetrialcenterlineandthetrialcontrollimits ImplementingtheControlChart Howmanypointsareneededbeforecontrollimitscanbecalculated Thegeneralruleisatleast20points representing100measurementstypically Sometimes becauseofshortproductionruns 10pointsmaybeusedtocomputetrialcontrollimits buttheestimateofmeanandsigmaarelessaccurate Thesepreliminarysubgroupsestablishtrialcontrollimitsthathelpusevaluateiftheprocesswasincontrolinthepast andifthelimitsaresuitableforcurrentorfutureproduction TrialControlLimits 4 Analysis Interpretation InvestigatethechartforlackofcontrolEliminateout of controlpointsifrequiredRecomputecontrollimitsifnecessaryDetermineprocesscapability ImplementingtheControlChart TheX Rchartmustbeinterpretedtogetheraswellasseparately ReadtheR chartfirsttodetermineifitisincontrol i e nopointsoutofthecontrollimitsornon randompattern tobediscussedlater TheR chartismoresensitivetochangesinuniformityorconsistency Anythingthatintroduceschangestotheprocessvariability suchaspoorm