Introduction to Statistical Quality Control, 5th edition.ppt

chapter8 1 chapter8 2 chapter8 3 learningobjectives chapter8 4 processcapability inshort theprocessmustfirstbebroughtintostatisticalcontrolsoitsperformancecanbepredicted thenitscapabilitytomeetspecificationscanbeassessed chapter8 5 processcontrol chapter8 6 processcapability chapter8 7 capablev s in controlprocess capableprocess aprocessthathasagreaterthe1 thismeansthatthehistogramdistributionandthenormalcurvearecontainedwithintheactualspecificationdimensions chapter8 8 capablev s in controlprocess in controlprocess aprocessthatwhenchartedonaspcchartandallmeasurementsarewithintheupperandlowercontrollimits thesemeasurementsplotsmustberandominnature i e nopointsoverorunderthecontrollimitsanddonotviolatethewesternelectricrules chapter8 9 capablev s in controlprocess aprocessmaybein control butnotcapable aprocessmaybein controlandcapable chapter8 10 processcapability naturaltolerance processspread ofaprocessisthegivenrangethattheprocesscanmaintainduringordinaryoperationwithouttheactionofanypersoninmakingprocessadjustments normallylimits 6sigma chapter8 11 howdoweknowaprocessiscapable theseindexestelliftheprocessiscapableofproducingfeatureswithintheengineeringtolerances thisisessentiallyagradefortheprocesswherethehighernumberisbetter cpandcpkstatisticalprocessindexes chapter8 12 thecpindex example supposethespecwidth 10unitsand 5unitsthisimpliesthespecistwiceaswideasthenaturalspread chapter8 13 cpandcpk capabilityindexesareusefultoolsintheanalysisofcapabilitydata theprocessmustbecapable cpisacapabilityindex formula chapter8 14 cpandcpk cpkisacapabilityindexformula whateverislessusl upperspeclimitlsl lowerspeclimit chapter8 15 cpandcpk statisticalprocesscontrol theuseofstatisticalmethodsortechniquessuchascontrolchartstoanalyzeaprocessoritsoutputsandtotakeappropriateactionstoachieveandmaintainastateofstatisticalcontrolandtoimprovetheprocesscapability chapter8 16 cpandcpk characteristic adistinguishingfeatureofaprocessoritsoutputonwhichvariabledataorattributedatacanbecollected chapter8 17 cpandcpk dominantcharacteristics thosecharacteristicsthatgreatlyinfluenceproductqualityandaremostimportanttoproductform fit orfunction variabledata quantitativedata wheremeasurementsareusedforanalysis key chapter8 18 cpandcpk attributedata qualitativedatathatcanbecountedforrecordingandanalysis suchasthepresenceofarequiredlabel theinstallationofalltherequiredfastenersortheabsenceoferrorsonanexpensereport itcanalsobecharacteristicsthatareinherentlymeasurablebutwheretheresultsarerecordedinasimpleyes nofashion suchas theacceptabilityofashaftdiameterwhencheckedonago no gogauge chapter8 19 cpandcpk sigma thestandarddeviationofastatisticalpopulation chapter8 20 cpandcpk capability whentheprocessaverageplusandminusthe3standarddeviations sigma spreadofthedistributioniscontainedwithinthespecificationtoleranceforvariabledata orwhenatleast99 73 ofindividualsproducedbytheprocessmeetspecificationforattributedata theprocessisconsideredtobecapable capabilitycanonlybedeterminedaftertheprocessisinstatisticalcontrol chapter8 21 cpandcpk capabilityindices ameasureofthecapabilityofaprocess cpistheinherentcapabilityofaprocessandisdefinedastheratioofthetolerancetotheprocessvariation cpkisameasureofthecapabilityofaprocessinrelationtotheprocessaverage itisbasedonthedistancebetweentheprocessaverageandtheclosestspecificationlimit chapter8 22 processfallouttable processcapabilitypartspermillionratiodefective0 50133 600 000 7524 400 001 002 700 001 10967 001 20318 001 3096 001 4026 001 506 801 601 601 700 341 800 062 000 0018 centeredprocess chapter8 23 relationshipofspecifications controllimits andnaturaltolerancelimitsintheprocess chapter8 24 relationshipofspecifications controllimits andnaturaltolerancelimitsintheprocess chapter8 25 relationshipofspecifications controllimits andnaturaltolerancelimitsintheprocess 3 2 3 2 spread target lsl usl istheratioofspec widthtothenaturalvariabilitypresentintheprocess i e chapter8 26 relationshipofspecifications controllimits andnaturaltolerancelimitsintheprocess avg target lsl usl istheratioofthedistancebetweentheprocesscenterandthenearestspec limittoonehalfofprocessvariability i e centerline chapter8 27 chapter8 28 chapter8 29 chapter8 30 processcapability priortotakingdeliveryofnewprocessequipmentbeforeapprovingnewly installedprocessequipmentforproductionuseasproductionbegins toestablishcapabilityoftheequipment tooling material operatorcombination onanongoingbasistoverifycontinuingcapability whenout of specificationconditionsarefound when chapter8 31 processcapability productsmustmeetspecifications itismoreefficientforcostandtimingtoproducetospecificationthantosorttospecification consistentperformancerequiresinherentcapability processcapabilityequalsmachinecapabilityplusprocesscontrol toverifycapability conductcapabilitystudies theneedforcapabilitystudies chapter8 32 processcapabilitystudyflowchart chapter8 33 proceduresfordeterminingprocesscapability definetheprocessisitaline machine operator portionofmanufacturing etc chapter8 34 proceduresfordeterminingprocesscapability determineifspecificationsarenowbeingmet conduct shortterm processcapabilitystudygetcurrentdatacalculateands usuallyfromgroupeddata toestimatethemeanandstandarddeviationoftheprocess n 30 chapter8 35 proceduresfordeterminingprocesscapability assumenormalityandestimatepercentmeetingspecifications determinefromfrequencydistributioniftheassumptionisvalid ifspecsarebeingmet generallygotoanotherproblem ifspecsarenotbeingmet proceedbelow chapter8 36 proceduresfordeterminingprocesscapability determineinherentvariability using r pre controlchartsa getconsecutivesamples two 2 ormoreatatimeinasamplegroup getatleasttwenty 20 groupsoverashiftorothershortproductionrunduringwhichoperationappearsstableorwithoutunusualproblems chapter8 37 proceduresfordeterminingprocesscapability b calculateaveragerange andcontrollimitsforr c discardanyrangesoutsidecontrollimits assumethatassignablecausewouldhavebeenidentifiedandremoved ifassumptioncannotbemade retaintherange chapter8 38 proceduresfordeterminingprocesscapability d recalculateaveragerangeandcontrollimits e repeatstepscandd removalofexcessiverangesandtherecalculationofcontrollimits untilallrangesincontrol chapter8 39 proceduresfordeterminingprocesscapability f estimatethestandarddeviationfromthelastaveragerange estimateof d2g usemidpointofspecificationlimitsastheprocessmean assumenormality andestimatepercentmeetingspecs chapter8 40 proceduresfordeterminingprocesscapability ifspecscanbemet investigateprocesstodeterminewhyspecsarenotbeingmet chapter8 41 proceduresfordeterminingprocesscapability i ifspecscannotbemet considermanagementalternatives changespecschangeprocessmakebestofitdropproductj setup rchartsforfuturecontrol chapter8 42 chapter8 43 spccontrolplan 1 controlcharacteristics sheetof 6 chapter8 44 spccontrolplan 7 8 9 10 11 12 13 14 15 submittedby title 16 approvedby date chapter8 45 datacollectionforcapabilityanalysis sampledata tallysheet chapter8 46 processcapabilitystudies 1 trainengineerstolearntheprocesscapabilitystudythatistomeasuretheinherentvariabilityoftheprocesssothattheperformancepotentialcanbedetectedundernormal incontrolconditions 2 trainengineerstousethecontrolchartmethodandthefrequencydistributionmethodformeasuringprocesscapabilityat99 7 confidencelevel chapter8 47 processcapabilitystudies 3 theapplicationsincludethefollowing informationtofacilitatethedesignoftheproductacceptanceofneworreconditionedpieceofequipment schedulingworktomachine chapter8 48 processcapabilitystudies d settingupthemachineforaproductionrun e selectionofoperators f introductionofanewproductorprocess chapter8 49 cpk akeycharacteristicwillbeconsideredcapableifthesuppliercandemonstratewith90 confidencethatthetruecpkexceeds1 0 insomecases analternatecpkrequirementwillbedefinedinthecontract whencomputingcpk seesection7 3 2 thenumberofmeasurementscollectedmustbetakenintoaccount table2 3 2mustbeusedtodeterminetheminimumcalculatedcpktodemonstratecapability chapter8 50 table2 3 2cpk chapter8 51 cpk thevaluesintheabovetablearethecalculatedcpkvaluesrequiredtobe90 confidentthattheactualcpkisgreaterthanorequaltothecpkvalueatthetopoftherespectivecolumn thevalueslistedinthecolumntitled numberofmeasurementstaken aretheactualnumberofmeasurements notthenumberofplotpoints thetableassumesthattheunderlyingdistributionoftheindividualmeasurementsarenormallydistributedwithafixedmeanandstandarddeviation chapter8 52 cpk examples if30partsaremeasuredandtherequiredcpkis1 0 thecalculatedcpkfromthe30partsneedstobeatleast1 23 if20partsaremeasuredandthecalculatedcpkis1 93 wehavesufficientconfidencethattheactualcpkis1 50orbetter chapter8 53 cp cpkindex processcapabilitystudies 1 thetestspecificationlimitsforincomingdiodesis 008ohms upper and 001 lower andthestandarddeviationforthispopulationis 002ohms whatiscpindexforthisprocess doesthisnumberindicatetheprocessiswithinthespecificationlimits chapter8 54 cp cpkindex processcapabilitystudies whyorwhynot a supposeactionwastakenonthisincomingtestprocessandthestandarddeviationisnow 001ohms whatisthecpkindex isitwithinthelimits giventhat 0 04 chapter8 55 cp cpkindex processcapabilitystudies 2 measurementsofthesolderthicknessesonprintcircuitboardsgoingthroughthewavesoldermachinearenaturallybetween 006and 012 giventhat whereasthespecificationlimitsareatfromthemeanof 009 whatisthecp cpkindexforthisprocess chapter8 56 cp cpkindex processcapabilitystudies 3 whenshouldaprocesscapabilitystudybeconducted chapter8 57 processcapability chapter8 58 usesofprocesscapabilitydata chapter8 59 reasonsforpoorprocesscapability chapter8 60 chapter8 61 chapter8 62 chapter8 63 probabilityplotting chapter8 64 thedistributionmaynotbenormal othertypesofprobabilityplotscanbeusefulindeterminingtheappropriatedistribution chapter8 65 chapter8 66 chapter8 67 forthehardbakeprocess chapter8 68 one sidedpcr chapter8 69 interpretationofthepcr chapter8 70 violationoftheseassumptionscanleadtobigtroubleinusingthedataintable8 2 assumptionsforinterpretationofnumbersintable8 2 chapter8 71 chapter8 72 cpdoesnottakeprocesscenteringintoaccountitisameasureofpotentialcapability notactualcapability chapter8 73 ameasureofactualcapability chapter8 74 normalityandprocesscapabilityratios theassumptionofnormalityiscriticaltotheusualinterpretationoftheseratios suchastable8 2 fornon normaldata optionsaretransformnon normaldatatonormalextendtheusualdefinitionsofpcrstohandlenon normaldatamodifythedefinitionsofpcrsforgeneralfamiliesofdistributions chapter8 75 othertypesofprocesscapabilityratios firstgenerationsecondgenerationthirdgenerationlotsofresearchhasbeendonetodevelopratiosthatovercomesomeoftheproblemswiththebasiconesnotmuchevidencethattheseratiosareusedtoanysignificantextentinpractice chapter8 76 chapter8 77 chapter8 78 chapter8 79 chapter8 80 chapter8 81 chapter8 82 processcapabilityanalysisusingcontrolcharts chapter8 83 sincelsl 200 chapter8 84 chapter8 85 chapter8 86 measurementaccuracy theclosenessofmeasurementtothetruevalue chapter8 87 accuracyandprecision wehavefocusedonlyonprecision chapter8 88 chapter8 89 gauger rstudies chapter8 90 chapter8 91 chapter8 92 7 8gaugeandmeasurementsystemscapabilitystudies determinehowmuchoftheobservedvariabilityisduetothegaugeormeasurementsystemisolatethecomponentsofvariabilityinthemeasurementsystemassesswhetherthegaugeiscapable suitablefortheintendedapplication chapter8 93 chapter8 94 chapter8 95 chapter8 96 thep tratio chapter8 97 chapter8 98 estimatingthevariancecomponents chapter8 99 chapter8 100 thegaugeisnotcapablebythiscriterion chapter8 101 discriminationratio chapter8 102 gauger rstudiesareusuallyconductedwithafactorialexperiment chapter8 103 thisisatwo factorfactorialexperimentanovamethodsareusedtoanalyzethedataandyoestimatethevariancecomponents chapter8 104 chapter8 105 chapter8 106 chapter8 107 chapter8 108 negativeestimatesofavariancecomponentwouldleadtofillingareducedmodel suchas forexample chapter8 109 chapter8 110 forthisexample chapter8 111 othertopicsingauger rstudies section8 7 3providesadescriptionofmethodstoobtainconfidenceintervalsonthevariancecomponentsandmeasuresofgauger rsection8 7 4presentsanewmeasureofgaugecapability theprobabilitiesofmisclassificationofpartsrejectinggoodunits producer srisk passingbadunits consumer srisk methodsforcalculatingthesetwoprobabilitiesaregiven chapter8 112 statisticaltolerance themorerealisticstatisticalapproachisbasedontherelationshipbetweenthevariancesofanumberofindependentcauses a b c andthevarianceoftheoverallresult thisrelationshipis chapter8 113 statisticaltolerance fromaprocesscapabilityof6 tandbysubstitution t tolerance theapproachtostatisticaltoleranceisillustratedbyssimplemechanicalassemblyofthreepartsasshownbelow chapter8 114 statisticaltolerance dimensionsofa b andcdeterminetheoverallassemblylength aconventionalspecificationontheassemblylengthwouldbe chapter8 115 statisticaltolerance thisisillustratedbyagainusingthepreviousassembly assumethatcapabilitystudiesindicatethatifthe 005toleranceoncomponentacouldbeexampleto 010 asecondaryoperationcouldbeeliminated whateffectwillthishaveonthetotallengthtolerance chapter8 116 statisticaltolerance thisisanincreaseofonly 0015foracomponentincreaseof 005 thisillustratesanimportantcharacteristicofthestatisticalcombinationofcomponentvariances theeffectofacomponentwithsmallvarianceisvarysmall thecomponentwiththelargestvariancehasthegreatesteffectonoverallvariance chapter8 117 statisticaltolerance exercisecomparethetolerancefoundusingtheconventionalengineeringapproachtothestatisticallycomputedassemblytolerance considerthefourblocks ab bc cdanddeshownbelow eachoftheseisindependent determinethespecificationforthetotalassemblyae chapter8 118 statisticaltolerance assumethateachpartcomponentwasstudiedforcapability andwefoundthateachrequiredprocesscreatingtherespectivecomponentlinearlengthwasstabilized thatis incontrol eachprocesshadrespectivedimensionalcharacteristicsasshownbelow chapter8 119 chapter8 120 statisticaltolerance fromthisdata itisapparentthatifweassemblethesefourcomponents thatthegrandaverageofthesepartswouldbe1 645 thisisdeterminedbythefollowingcalculation chapter8 121 statisticalapproach assumethateachpartcomponentwasstudiedforcapability andwefoundhateachrequiredprocesscreatingtherespectivecomponentlinearlengthwasstabilized thatis incontrol eachprocesshadrespectivedimensioncharacteristicasshownbelow chapter8 122 componentxab 750 00067 bc 320 00033 cd 475 001 de 100 00067 chapter8 123 formthisdata itisapparentthatifweassemblethesefourcomponents thatthegrandaverageofthosepartswouldbe1 645 thisisdeterminedbythefollowingcalculation 750 320 475 100 total 1 645 assemblyaverage chapter8 124 ifwecoulddeterminethestandarddeviationofae thenwecouldbeabletofindthatregionwithinwhich99 7 ofalllinearlengthsofae theassembly wouldlie thisregionbedefinedas chapter8 125 thestandarddeviationoftheassemblyaecanbefoundbycalculatingthesquarerootofthesumofthesquareofeachcomponent thiscanbestatedmathematicallyasfollows therefore uppertolerancelowertolerancetotalstatisticaltolerancewhatpercentisthisofthe worstcase tolerance chapter8 126 suchshaftsandbearingsfittogether istheoverlaptoomuchsatisfactoryassembly chapter8 127 thesituationpicturedinfigure11 6canbeanalyzedasfollows letavalueforshafto d avalueforbearingi d ananalysis chapter8 128 chapter8 129 andhencethestandarddeviationforthebearingi d maybeapproximatedassimilarly thestandarddeviationforthebearingi d maybeapproximatedusing chapter8 130 hence thestandarddeviationforthedifference maybeapproximatedusingtheequationwithandasbelow thisdistributionofthedifference willbenormal sinceandarenormal withtheapproximatemeanvalueandstandarddeviationobtainedabove thissituationispicture