>> P.497
Specicexamplesofaprocesscapabilityindex(Cp)(bilateraltolerance)LSLUSLCp=1Cp=1.33Cp=1.67LSLUSLTheprocesscapabilityisbarelyachievedasthe6sigmaprocesslimitsarecoincidentwiththetolerancelimits.Theprocesscapabilityistheminimumvaluethatcanbegenerallyacceptedasitisnocloserthan1sigmatothetolerancelimits.σ6σσ6σ8σLSLUSLTheprocesscapabilityissufcientasitisnocloserthan2sigmatothetolerancelimits.σ6σ10σNotethatCponlyrepresentstherelationshipbetweenthetolerancelimitsandtheprocessdispersionanddoesnotconsiderthepositionoftheprocessmean.Note:AprocesscapabilityindexthattakesthedifferencebetweentheprocessmeanfromthetargetprocessmeanintoconsiderationisgenerallycalledCpk,whichistheuppertolerance(USLminusthemean)dividedby3(themeanvalueminusLSL)dividedby3(halfofprocesscapability)orthelowertolerance,whicheverissmaller.ControlchartUsedtocontroltheprocessbyseparatingtheprocessvariationintothatduetochancecausesandthatduetoamalfunction.Thecontrolchartconsistsofonecenterline(CL)andthecontrollimitlinesrationallydeterminedaboveandbelowit(UCLandLCL).Itcanbesaidthattheprocessisinastateofstatisticalcontrolifallpointsarewithintheupperandlowercontrollimitlineswithoutnotabletrendswhenthecharacteristicvaluesthatrepresenttheprocessoutputareplotted.Thecontrolchartisausefultoolforcontrollingprocessoutput,andthereforequality.Uppercontrollimit(UCL)Lowercontrollimit(LCL)1243Subgroupnumber5Centerline(CL)67ChancecausesThesecausesofvariationareofrelativelylowimportance.Chancecausesaretechnologicallyoreconomicallyimpossibletoeliminateeveniftheycanbeidentied.X-RcontrolchartAcontrolchartusedforprocesscontrolthatprovidesthemostinformationontheprocess.TheX-RcontrolchartconsistsoftheXcontrolchartthatusesthemeanofeachsubgroupforcontroltomonitorabnormalbiasoftheprocessmeanandtheRcontrolchartthatusestherangeforcontroltomonitorabnormalvariation.Usually,bothchartsareusedtogether.HowtoreadthecontrolchartTypicaltrendsofsuccessivepointpositioninthecontrolchartthatareconsideredundesirableareshownbelow.Thesetrendsaretakentomeanthata‘specialcause’isaffectingtheprocessoutputandthatactionfromtheprocessoperatorisrequiredtoremedythesituation.Thesedeterminationrulesonlyprovideaguideline.Taketheprocess-specicvariationintoconsiderationwhenactuallymakingdeterminationrules.Assumingthattheupperandthelowercontrollimitsare3awayfromthecenterline,dividethecontrolchartintosixregionsatintervalsof1rules.TheserulesareapplicabletotheXcontrolchartandtheXcontrolchart.Notethatthese'trendrulesforaction'wereformulatedassuminganormaldistribution.Rulescanbeformulatedtosuitanyotherdistribution.toapplythefollowingUCLXLCLUCLXLCLUCLXLCLUCLXLCLX+3X+2X+1X-1X-2X-31)Thereisapointbeyondeitherofthecontrollimitlines(±3).3)Sixpointsconsecutivelyincreaseordecrease.X+3X+2X+1X-1X-2X-3X+3X+2X+1X-1X-2X-35)Twoofthreeconsecutivepointsareover±2fromthecenterlineoneitherside.X+3X+2X+1X-1X-2X-3UCLXLCLUCLXLCLUCLXLCLUCLXLCL2)Nineconsecutivepointsaretoonesideofthecenterline.4)14pointsalternatelyincreaseanddecrease.X+3X+2X+1X-1X-2X-3X+3X+2X+1X-1X-2X-3X+3X+2X+1X-1X-2X-36)Fouroffiveconsecutivepointsareover±1fromthecenterlineoneitherside.X+3X+2X+1X-1X-2X-37)Thereare15consecutivepointswithin±1fromthecenterline.8)Thereareeightconsecutivepointsover±1fromthecenterline.Note:Thispartof'QuickGuidetoPrecisionMeasuringInstruments'(09-31to09-32)hasbeenwrittenbyMitutoyobasedonitsowninterpretationoftheJISQualityControlHandbookpublishedbytheJapaneseStandardsAssociation.References-JISQualityControlHandbook(JapaneseStandardsAssociation)Z8101:1981Z8101-1:1999Z8101-2:1999Z9020:1999Z9021:199809-32
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