Cg/CgkareInstrumentCapabilityIndexes.
TheideaforCgisthesamethanforCp,the"conceptual"formulaforCgis:
Cg=(allowablevariation)/(actualvariation
Thedifferencesarewhatwetakeforallowableandactualvariation.ForCp,theactualvariationistheprocessvariation,andtheallowedvariationisthespecificationrange.
ForCg,theactualvariationistheINSTRUMENTALONEvariation(6xSinstNobetweenparts,withinpart,betweenoperatorsoralongtimevariationisincluded.About50measurementsaremadeconsecutivelyonamastergaugeor"bestavailable"part,andalwaysonthesamepointofthepart,andbythesameperson,andinacontrolledenvironment(usuallythemetrologyroom
Theallowablevariationistakenas1/5oftheprocessvariation(6xSproc)or1/5oftheproductspecificationrange,dependingonwhetheryouwanttheinstrumenttocontroltheprocessortocheckconformanceoftheparts,then:
Cg=(0.2x6xSproc)/(6xSinst)=Sproc/5Sinst
or
Cg=(0.2xTol))/(6xSinst)=Tol/30Sinst
Cgk,asCpk,takesintoaccounttheposition(whichwouldbethebias):
Cgk=(0.5oftheallowablevariation-|bias|)/(0.5oftheactualvariation)
TheideaofCg/Cgkistohavethisinformationinadvancetouseitforthedecisionaboutiftheinstrumentwouldbe"selectable"foragivenmeasurement.Ifyoudecidetoincludetheinstrumentinameasurementsystemthatyouwillincludeinthecontrolplan,onlythenyoumaketheGaugeR&Rwiththefullsystem,therealprocesspartsandthefullmeasurementvariation.Butyoudon＇twanttodevelopameasuringsystem,designandbuildameasurementdevice,andwritethemeasuringinstructionsonlytofindthattheinstrumentitselfcouldhaveneverbeencapableofsuchameasurement