SOLUTIONmMANUA
L
, PROBLEM 1.1 m
FIND: Explain the hierarchy of standards. Explain the term standard. Cite example.
m m m m m m m m m m m
SOLUTION
Themtermmstandardmrefersmtomanmobjectmorminstrument,mammethodmormamproceduremthatmprovidesma
valuemofmanmacceptablemaccuracymformcomparison.
m
Amprimarymstandardmdefinesmthemvaluemofmthemunitmtomwhichmitmismassociated.mSecondarymstan
dards,mwhilem basedmonmthemprimarymstandard,m arem moremreadilymaccessiblemandmamenablemform
useminmamcalibration.mTheremismamhierarchymofmsecondarymstandards:mAmtransfermstandardmmigh
tmbemmaintainedmbymamnationalmstandardsmlabm(suchmasmNISTminmthemUnitedmStates)mtomcalibrat
emindustrialm“laboratorymstandards”.mItmismcostlymandmtime-
consumingmtomcertifymamlaboratorymstandard,msomtheymaremtreatedmcarefullymandmnotmusedmtoomr
egularly.mAmlaboratorymstandardmwouldmbemmaintainedmbymamcompanymtombemusedmtomcertifyma
mmoremcommonmin-
housemreferencemcalledmthemworkingmstandard.mAmworkingmstandardmwouldmbemcalibratedmagai
nstmthemlaboratorymstandard.mThemworkingmstandardmismusedmonmammoremregularmbasismtomcalibr
atemeverydaymmeasurementmdevicesmormproductsmbeingmmanufactured.mWorkingmstandardsmare
mmoremthemnormmformmostmofmus.mAmworkingmstandardmismsimplymthemvaluemorminstrumentmthatm
wemassumemismcorrectm inmcheckingmthemoutputmoperationmofmanotherminstrument.
Example:mAmgovernmentmlabmmaintainsmthemprimarymstandardmformpressure.mItmcalibratesmaman
minstrumentmcalledmam“deadweightmtester”m(seemC9mdiscussion)mformhighmpressuremcalibrations.
mThesemformmitsmtransfermstandardmformhighmpressure.mAmcompanymthatmmakesmpressuremtransd
ucersmneedsmanmin-
housemstandardmtomcertifymtheirmproducts.mTheympurchasemtwomdeadweightmtesters.mTheymsend
monemtestermtomthemnationalmlabmtombemcalibrated;mthismbecomesmtheirmlaboratorymstandard.mOnm
return,mtheymusemitmtomcalibratemthemother;mthismbecomesmtheirmworkingmstandard.mTheymtestmth
eirmmanufacturedmtransducersmusingmthemworkingmstandardm–
musuallym atmonemormtwompointsmovermthemtransducermrangemtomassuremthatmitmismworking.mBecau
semthemworkingmstandardmismbeingmusedmregularly,mitmcanmgomoutmofmcalibration.mPeriodically,m
theymcheckmthemworkingmstandardmcalibrationmagainstmthemlaboratorymstandard.
SeemASMEmPTCm19.2mPressuremMeasurementsmformamfurthermdiscussion
.mAmtestmstandardmdefinesmamspecificmproceduremthatmismtombemfollowed.
, PROBLEM 1.2 m
FIND: Why calibrate? What does calibrated mean?
m m m m m m
SOLUTION:
Thempurposemofmamcalibrationmismtomevaluatemandmdocumentmthemaccuracymofmammeasuringmdevi
ce.mAmcalibrationmshouldmbemperformedmwhenevermthemaccuracymlevelmofmammeasuredmvaluemm
ustmbemascertained.
Anminstrumentmthatmhasmbeenmcalibratedmprovidesmthemengineermambasismforminterpretingmthemd
evice’smoutputmindication.mItmprovidesmassuranceminmthemmeasurement.mBesidesmthismpurpose,m
amcalibrationmassuresmthemengineermthatmthemdevicemismworkingmasmexpected.
Amperiodicmcalibrationmofmmeasuringminstrumentsmservesmasmamperformancemcheckmonmthos
eminstrumentsmandmprovidesmamlevelmofmconfidenceminmtheirmindicatedmvalues.mAmgoodmrule
mismtom
calibratemmeasuringmsystemsmannuallymormmoremoftenmasmneeded.
ISOm9000mcertificationsmhavemstrictmrulesmonmcalibrationmresultsmandmthemfrequencym
ofmcalibration.
, PROBLEM 1.3 m
FIND: Suggest methods to estimate the accuracy and random and systematic errors of
m m m m m m m m m m m m
m amdialmthermometer.
SOLUTION:
Randommerrormismrelatedmtomrepeatability:mhowmcloselymanminstrumentmindicatesmthemsamemval
ue.mSomammethodmthatmrepeatedlymexposesmtheminstrumentmtomonemormmoremknownmtemperature
smcouldmbemdevelopedmtomestimatemthemrandommerror.mThismismusuallymstatedmasmamstatisticalmes
timatemofmthemvariationmofmthemreadings.mAnmimportantmaspectmofmsuchmamtestmismtomincludemso
memmechanismmtomallowmtheminstrumentmtomchangemitsmindicatedmvaluemfollowingmeachmreadin
gmsomthatm itm mustm readjustm itself.
Formexample,mwemcouldmplacemtheminstrumentminmanmenvironmentmofmconstantmtemperaturemand
mnotemitsmindicatedmvaluemandmthenmmovemthem instrumentmtom anotherm constantmtemperaturemenv
ironmentmandmnotemitsmvaluemthere.mThemtwomchosenmtemperaturesmcouldmbemrepresentativemofmt
hemrangemofmintendedmusemofmtheminstrument.mBymalternatingmbetweenmthemtwomconstantmtemper
aturemenvironments,mdifferencesminmindicatedmvaluesmwithinmeachmenvironmentmwouldmbemindic
ativemofmthemprecisionmerrormtombemexpectedmofmtheminstrumentmatmthatmtemperature.mOfmcourse,
mthismassumesmthatmthemconstantmtemperaturesmdomindeedmremainmconstantmthroughoutmthem testm
andmtheminstrumentmismusedminmanmidenticalmmannermformeachmmeasurement.
Systematicmerrormismamfixedmoffset.mInmthemabsencemofmrandommerror,mthismwouldmbemhowmclosel
ymtheminstrumentmindicatesmthemcorrectmvalue.mThismoffsetmwouldmbempresentminmeverymreading.m
Somanmimportantmaspectmofmthismcheckmismtomcalibratemitmagainstmamvaluemthatmismatmleastmasmaccu
ratemasmyoumneed.mThismismnotmtrivial.
Formexample,m youmcouldmusemthemicempointm(0oC)masmamcheckmformsystematicmerror.mThemicemp
ointmismformedmfrommamcarefullympreparedmbathmofmsolidmicemandmliquidmwater.mAsmanothermch
eck,mthemmeltingmpointmofmampuremsubstance,msuchmasmsilver,mcouldmbemused.mOrmeasier,mthemste
ammpoint.
Accuracymrequiresmamcalibrationmtomassessmbothmrandommandmsystematicmerrors.mIfminmthempre
cedingmtestmthemtemperaturesmofmthemtwomconstantmtemperaturemenvironmentsmweremknown,mt
hemabovemproceduremcouldmservemtomestablishmthemsystematicmerror,masmwellmasmrandommerrorm
ofmtheminstrument.mTomdomthis:mThemdifferencembetweenmthemaveragemofmthemreadingsmobtained
matmsomemknownmtemperaturemandmthemknownmtemperaturemwouldmprovidemanmestimatemofmth
emsystematicmerror.
L
, PROBLEM 1.1 m
FIND: Explain the hierarchy of standards. Explain the term standard. Cite example.
m m m m m m m m m m m
SOLUTION
Themtermmstandardmrefersmtomanmobjectmorminstrument,mammethodmormamproceduremthatmprovidesma
valuemofmanmacceptablemaccuracymformcomparison.
m
Amprimarymstandardmdefinesmthemvaluemofmthemunitmtomwhichmitmismassociated.mSecondarymstan
dards,mwhilem basedmonmthemprimarymstandard,m arem moremreadilymaccessiblemandmamenablemform
useminmamcalibration.mTheremismamhierarchymofmsecondarymstandards:mAmtransfermstandardmmigh
tmbemmaintainedmbymamnationalmstandardsmlabm(suchmasmNISTminmthemUnitedmStates)mtomcalibrat
emindustrialm“laboratorymstandards”.mItmismcostlymandmtime-
consumingmtomcertifymamlaboratorymstandard,msomtheymaremtreatedmcarefullymandmnotmusedmtoomr
egularly.mAmlaboratorymstandardmwouldmbemmaintainedmbymamcompanymtombemusedmtomcertifyma
mmoremcommonmin-
housemreferencemcalledmthemworkingmstandard.mAmworkingmstandardmwouldmbemcalibratedmagai
nstmthemlaboratorymstandard.mThemworkingmstandardmismusedmonmammoremregularmbasismtomcalibr
atemeverydaymmeasurementmdevicesmormproductsmbeingmmanufactured.mWorkingmstandardsmare
mmoremthemnormmformmostmofmus.mAmworkingmstandardmismsimplymthemvaluemorminstrumentmthatm
wemassumemismcorrectm inmcheckingmthemoutputmoperationmofmanotherminstrument.
Example:mAmgovernmentmlabmmaintainsmthemprimarymstandardmformpressure.mItmcalibratesmaman
minstrumentmcalledmam“deadweightmtester”m(seemC9mdiscussion)mformhighmpressuremcalibrations.
mThesemformmitsmtransfermstandardmformhighmpressure.mAmcompanymthatmmakesmpressuremtransd
ucersmneedsmanmin-
housemstandardmtomcertifymtheirmproducts.mTheympurchasemtwomdeadweightmtesters.mTheymsend
monemtestermtomthemnationalmlabmtombemcalibrated;mthismbecomesmtheirmlaboratorymstandard.mOnm
return,mtheymusemitmtomcalibratemthemother;mthismbecomesmtheirmworkingmstandard.mTheymtestmth
eirmmanufacturedmtransducersmusingmthemworkingmstandardm–
musuallym atmonemormtwompointsmovermthemtransducermrangemtomassuremthatmitmismworking.mBecau
semthemworkingmstandardmismbeingmusedmregularly,mitmcanmgomoutmofmcalibration.mPeriodically,m
theymcheckmthemworkingmstandardmcalibrationmagainstmthemlaboratorymstandard.
SeemASMEmPTCm19.2mPressuremMeasurementsmformamfurthermdiscussion
.mAmtestmstandardmdefinesmamspecificmproceduremthatmismtombemfollowed.
, PROBLEM 1.2 m
FIND: Why calibrate? What does calibrated mean?
m m m m m m
SOLUTION:
Thempurposemofmamcalibrationmismtomevaluatemandmdocumentmthemaccuracymofmammeasuringmdevi
ce.mAmcalibrationmshouldmbemperformedmwhenevermthemaccuracymlevelmofmammeasuredmvaluemm
ustmbemascertained.
Anminstrumentmthatmhasmbeenmcalibratedmprovidesmthemengineermambasismforminterpretingmthemd
evice’smoutputmindication.mItmprovidesmassuranceminmthemmeasurement.mBesidesmthismpurpose,m
amcalibrationmassuresmthemengineermthatmthemdevicemismworkingmasmexpected.
Amperiodicmcalibrationmofmmeasuringminstrumentsmservesmasmamperformancemcheckmonmthos
eminstrumentsmandmprovidesmamlevelmofmconfidenceminmtheirmindicatedmvalues.mAmgoodmrule
mismtom
calibratemmeasuringmsystemsmannuallymormmoremoftenmasmneeded.
ISOm9000mcertificationsmhavemstrictmrulesmonmcalibrationmresultsmandmthemfrequencym
ofmcalibration.
, PROBLEM 1.3 m
FIND: Suggest methods to estimate the accuracy and random and systematic errors of
m m m m m m m m m m m m
m amdialmthermometer.
SOLUTION:
Randommerrormismrelatedmtomrepeatability:mhowmcloselymanminstrumentmindicatesmthemsamemval
ue.mSomammethodmthatmrepeatedlymexposesmtheminstrumentmtomonemormmoremknownmtemperature
smcouldmbemdevelopedmtomestimatemthemrandommerror.mThismismusuallymstatedmasmamstatisticalmes
timatemofmthemvariationmofmthemreadings.mAnmimportantmaspectmofmsuchmamtestmismtomincludemso
memmechanismmtomallowmtheminstrumentmtomchangemitsmindicatedmvaluemfollowingmeachmreadin
gmsomthatm itm mustm readjustm itself.
Formexample,mwemcouldmplacemtheminstrumentminmanmenvironmentmofmconstantmtemperaturemand
mnotemitsmindicatedmvaluemandmthenmmovemthem instrumentmtom anotherm constantmtemperaturemenv
ironmentmandmnotemitsmvaluemthere.mThemtwomchosenmtemperaturesmcouldmbemrepresentativemofmt
hemrangemofmintendedmusemofmtheminstrument.mBymalternatingmbetweenmthemtwomconstantmtemper
aturemenvironments,mdifferencesminmindicatedmvaluesmwithinmeachmenvironmentmwouldmbemindic
ativemofmthemprecisionmerrormtombemexpectedmofmtheminstrumentmatmthatmtemperature.mOfmcourse,
mthismassumesmthatmthemconstantmtemperaturesmdomindeedmremainmconstantmthroughoutmthem testm
andmtheminstrumentmismusedminmanmidenticalmmannermformeachmmeasurement.
Systematicmerrormismamfixedmoffset.mInmthemabsencemofmrandommerror,mthismwouldmbemhowmclosel
ymtheminstrumentmindicatesmthemcorrectmvalue.mThismoffsetmwouldmbempresentminmeverymreading.m
Somanmimportantmaspectmofmthismcheckmismtomcalibratemitmagainstmamvaluemthatmismatmleastmasmaccu
ratemasmyoumneed.mThismismnotmtrivial.
Formexample,m youmcouldmusemthemicempointm(0oC)masmamcheckmformsystematicmerror.mThemicemp
ointmismformedmfrommamcarefullympreparedmbathmofmsolidmicemandmliquidmwater.mAsmanothermch
eck,mthemmeltingmpointmofmampuremsubstance,msuchmasmsilver,mcouldmbemused.mOrmeasier,mthemste
ammpoint.
Accuracymrequiresmamcalibrationmtomassessmbothmrandommandmsystematicmerrors.mIfminmthempre
cedingmtestmthemtemperaturesmofmthemtwomconstantmtemperaturemenvironmentsmweremknown,mt
hemabovemproceduremcouldmservemtomestablishmthemsystematicmerror,masmwellmasmrandommerrorm
ofmtheminstrument.mTomdomthis:mThemdifferencembetweenmthemaveragemofmthemreadingsmobtained
matmsomemknownmtemperaturemandmthemknownmtemperaturemwouldmprovidemanmestimatemofmth
emsystematicmerror.
