SOLUTIONhMANUAL
, PROBLEM 1.1 h
FIND: Explain the hierarchy of standards. Explain the term standard. Cite example.
h h h h h h h h h h h
SOLUTION
Thehtermhstandardhrefershtohanhobjecthorhinstrument,hahmethodhorhahprocedurehthathprovideshahval
uehofhanhacceptablehaccuracyhforhcomparison.
Ahprimaryhstandardhdefineshthehvaluehofhthehunithtohwhichhithishassociated.h Secondaryhstandard
s,hwhilehbasedhonhthehprimaryhstandard,harehmorehreadilyhaccessiblehandhamenableh forhusehinhah
calibration.hTherehishahhierarchyhofhsecondaryhstandards:hAhtransferhstandardhmighthbehmaintai
nedhbyhahnationalhstandardshlabh(suchhashNISThinhthehUnitedhStates)htohcalibratehindustrialh“labo
ratoryhstandards”.hIthishcostlyhandhtime-
consuminghtohcertifyhahlaboratoryhstandard,hsohtheyharehtreatedhcarefullyhandhnothusedhtoohregul
arly.hAhlaboratoryhstandardhwouldhbehmaintainedhbyhahcompanyhtohbehusedhtohcertifyhahmorehco
mmonhin-
househreferencehcalledhthehworkinghstandard.hAhworkinghstandardhwouldhbehcalibratedhagainsth
thehlaboratoryhstandard.hThehworkinghstandardhishusedhonhahmorehregularhbasishtohcalibratehever
ydayhmeasurementhdeviceshorhproductshbeinghmanufactured.hWorkinghstandardsharehmorehthehn
ormhforhmosthofhus.hAhworkinghstandardhishsimplyhthehvaluehorhinstrumenththathwehassumehishcor
recthinhcheckinghthehoutputhoperationhofhanotherhinstrument.
Example:hAhgovernmenthlabhmaintainshthehprimaryhstandardhforhpressure.hIthcalibrateshahanhinst
rumenthcalledhah“deadweighthtester”h(seehC9hdiscussion)hforhhighhpressurehcalibrations.hTheseh
formhitshtransferhstandardhforhhighhpressure.hAhcompanyhthathmakeshpressurehtransducershneeds
hanhin-
househstandardhtohcertifyhtheirhproducts.hTheyhpurchasehtwohdeadweighthtesters.hTheyhsendhone
htesterhtohthehnationalhlabhtohbehcalibrated;hthishbecomeshtheirhlaboratoryhstandard.hOnhreturn,hth
eyhusehithtohcalibratehthehother;hthishbecomeshtheirhworkinghstandard.hTheyhtesththeirhmanufactu
redhtransducershusinghthehworkinghstandardh–
husuallyhathonehorhtwohpointshoverhthehtransducerhrangehtohassurehthathithishworking.hBecausehthe
hworkinghstandardhishbeinghusedhregularly,hithcanhgohouthofhcalibration.h Periodically,htheyh check
hthehworkinghstandardhcalibrationhagainsththehlaboratoryhstandard.
SeehASMEhPTCh19.2hPressurehMeasurementshforhahfurtherhdiscussion.hA
h testhstandardhdefineshahspecifichprocedurehthathishtohbehfollowed.
, PROBLEM 1.2 h
FIND: Why calibrate? What does calibrated mean?
h h h h h h
SOLUTION:
Thehpurposehofhahcalibrationhishtohevaluatehandhdocumenththehaccuracyhofhahmeasuringhdevice.h
Ahcalibrationhshouldhbehperformedhwheneverhthehaccuracyhlevelhofhahmeasuredhvaluehmusthbeha
scertained.
Anhinstrumenththathhashbeenhcalibratedhprovideshthehengineerhahbasishforhinterpretinghthehdevice
’shoutputhindication.hIthprovideshassurancehinhthehmeasurement.hBesideshthishpurpose,hahcalibrati
onhassureshthehengineerhthaththehdevicehishworkinghashexpected.
Ahperiodichcalibrationhofhmeasuringhinstrumentshserveshashahperformancehcheckhonhthosehinstru
mentshandhprovideshahlevelhofhconfidencehinhtheirhindicatedhvalues.hAhgoodhrulehishtohcalibratehm
easuringhsystemshannuallyhorhmorehoftenhashneeded.
ISOh9000hcertificationshhavehstricthruleshonhcalibrationhresultshandhthehfrequencyhofhcalibration
.
, PROBLEM 1.3 h
FIND: Suggest methods to estimate the accuracy and random and systematic errors of a dial
h h h h h h h h h h h h h h h
thermometer.
SOLUTION:
Randomherrorhishrelatedhtohrepeatability:hhowhcloselyhanhinstrumenthindicateshthehsamehvalue.hS
ohahmethodhthathrepeatedlyhexposeshthehinstrumenthtohonehorhmorehknownhtemperatureshcouldhb
ehdevelopedhtohestimatehthehrandomherror.hThishishusuallyhstatedhashahstatisticalhestimatehofhtheh
variationhofhthehreadings.hAnhimportanthaspecthofhsuchhahtesthishtohincludehsomehmechanismhtoh
allowhthehinstrumenthtohchangehitshindicatedhvaluehfollowingheachhreadinghsohthathithmusthreadj
usthitself.
Forhexample,hwehcouldhplacehthehinstrumenthinhanhenvironmenthofhconstanthtemperaturehandhnot
ehitshindicatedhvaluehandhthenhmovehthehinstrumenthtohanotherhconstanthtemperaturehenvironmen
thandhnotehitshvaluehthere.hThehtwohchosenhtemperatureshcouldhbehrepresentativehofhthehrangehofhi
ntendedhusehofhthehinstrument.hByhalternatinghbetweenhthehtwohconstanthtemperaturehenvironme
nts,hdifferenceshinhindicatedhvalueshwithinheachhenvironmenthwouldhbehindicativehofhthehprecisi
onherrorhtohbehexpectedhofhthehinstrumenthaththathtemperature.hOfhcourse,hthishassumeshthaththehc
onstanthtemperatureshdohindeedhremainhconstanththroughouththehtesthandhthehinstrumenthishusedhi
nhanhidenticalhmannerhforheachhmeasurement.
Systematicherrorhishahfixedhoffset.hInhthehabsencehofhrandomherror,hthishwouldhbehhowhcloselyhth
ehinstrumenthindicateshthehcorrecthvalue.hThishoffsethwouldhbehpresenthinheveryhreading.hSohanhi
mportanthaspecthofhthishcheckhishtohcalibratehithagainsthahvaluehthathishathleasthashaccuratehashyouhn
eed.hThishishnothtrivial.
Forhexample,hyouhcouldhusehthehicehpointh(0oC)hashahcheckhforhsystematicherror.hThehicehpointhis
hformedhfromhahcarefullyhpreparedhbathhofhsolidhicehandhliquidhwater.hAshanotherhcheck,hthehme
ltinghpointhofhahpurehsubstance,hsuchhashsilver,hcouldhbehused.hOrheasier,hthehsteamhpoint.
Accuracyhrequireshahcalibrationhtohassesshbothhrandomhandhsystematicherrors.hIfhinhthehprecedin
ghtesththehtemperatureshofhthehtwohconstanthtemperaturehenvironmentshwerehknown,hthehaboveh
procedurehcouldhservehtohestablishhthehsystematicherror,hashwellhashrandomherrorhofhthehinstrume
nt.hTohdohthis:hThehdifferencehbetweenhthehaveragehofhthehreadingshobtainedhathsomehknownhte
mperaturehandhthehknownhtemperaturehwouldhprovidehanhestimatehofhthehsystematicherror.
, PROBLEM 1.1 h
FIND: Explain the hierarchy of standards. Explain the term standard. Cite example.
h h h h h h h h h h h
SOLUTION
Thehtermhstandardhrefershtohanhobjecthorhinstrument,hahmethodhorhahprocedurehthathprovideshahval
uehofhanhacceptablehaccuracyhforhcomparison.
Ahprimaryhstandardhdefineshthehvaluehofhthehunithtohwhichhithishassociated.h Secondaryhstandard
s,hwhilehbasedhonhthehprimaryhstandard,harehmorehreadilyhaccessiblehandhamenableh forhusehinhah
calibration.hTherehishahhierarchyhofhsecondaryhstandards:hAhtransferhstandardhmighthbehmaintai
nedhbyhahnationalhstandardshlabh(suchhashNISThinhthehUnitedhStates)htohcalibratehindustrialh“labo
ratoryhstandards”.hIthishcostlyhandhtime-
consuminghtohcertifyhahlaboratoryhstandard,hsohtheyharehtreatedhcarefullyhandhnothusedhtoohregul
arly.hAhlaboratoryhstandardhwouldhbehmaintainedhbyhahcompanyhtohbehusedhtohcertifyhahmorehco
mmonhin-
househreferencehcalledhthehworkinghstandard.hAhworkinghstandardhwouldhbehcalibratedhagainsth
thehlaboratoryhstandard.hThehworkinghstandardhishusedhonhahmorehregularhbasishtohcalibratehever
ydayhmeasurementhdeviceshorhproductshbeinghmanufactured.hWorkinghstandardsharehmorehthehn
ormhforhmosthofhus.hAhworkinghstandardhishsimplyhthehvaluehorhinstrumenththathwehassumehishcor
recthinhcheckinghthehoutputhoperationhofhanotherhinstrument.
Example:hAhgovernmenthlabhmaintainshthehprimaryhstandardhforhpressure.hIthcalibrateshahanhinst
rumenthcalledhah“deadweighthtester”h(seehC9hdiscussion)hforhhighhpressurehcalibrations.hTheseh
formhitshtransferhstandardhforhhighhpressure.hAhcompanyhthathmakeshpressurehtransducershneeds
hanhin-
househstandardhtohcertifyhtheirhproducts.hTheyhpurchasehtwohdeadweighthtesters.hTheyhsendhone
htesterhtohthehnationalhlabhtohbehcalibrated;hthishbecomeshtheirhlaboratoryhstandard.hOnhreturn,hth
eyhusehithtohcalibratehthehother;hthishbecomeshtheirhworkinghstandard.hTheyhtesththeirhmanufactu
redhtransducershusinghthehworkinghstandardh–
husuallyhathonehorhtwohpointshoverhthehtransducerhrangehtohassurehthathithishworking.hBecausehthe
hworkinghstandardhishbeinghusedhregularly,hithcanhgohouthofhcalibration.h Periodically,htheyh check
hthehworkinghstandardhcalibrationhagainsththehlaboratoryhstandard.
SeehASMEhPTCh19.2hPressurehMeasurementshforhahfurtherhdiscussion.hA
h testhstandardhdefineshahspecifichprocedurehthathishtohbehfollowed.
, PROBLEM 1.2 h
FIND: Why calibrate? What does calibrated mean?
h h h h h h
SOLUTION:
Thehpurposehofhahcalibrationhishtohevaluatehandhdocumenththehaccuracyhofhahmeasuringhdevice.h
Ahcalibrationhshouldhbehperformedhwheneverhthehaccuracyhlevelhofhahmeasuredhvaluehmusthbeha
scertained.
Anhinstrumenththathhashbeenhcalibratedhprovideshthehengineerhahbasishforhinterpretinghthehdevice
’shoutputhindication.hIthprovideshassurancehinhthehmeasurement.hBesideshthishpurpose,hahcalibrati
onhassureshthehengineerhthaththehdevicehishworkinghashexpected.
Ahperiodichcalibrationhofhmeasuringhinstrumentshserveshashahperformancehcheckhonhthosehinstru
mentshandhprovideshahlevelhofhconfidencehinhtheirhindicatedhvalues.hAhgoodhrulehishtohcalibratehm
easuringhsystemshannuallyhorhmorehoftenhashneeded.
ISOh9000hcertificationshhavehstricthruleshonhcalibrationhresultshandhthehfrequencyhofhcalibration
.
, PROBLEM 1.3 h
FIND: Suggest methods to estimate the accuracy and random and systematic errors of a dial
h h h h h h h h h h h h h h h
thermometer.
SOLUTION:
Randomherrorhishrelatedhtohrepeatability:hhowhcloselyhanhinstrumenthindicateshthehsamehvalue.hS
ohahmethodhthathrepeatedlyhexposeshthehinstrumenthtohonehorhmorehknownhtemperatureshcouldhb
ehdevelopedhtohestimatehthehrandomherror.hThishishusuallyhstatedhashahstatisticalhestimatehofhtheh
variationhofhthehreadings.hAnhimportanthaspecthofhsuchhahtesthishtohincludehsomehmechanismhtoh
allowhthehinstrumenthtohchangehitshindicatedhvaluehfollowingheachhreadinghsohthathithmusthreadj
usthitself.
Forhexample,hwehcouldhplacehthehinstrumenthinhanhenvironmenthofhconstanthtemperaturehandhnot
ehitshindicatedhvaluehandhthenhmovehthehinstrumenthtohanotherhconstanthtemperaturehenvironmen
thandhnotehitshvaluehthere.hThehtwohchosenhtemperatureshcouldhbehrepresentativehofhthehrangehofhi
ntendedhusehofhthehinstrument.hByhalternatinghbetweenhthehtwohconstanthtemperaturehenvironme
nts,hdifferenceshinhindicatedhvalueshwithinheachhenvironmenthwouldhbehindicativehofhthehprecisi
onherrorhtohbehexpectedhofhthehinstrumenthaththathtemperature.hOfhcourse,hthishassumeshthaththehc
onstanthtemperatureshdohindeedhremainhconstanththroughouththehtesthandhthehinstrumenthishusedhi
nhanhidenticalhmannerhforheachhmeasurement.
Systematicherrorhishahfixedhoffset.hInhthehabsencehofhrandomherror,hthishwouldhbehhowhcloselyhth
ehinstrumenthindicateshthehcorrecthvalue.hThishoffsethwouldhbehpresenthinheveryhreading.hSohanhi
mportanthaspecthofhthishcheckhishtohcalibratehithagainsthahvaluehthathishathleasthashaccuratehashyouhn
eed.hThishishnothtrivial.
Forhexample,hyouhcouldhusehthehicehpointh(0oC)hashahcheckhforhsystematicherror.hThehicehpointhis
hformedhfromhahcarefullyhpreparedhbathhofhsolidhicehandhliquidhwater.hAshanotherhcheck,hthehme
ltinghpointhofhahpurehsubstance,hsuchhashsilver,hcouldhbehused.hOrheasier,hthehsteamhpoint.
Accuracyhrequireshahcalibrationhtohassesshbothhrandomhandhsystematicherrors.hIfhinhthehprecedin
ghtesththehtemperatureshofhthehtwohconstanthtemperaturehenvironmentshwerehknown,hthehaboveh
procedurehcouldhservehtohestablishhthehsystematicherror,hashwellhashrandomherrorhofhthehinstrume
nt.hTohdohthis:hThehdifferencehbetweenhthehaveragehofhthehreadingshobtainedhathsomehknownhte
mperaturehandhthehknownhtemperaturehwouldhprovidehanhestimatehofhthehsystematicherror.
