SOLUTIONbMANUAL
, PROBLEM 1.1 b
FIND: Explain the hierarchy of standards. Explain the term standard. Cite example.
b b b b b b b b b b b
SOLUTION
Thebtermbstandardbrefersbtobanbobjectborbinstrument,babmethodborbabprocedurebthatbprovidesbabval
uebofbanbacceptablebaccuracybforbcomparison.
Abprimarybstandardbdefinesbthebvaluebofbthebunitbtobwhichbitbisbassociated.b Secondarybstandard
s,bwhilebbasedbonbthebprimarybstandard,barebmorebreadilybaccessiblebandbamenableb forbusebinbab
calibration.bTherebisbabhierarchybofbsecondarybstandards:bAbtransferbstandardbmightbbebmaintai
nedbbybabnationalbstandardsblabb(suchbasbNISTbinbthebUnitedbStates)btobcalibratebindustrialb“labo
ratorybstandards”.bItbisbcostlybandbtime-
consumingbtobcertifybablaboratorybstandard,bsobtheybarebtreatedbcarefullybandbnotbusedbtoobregul
arly.bAblaboratorybstandardbwouldbbebmaintainedbbybabcompanybtobbebusedbtobcertifybabmorebco
mmonbin-
housebreferencebcalledbthebworkingbstandard.bAbworkingbstandardbwouldbbebcalibratedbagainstb
theblaboratorybstandard.bThebworkingbstandardbisbusedbonbabmorebregularbbasisbtobcalibratebever
ydaybmeasurementbdevicesborbproductsbbeingbmanufactured.bWorkingbstandardsbarebmorebthebn
ormbforbmostbofbus.bAbworkingbstandardbisbsimplybthebvalueborbinstrumentbthatbwebassumebisbcor
rectbinbcheckingbtheboutputboperationbofbanotherbinstrument.
Example:bAbgovernmentblabbmaintainsbthebprimarybstandardbforbpressure.bItbcalibratesbabanbin
strumentbcalledbab“deadweightbtester”b(seebC9bdiscussion)bforbhighbpressurebcalibrations.bThe
sebformbitsbtransferbstandardbforbhighbpressure.bAbcompanybthatbmakesbpressurebtransducersbn
eedsbanbin-
housebstandardbtobcertifybtheirbproducts.bTheybpurchasebtwobdeadweightbtesters.bTheybsendbo
nebtesterbtobthebnationalblabbtobbebcalibrated;bthisbbecomesbtheirblaboratorybstandard.bOnbretur
n,btheybusebitbtobcalibratebthebother;bthisbbecomesbtheirbworkingbstandard.bTheybtestbtheirbman
ufacturedbtransducersbusingbthebworkingbstandardb–
busuallybatboneborbtwobpointsboverbthebtransducerbrangebtobassurebthatbitbisbworking. bBecausebth
ebworkingbstandardbisbbeingbusedbregularly,bitbcanbgoboutbofbcalibration.b Periodically,btheybche
ckbthebworkingbstandardbcalibrationbagainstbtheblaboratorybstandard.
SeebASMEbPTCb19.2bPressurebMeasurementsbforbabfurtherbdiscussion.bA
testbstandardbdefinesbabspecificbprocedurebthatbisbtobbebfollowed.
b
, PROBLEM 1.2 b
FIND: Why calibrate? What does calibrated mean?
b b b b b b
SOLUTION:
Thebpurposebofbabcalibrationbisbtobevaluatebandbdocumentbthebaccuracybofbabmeasuringbdevice.b
Abcalibrationbshouldbbebperformedbwheneverbthebaccuracyblevelbofbabmeasuredbvaluebmustbbeba
scertained.
Anbinstrumentbthatbhasbbeenbcalibratedbprovidesbthebengineerbabbasisbforbinterpretingbthebdevice
’sboutputbindication.bItbprovidesbassurancebinbthebmeasurement.bBesidesbthisbpurpose,babcalibrati
onbassuresbthebengineerbthatbthebdevicebisbworkingbasbexpected.
Abperiodicbcalibrationbofbmeasuringbinstrumentsbservesbasbabperformancebcheckbonbthosebinstru
mentsbandbprovidesbablevelbofbconfidencebinbtheirbindicatedbvalues.bAbgoodbrulebisbtobcalibratebm
easuringbsystemsbannuallyborbmoreboftenbasbneeded.
ISOb9000bcertificationsbhavebstrictbrulesbonbcalibrationbresultsbandbthebfrequencybofbcalibration
.
, PROBLEM 1.3 b
FIND: Suggest methods to estimate the accuracy and random and systematic errors of a dial
b b b b b b b b b b b b b b b
thermometer.
SOLUTION:
Randomberrorbisbrelatedbtobrepeatability:bhowbcloselybanbinstrumentbindicatesbthebsamebvalue.bS
obabmethodbthatbrepeatedlybexposesbthebinstrumentbtoboneborbmorebknownbtemperaturesbcouldbb
ebdevelopedbtobestimatebthebrandomberror.bThisbisbusuallybstatedbasbabstatisticalbestimatebofbtheb
variationbofbthebreadings.bAnbimportantbaspectbofbsuchbabtestbisbtobincludebsomebmechanismbtob
allowbthebinstrumentbtobchangebitsbindicatedbvaluebfollowingbeachbreadingbsobthatbitbmustbreadj
ustbitself.
Forbexample,bwebcouldbplacebthebinstrumentbinbanbenvironmentbofbconstantbtemperaturebandbnot
ebitsbindicatedbvaluebandbthenbmovebthebinstrumentbtobanotherbconstantbtemperaturebenvironmen
tbandbnotebitsbvaluebthere.bThebtwobchosenbtemperaturesbcouldbbebrepresentativebofbthebrangebofbi
ntendedbusebofbthebinstrument.bBybalternatingbbetweenbthebtwobconstantbtemperaturebenvironme
nts,bdifferencesbinbindicatedbvaluesbwithinbeachbenvironmentbwouldbbebindicativebofbthebprecisi
onberrorbtobbebexpectedbofbthebinstrumentbatbthatbtemperature.bOfbcourse,bthisbassumesbthatbthebc
onstantbtemperaturesbdobindeedbremainbconstantbthroughoutbthebtestbandbthebinstrumentbisbusedbi
nbanbidenticalbmannerbforbeachbmeasurement.
Systematicberrorbisbabfixedboffset.bInbthebabsencebofbrandomberror,bthisbwouldbbebhowbcloselybth
ebinstrumentbindicatesbthebcorrectbvalue.bThisboffsetbwouldbbebpresentbinbeverybreading.bSobanbi
mportantbaspectbofbthisbcheckbisbtobcalibratebitbagainstbabvaluebthatbisbatbleastbasbaccuratebasbyoubn
eed.bThisbisbnotbtrivial.
Forbexample,byoubcouldbusebthebicebpointb(0oC)basbabcheckbforbsystematicberror.bThebicebpointbis
bformedbfrombabcarefullybpreparedbbathbofbsolidbicebandbliquidbwater.bAsbanotherbcheck,bthebme
ltingbpointbofbabpurebsubstance,bsuchbasbsilver,bcouldbbebused.bOrbeasier,bthebsteambpoint.
Accuracybrequiresbabcalibrationbtobassessbbothbrandombandbsystematicberrors.bIfbinbthebprecedin
gbtestbthebtemperaturesbofbthebtwobconstantbtemperaturebenvironmentsbwerebknown,bthebaboveb
procedurebcouldbservebtobestablishbthebsystematicberror,basbwellbasbrandomberrorbofbthebinstrume
nt.bTobdobthis:bThebdifferencebbetweenbthebaveragebofbthebreadingsbobtainedbatbsomebknownbte
mperaturebandbthebknownbtemperaturebwouldbprovidebanbestimatebofbthebsystematicberror.
, PROBLEM 1.1 b
FIND: Explain the hierarchy of standards. Explain the term standard. Cite example.
b b b b b b b b b b b
SOLUTION
Thebtermbstandardbrefersbtobanbobjectborbinstrument,babmethodborbabprocedurebthatbprovidesbabval
uebofbanbacceptablebaccuracybforbcomparison.
Abprimarybstandardbdefinesbthebvaluebofbthebunitbtobwhichbitbisbassociated.b Secondarybstandard
s,bwhilebbasedbonbthebprimarybstandard,barebmorebreadilybaccessiblebandbamenableb forbusebinbab
calibration.bTherebisbabhierarchybofbsecondarybstandards:bAbtransferbstandardbmightbbebmaintai
nedbbybabnationalbstandardsblabb(suchbasbNISTbinbthebUnitedbStates)btobcalibratebindustrialb“labo
ratorybstandards”.bItbisbcostlybandbtime-
consumingbtobcertifybablaboratorybstandard,bsobtheybarebtreatedbcarefullybandbnotbusedbtoobregul
arly.bAblaboratorybstandardbwouldbbebmaintainedbbybabcompanybtobbebusedbtobcertifybabmorebco
mmonbin-
housebreferencebcalledbthebworkingbstandard.bAbworkingbstandardbwouldbbebcalibratedbagainstb
theblaboratorybstandard.bThebworkingbstandardbisbusedbonbabmorebregularbbasisbtobcalibratebever
ydaybmeasurementbdevicesborbproductsbbeingbmanufactured.bWorkingbstandardsbarebmorebthebn
ormbforbmostbofbus.bAbworkingbstandardbisbsimplybthebvalueborbinstrumentbthatbwebassumebisbcor
rectbinbcheckingbtheboutputboperationbofbanotherbinstrument.
Example:bAbgovernmentblabbmaintainsbthebprimarybstandardbforbpressure.bItbcalibratesbabanbin
strumentbcalledbab“deadweightbtester”b(seebC9bdiscussion)bforbhighbpressurebcalibrations.bThe
sebformbitsbtransferbstandardbforbhighbpressure.bAbcompanybthatbmakesbpressurebtransducersbn
eedsbanbin-
housebstandardbtobcertifybtheirbproducts.bTheybpurchasebtwobdeadweightbtesters.bTheybsendbo
nebtesterbtobthebnationalblabbtobbebcalibrated;bthisbbecomesbtheirblaboratorybstandard.bOnbretur
n,btheybusebitbtobcalibratebthebother;bthisbbecomesbtheirbworkingbstandard.bTheybtestbtheirbman
ufacturedbtransducersbusingbthebworkingbstandardb–
busuallybatboneborbtwobpointsboverbthebtransducerbrangebtobassurebthatbitbisbworking. bBecausebth
ebworkingbstandardbisbbeingbusedbregularly,bitbcanbgoboutbofbcalibration.b Periodically,btheybche
ckbthebworkingbstandardbcalibrationbagainstbtheblaboratorybstandard.
SeebASMEbPTCb19.2bPressurebMeasurementsbforbabfurtherbdiscussion.bA
testbstandardbdefinesbabspecificbprocedurebthatbisbtobbebfollowed.
b
, PROBLEM 1.2 b
FIND: Why calibrate? What does calibrated mean?
b b b b b b
SOLUTION:
Thebpurposebofbabcalibrationbisbtobevaluatebandbdocumentbthebaccuracybofbabmeasuringbdevice.b
Abcalibrationbshouldbbebperformedbwheneverbthebaccuracyblevelbofbabmeasuredbvaluebmustbbeba
scertained.
Anbinstrumentbthatbhasbbeenbcalibratedbprovidesbthebengineerbabbasisbforbinterpretingbthebdevice
’sboutputbindication.bItbprovidesbassurancebinbthebmeasurement.bBesidesbthisbpurpose,babcalibrati
onbassuresbthebengineerbthatbthebdevicebisbworkingbasbexpected.
Abperiodicbcalibrationbofbmeasuringbinstrumentsbservesbasbabperformancebcheckbonbthosebinstru
mentsbandbprovidesbablevelbofbconfidencebinbtheirbindicatedbvalues.bAbgoodbrulebisbtobcalibratebm
easuringbsystemsbannuallyborbmoreboftenbasbneeded.
ISOb9000bcertificationsbhavebstrictbrulesbonbcalibrationbresultsbandbthebfrequencybofbcalibration
.
, PROBLEM 1.3 b
FIND: Suggest methods to estimate the accuracy and random and systematic errors of a dial
b b b b b b b b b b b b b b b
thermometer.
SOLUTION:
Randomberrorbisbrelatedbtobrepeatability:bhowbcloselybanbinstrumentbindicatesbthebsamebvalue.bS
obabmethodbthatbrepeatedlybexposesbthebinstrumentbtoboneborbmorebknownbtemperaturesbcouldbb
ebdevelopedbtobestimatebthebrandomberror.bThisbisbusuallybstatedbasbabstatisticalbestimatebofbtheb
variationbofbthebreadings.bAnbimportantbaspectbofbsuchbabtestbisbtobincludebsomebmechanismbtob
allowbthebinstrumentbtobchangebitsbindicatedbvaluebfollowingbeachbreadingbsobthatbitbmustbreadj
ustbitself.
Forbexample,bwebcouldbplacebthebinstrumentbinbanbenvironmentbofbconstantbtemperaturebandbnot
ebitsbindicatedbvaluebandbthenbmovebthebinstrumentbtobanotherbconstantbtemperaturebenvironmen
tbandbnotebitsbvaluebthere.bThebtwobchosenbtemperaturesbcouldbbebrepresentativebofbthebrangebofbi
ntendedbusebofbthebinstrument.bBybalternatingbbetweenbthebtwobconstantbtemperaturebenvironme
nts,bdifferencesbinbindicatedbvaluesbwithinbeachbenvironmentbwouldbbebindicativebofbthebprecisi
onberrorbtobbebexpectedbofbthebinstrumentbatbthatbtemperature.bOfbcourse,bthisbassumesbthatbthebc
onstantbtemperaturesbdobindeedbremainbconstantbthroughoutbthebtestbandbthebinstrumentbisbusedbi
nbanbidenticalbmannerbforbeachbmeasurement.
Systematicberrorbisbabfixedboffset.bInbthebabsencebofbrandomberror,bthisbwouldbbebhowbcloselybth
ebinstrumentbindicatesbthebcorrectbvalue.bThisboffsetbwouldbbebpresentbinbeverybreading.bSobanbi
mportantbaspectbofbthisbcheckbisbtobcalibratebitbagainstbabvaluebthatbisbatbleastbasbaccuratebasbyoubn
eed.bThisbisbnotbtrivial.
Forbexample,byoubcouldbusebthebicebpointb(0oC)basbabcheckbforbsystematicberror.bThebicebpointbis
bformedbfrombabcarefullybpreparedbbathbofbsolidbicebandbliquidbwater.bAsbanotherbcheck,bthebme
ltingbpointbofbabpurebsubstance,bsuchbasbsilver,bcouldbbebused.bOrbeasier,bthebsteambpoint.
Accuracybrequiresbabcalibrationbtobassessbbothbrandombandbsystematicberrors.bIfbinbthebprecedin
gbtestbthebtemperaturesbofbthebtwobconstantbtemperaturebenvironmentsbwerebknown,bthebaboveb
procedurebcouldbservebtobestablishbthebsystematicberror,basbwellbasbrandomberrorbofbthebinstrume
nt.bTobdobthis:bThebdifferencebbetweenbthebaveragebofbthebreadingsbobtainedbatbsomebknownbte
mperaturebandbthebknownbtemperaturebwouldbprovidebanbestimatebofbthebsystematicberror.
