UncertaintyinHumidityMeasurement

Helping you make a better measurement.

BruceMcDuffee MichaelBoetzkes

WebinarPresenters

Agenda

• Terms&Definitions• UnderstandtheUncertaintyofYourInstrument• UnderstandingtheUncertaintyontheCalibrationCertificate• HowtoAvoidtheDreadedO.O.T.• FinalQ&A

Terms&Definitions

TheTruthAboutMeasurement

• Thereisnosuchthingasatrueorperfectmeasurement.• Apropermeasurementresultisincompletewithoutastatementofuncertainty.• Knowingtheuncertaintyhelpsusdeterminethefitnessofthemeasurement• Understandinguncertaintyisthefirststeptoreducingit.

Accuracy

“closenessofagreementbetweenameasuredquantityvalueandatruequantityvalueofameasurand”

• Measurand - quantityintendedtobemeasured

• MeasuredQuantityValue- quantityvaluerepresentingameasurementresult

• TrueQuantityValue- quantityvalueconsistentwiththedefinitionofaquantity

• QuantityValue- numberandreferencetogetherexpressingmagnitudeofaquantity,forexample5°C,543meters

Error

• Erroristhedifferencebetweenthemeasuredvalueandthe‘truevalue’ofthethingbeingmeasured.• Like‘accuracy’,itisqualitative,notquantitative

Uncertainty

• “Uncertaintyisthequantificationofthedoubtaboutthemeasurementresult.”• “Acalculatedstatementconcerningthelevelofconfidenceinareportedmeasurement.”

StatementofUncertainty:50%RH± 1%RHk=2

UnderstandingtheUncertaintyoftheHumidityInstrument

CalculatingtheInstrumentUncertainty

• InstrumentCalibration• Resolution• Longtermdrift• Temperatureeffects• Hysteresis• Linearity(accuracy)• Sensitivitytocontamination

CalculatingtheInstrumentUncertainty

𝑈 = 𝑘%𝑢12 + 𝑢22 + 𝑢32 + 𝑢42 + 𝑢52 …

LevelofConfidence CoverageFactor(k)68.27% 190% 1.64595% 1.96

95.45% 299% 2.576

99.73% 3

ImpactoftheInstrumentUncertainty

• Eachinstrumentisuniqueinbehavior• Environmentalfactorscanchangedriftcharacteristics• Understandtheimpactofcalibrations

Understandtotalinstrumentperformance!

Comments&Questions

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CalibrationCertificateUncertainty

DividedFlowSystemwithChilledMirrorTestPoint: 80%RHat23°C

4.96 %RH/°C

Reference UncertaintySource Value Units Distribution DivisorStandard

UncertaintySensitivityCoefficient

StandardUncertainty

(%RH)

%ofTotalExpandedUncertainty

1 ChilledMirrorUncertainty 0.05 °C Normal 2 0.025 4.96 0.124 18%2 ChilledMirrorDrift(1year) 0.04 °C Rectangular 1.732 0.023 4.96 0.115 16%3 TemperatureUncertainty 0.007 °C Normal 2 0.004 4.96 0.018 3%4 Repeatabilityofhumidity 0.10 %RH Normal 1 0.100 1 0.100 14%5 Chambertemperaturegradients 0.05 °C Rectangular 1.732 0.029 4.96 0.143 20%6 Temperaturestabilization 0.01 °C Rectangular 1.732 0.003 4.96 0.014 2%7 Temperaturerepeatability 0.05 °C Normal 1 0.050 4.96 0.248 35%8 Humiditystabilization 0.05 %RH Rectangular 1.732 0.029 1 0.029 4%9 Humidityfluctuations 0.05 %RH Rectangular 1.732 0.029 1 0.029 4%

0.3500.70

TemperatureSensitivity

ExpandedUncertainty(95%confidencelevel)StandardUncertainty

DividedFlowSystemwithInternalProbeTestPoint: 80%RHat23°C

TemperatureSensitivity 4.96%RH/°C

Reference UncertaintySource Value Units Distribution DivisorStandard

UncertaintySensitivityCoefficient

StandardUncertainty

(%RH)

%ofTotalExpandedUncertainty

1 ReferenceProbeUncertainty 1.10 %RH Normal 2 0.550 1 0.550 32%2 ReferenceProbeDrift 1.00 %RH Rectangular 1.732 0.577 1 0.577 34%3 ReferenceProbeResolution 0.05 %RH Rectangular 3.464 0.014 1 0.014 1%4 Repeatabilityofhumidity 0.10 %RH Normal 1 0.100 1 0.100 6%5 Chambertemperaturegradients 0.05 °C Rectangular 1.732 0.029 4.96 0.143 8%6 Temperaturestabilization 0.01 °C Rectangular 1.732 0.003 4.96 0.014 1%7 Temperaturerepeatability 0.05 °C Normal 1 0.050 4.96 0.248 15%8 Humiditystabilization 0.05 %RH Rectangular 1.732 0.029 1 0.029 2%9 Humidityfluctuations 0.05 %RH Rectangular 1.732 0.029 1 0.029 2%

StandardUncertainty 0.854ExpandedUncertainty(95%confidencelevel) 1.71

WhyisUncertaintyImportant

• RequiredforMetrologicalTraceability• Insightintothequalityofthecalibration• Makesthedifferencebetweeninstrumentmeetingmanufacturerspecificationornot!

DividedFlowwithChilledMirror

Parameter U Distribution DivisorStandard

Uncertainty CommentAccuracy 0.8 Rectangular 1.732 0.462 FromDataSheet

CalibrationUncertainty 0.7 Normal 2 0.350FromCalibrationCertificate

AnnualDrift 1 Rectangular 1.732 0.577 FromDataSheetCombinedUncertainty 0.818

ExpandedUncertaintyk=2 ±1.7%RH

DividedFlowwithInternalProbe

Parameter U Distribution DivisorStandard

Uncertainty CommentAccuracy 0.8 Rectangular 1.732 0.462 FromDataSheet

CalibrationUncertainty 1.71 Normal 2 0.855FromCalibrationCertificate

AnnualDrift 1 Rectangular 1.732 0.577 FromDataSheetCombinedUncertainty 1.130

ExpandedUncertaintyk=2 ±2.3%RH

TakingUncertaintyintoAccount

• UncertaintyofmeasurementleadstoriskofFalseAccept• Guardband methodsavailabletodefineandlimittherisk• Creates3rd optionforresult:Indeterminate

HowtoAvoidtheDreadedOOT

CausesofOOT

• Instrument/SensorDrift• Accuracyspecificationusedinsteadof1-yearuncertainty• Previouscalibrationwasnotsuitable

Typicallycanbetracedbacktoanerrorinorlackofuncertaintyanalysis!

AvoidingOOT

• Knowthesensitivitiesoftheinstrument• UsetheLongTermUncertaintyastheacceptancelimit• Ensureappropriatecalibrationprovidercanprovidesuitablecalibrationuncertainties

Takeaways

1. Instrumentperformanceismorethanjustanaccuracyspecification2. Twoinstrumentsofthesamemodelcanhavedifferentmeasurement

uncertainties3. OOTresultscanbereducedbyunderstandingtheinstrument

uncertainty

Comments&Questions

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MeasurementAcademy

• Resourcesformakingabettermeasurement• Psychrometric charts• Technicalnotes• Humiditycalculator• Applicationnotes• More

www.rotronic-usa.com/academy

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