03 Calibration & Uncertainty of measurement -RRM July 2023.pdf

Uncertainty evaluation

1. 18 July 2023 DR. R RAJAMANI, PSG CT, COIMBATORE 1
Calibration of Measuring Instruments
Dr. RAJAMANI R
Department of Production Engineering
PSG College of Technology,
Coimbatore -641004

2. 18 July 2023 DR. R RAJAMANI, PSG CT, COIMBATORE 2
Calibration
AccordingtotheInternationalOrganizationforStandardizationpublicationentitled
InternationalVocabularyofBasicandGeneralTermsinMetrology(VIM,1993)
Calibrationisthesetofoperationsthatestablish,underspecifiedconditions,
therelationshipbetweenvaluesindicatedbyameasuringinstrument,ameasuring
systemorvaluesrepresentedbyamaterialmeasure,andthecorrespondingknown
valuesofameasurand.

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4. 18 July 2023 DR. R RAJAMANI, PSG CT, COIMBATORE 4
Calibrationisessentiallythecomparison,underspecifiedconditions,witha
higherstandard,whichistraceabletoanationalorinternationalstandard,oran
acceptablealternative.
Calibration
Calibration fulfils two objectives:
It determines accuracy of the measured data.
It provides traceability to the measurement.

5. 18 July 2023 DR. R RAJAMANI, PSG CT, COIMBATORE 5
Calibration
A higher standard means:
• A higher accuracy/uncertainty
• A better resolution
TestAccuracyRatio(TAR)shouldbeaslargeaseconomicallyviablesincethe
higherthisratio,thelesseristhemeasurementdecisionrisk.Also,calledTest
UncertaintyRatio.
In accordance with ISO 10012:2003, the test accuracy ratio should be 3:1

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Benefits of calibration
The accuracy of the measurement is maintained.
The accuracy of the measuring instrument is controlled.
Quality is maintained in the measurement process.
Satisfied customers.
Scrap reduces drastically.
Reliable products are produced.

7. Elements of calibration system
Measuring instruments and gauges to be calibrated.
Standards used for calibration.
Traceability.
Work instruction to carry out the calibration process.
Environmental condition of the calibration laboratory.
Operator skill.
Records/History cards.
Actions based on calibration.
718 July 2023 DR. R RAJAMANI, PSG CT, COIMBATORE

8. List of Indian Standard Specifications on
Dimensional Metrology
18 July 2023 DR. R RAJAMANI, PSG CT, COIMBATORE 8
IS:2966-1964 InternalMicrometers
IS:2967-1983 ExternalMicrometer
IS:3651(Part1)-1982VernierCaliperswithleastcount0.1mmand0.05mm
IS:3651(Part2)-1985VernierCaliperswithleastcount0.02mm
IS:2092-1983 PlungerTypeDialGauges
IS:11498-1985 LeverTypeDialGauges
IS:2984-2003 SlipGauges
Ref : https://bis.gov.in

9. Measure thrice, cut once
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Measurement Errors

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A Measure of Confidence Level…..
Uncertainty of measurement

12. Uncertainty of measurement
Theuncertainty(ofmeasurement),parameter,associatedwiththeresultofameasurement,that
characterizesthedispersionofthevaluesthatcouldreasonablybeattributedtothemeasurand.
Uncertaintyofmeasurementisthedoubtthatexistsabouttheresultofanymeasurement.
Insimplewords,uncertaintyofmeasurementisnothingbuthowfaronecanrelythegiven
measurement.
e.g.:30±.01mm,atalevelofconfidenceof95%.
Ref:Evaluationofmeasurementdata—Guidetotheexpressionofuncertaintyinmeasurement-JCGM
100:2008
1218 July 2023 Dr. R Rajamani, PSG CT, Coimbatore

13. Error versus Uncertainty
Erroris the difference between the measured value and the ‘true value’ of the thing
being measured.
Whenever possible we try to correct for any known errors
Uncertaintyis a quantification of the doubt about the measurement result.
But any error whose value we do not know is a source of uncertainty.
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14. 18 July 2023 DR. R RAJAMANI, PSG CT, COIMBATORE 14
Evaluation of uncertainties
TypeA:“Componentofuncertaintyarisingfromarandomeffect”.
TypeAuncertaintyevaluatedbystatisticalmethods.
Estimatedformtherepeatedobservations.
Eachcomponentofuncertainty,isrepresentedbyanestimatedstandarddeviations
i,termed
standarduncertaintyu
i,andequaltothepositivesquarerootoftheestimatedvariances
i
2
.

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Evaluation of uncertainties
Type B : “Component of uncertainty arising from a systematic effect,”
Uncertainties are evaluated by non-statistical methods
Evaluated by scientific judgement based on all of the available information from
previous measurement data;
experience with or general knowledge of the behaviour and properties of relevant
materials and instruments;
manufacturer's specifications;
data provided in calibration and other certificates;
uncertainties assigned to reference data taken from handbooks.

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Broadlyspeaking,typeBuncertaintyiseitherobtainedfromanoutsidesource,orobtained
fromanassumeddistribution.
Evaluation of uncertainties

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Ref:AnIntroductiontoUncertaintyinMeasurement:UsingtheGUM
ByL.Kirkup,R.B.Frenkel

18. Rectangular Distribution
18 July 2023 DR. R RAJAMANI, PSG CT, COIMBATORE 18
A probability function f.(X) defined as follows
The stated value may lie between the limits of uncertainty with equal probability
Rectangulardistribution–measurementresulthasanequalprobabilityofbeinganywherewithintherange
of–atoa.3
i
i
a
u

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Variance of Rectangular Function
Mean of the Rectangular Function
Rectangular Distribution

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Standard deviation , ??????=
??????
??????
Rectangular Distribution
Variance of Rectangular Function

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Normal Distribution
Probability density function is

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Confidence level is the probability that the measured value will lie within the two limits.
k is the coverage factor (k = 2 for 95% confidence level ).
Example: Measured Value = 20.01 mm and
Uncertainty = 0.01 mm at 95% CL
Or
Uncertainty = 0.01 mm ; k =2

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kisthecoveragefactor
k=1.96≈2for95%confidenceLevelk
U
u
i
i
The expanded uncertainty U
i

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Checking flatness and parallelism of measuring faces
using optical flat.
flatness
parallelism

25. EVALUATION OF UNCERTAINTY FOR A MEASUREMENT PROCESS USING AN OUTSIDE MICROMETER
1) Equipment used : Outside micrometer
Range :0 to 25 mm
Resolution :1 microns
Accuracy :4 µm (from calibration certificate)
2) Reference standard used : Slip gauge of nominal value 25 mm
Actual calibrated length = 25.001 mm
Uncertainty of calibration (K = 2) = ±0.060 µm
(The above two are obtained from the calibration certificate of slip gauge)
3) Temperature maintained in the Laboratory: 20 ±2°C
Temperature at start of exercise= 20°C
Temperature at endof exercise = 21°C
Resolutionof the thermometer = 1°C.
Estimate Type ‘A’ and Type ‘B’ Uncertainties
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EVALUATION OF UNCERTAINTIES -
MICROMETER

26. 18 July 2023 DR. R RAJAMANI, PSG CT, COIMBATORE 26
EVALUATION OF UNCERTAINTIES -
RING GAUGE
Aringgaugeofnominaldiameter80mmistobecalibratedusingaLengthMeasuringMachine(LMM)anda
standardringgaugeofdiameter50mmatanaveragetemperatureof20.2°C.Thediameterofstandardring
gaugeasgiveninitscalibrationcertificateis50.00031mm±0.1µmatk=2fornormaldistribution.FindTypeA
uncertaintyusingthereadingsobtainedduringrepeatedexperiments29.9991,29.9982,30.0011,30.0012and
29.999mm.Also,estimateTypeBuncertaintybyconsideringthedatagivenintable1.Assumesuitable
probabilitydistributionswherevernecessary.Estimateexpandeduncertaintyat95%confidencelevel.
Uncertainty
Component
Accuracy of
standard ring
gauge
Error in the LMM as specified
in its calibration certificate
Error due to elastic deformation
of the ring gauge
Abbe’s
error
Value 0.1 µm ±(0.3+1.5 L) µm; L is the
length being measured in
meter.
±0.4 µm ±0.04 µm
Table -1

27. Reference
N.V.RaghavendraandL.Krishnamurthy,EngineeringMetrologyandMeasurements,Oxford
UniversityPress,2013
Gupta,S.V.Measurementuncertainties:physicalparametersandcalibrationofinstruments.
SpringerScience&BusinessMedia,2012.
Vim,I.S.O."Internationalvocabularyofbasicandgeneraltermsinmetrology(VIM)."
InternationalOrganization2004
https://slideplayer.com/slide/3279509/
18 July 2023 DR. R RAJAMANI, PSG CT, COIMBATORE 27