Calibration of Uncertainty Measurement .

Measurement Uncertainty

1. FOR MEASUREMENT
DATA TO BE RELIABLE
MEASUREMENT SHOULD BE
ACCURATE
PRECISE
REPRODUCIBLE

2. ACCURACY ISTHECLOSENESS OF
AGREEMENT BETWEEN THERESULTOF
MEASUREMENT ANDTHETRUEVALUEOF
THEMEASURAND
 ACCURACY IS ALSO CALLED BIAS

3. PRECISION ISTHECLOSENESS OF
AGREEMENT BETWEEN THERESULTS
OFSUCCESIVEMEASUREMENT OFTHE
SAMEVALUEOFAQUANTITYCARRIED
OUTUNDERIDENTICALCONDITIONAT
SHORTINTERVALSOFTIME.
•PRECISION ISALSO CALLED
REPETABILITY

4. REPRODUCIBILITY ISTHECLOSNESS
OFAGREEMENT BETWEEN CORRECTED
RESULTSOFMEASUREMENT OFTHE
SAME VALUEOFAQUANTITYWHEN
MEASUREMENTS ARE MADE UNDER
DIFFERENTCONDITIONS.

5. Evenwhenallthefactorsina
measurementprocessarecontrolled.
Repeatedobservationmadeduring
precisionmeasurementofanyparameter.
Evenundersameconditionsarerarely
foundidentical.

6. This is due to the presence of
Inherent variable of every
measurement process.

7. •FACTORS AFFECTING THE STANDARD
•FACTORS AFFECTING THE WORKPIECE
•FACTORS AFFECTING THE INSTRUMENTS
•FACTORS AFFECTING THE PERSON
•FACTORS AFFECTING THE ENVIROMENT
5 BASIC METROLOGY ELEMENTS

8. •BECAUSE OF
SWIPE,NO
MEASUREMENT
RESULT CAN BE
ACCEPTED AS A
CERTAINTY.

9. MEASUREMENT OF PHYSICAL QUANTITY
RESULT
QUALITY INDICATOR
RELIABILITY

10. ERROR OF MEASUREMENT
•DISCREPANCY BETWEEN THEMEASURED
ANDTRUEVALUESOFTHEQUANTITY
•“ITISTHEMEASUREMENT RESULTMINUS
THETRUEVALUE”

11. TRUE VALUE
(of a quantity)
•THEVALUEWHICHCHARACTERIZES A
PERFECTLY DEFINEDQUANTITYINTHE
CONDITION WHICHEXISTWHEN THAT
QUANTITYISCONSIDERED.
Truevalueisatheoreticalconceptand
cannotbeknownexactly.

12. ERROR OF MEASUREMENT
ARISES OUT OF TWO FACTORS
•DUE TO SYSTEM
EFFECTS
•DUE TO RANDOM
EFFECTS
On which remains
constant during a
number ofidentical
measurementsorwhich
variesinapredictable
mannerwhenconditions
change
Onewhichvariesina
unpredictablemanner
duringanumberof
identicalmeasurements

13. MEASUREMENT UNCERTAINTY
•Itisanestimatecharacterizingtherange
ofvalueswithinwhichtheerrorisasserted
tolie.
•Itisanexpressionoffactthatforagiven
resultofmeasurementthereisnotone
value,butaninfinitenumberofvalues
dispersedabouttheresult,withavarying
degreeofcredibility.

14. CONFIDENCE LEVEL
Theprobabilityexpressedinadecimalor
percentage,thatthetruevaluelieswithina
specifiedrangeofvalues.

15. UNCERTAINITYIS A
PARAMETER TO QUANTIFY
THE RELIABILITY OF THE
MEASURAND.

16. DIFFERENT UNCERTAINITY TERMS
•RANDOM
•SYSTEMATIC
•MEASUREMENT
•CALIBRATION
•STANDARD
•COMBINED STANDARD
•EXPANDED

17. MEASUREMENT OF TEMPERATURE
•Resolution of thermometer = 1
o
c
•Accuracy of thermometer = 2
o
c
•Uncertainty of thermometer
Calibration (at 95% CL) = +0.7
o
c
•Measurement data :
101, 99, 100, 100,101,99,99,100,101,101
o
c
•Average value = 100.1
o
c
•REQUIREMENT = 100 +2
o
c

18. TEMPERATURE MEASUREMENT ( Cont’d)
SOURCE TYPE U
1 VALUE PROB STD.U
Thermometer
accuracy
B U
1 2.0 Rectangular 1.15
Them.
Calib.Uncert
B U
2 0.7 Normal 0.35
Repeatability A U
3 0.876 Normal 0.277
U
C= [ (1.15)
2
+ (0.35)
2
+ (0.277)
2
] = 1.23
0
C
V
EFF = (1.23)
4
*(10-1) / (0.277)
4
= 388.8 > 50 
Therefore, K = 2 FOR 95% Confidence level
U
E = K * U
C = 2 * 1.23 = 2.46
0
C
FINAL RESULT = 100 + 250C 100 + 3
0
C

19. MEASUREMENT UNCERTAINTY GIVES
RISETOMEASUREMENT DECISIONS
RISEWHENEVER DECISIONS ARE
MADEBASEDONMEASUREMENT

20. TWO TYPES OF RISK
Risk of false
acceptance, in which out-
of-tolerance Parameters
are mistaken as in
tolerance ones
Risk of false rejection,
which is the risk of
mistaking in tolerance
parameters for
out-of-tolerance ones

21. THEMOSTCOMMON ANDEASYWAYTO
CONTROL THESE RISKISTOUSE
APPROPRIATE TESTUNCERTAINTY RATIO
(TURORTAR)FORMEASUREMENTS .

22. Uncertainty of UUC
TUR =
Uncertainty Standard
TEST ACCURACY RATIO (TAR) / TEST
UNCERTAINTY RATIO (TUR) IS

23. If
S = Specification of the parameter being measured
U=UncertaintyofMeasurement
R=Resultantspecification
ThenwithS:V=10:1,R=10.05
THERESULTANTSPECIFICATIONEXPANDSBY0.5%
•If S:U = 4:1, the resultant specification
expands by 3.1%
•IfS:U=3:1,thespecificationexpandsby5.4%
•IfS:U=2:1,thespecificationexpandsby11.8%
•IfS:U=1:1,thespecificationexpandsby41.4%
•IfS:U=1:2,thespecificationexpandsby123.6%

24. Thismeansthatifaninstrumentis
calibratedagainstastandardwithaTURof
2:1,
Theneveniftheinstrumentisfoundtobe
withinthestatedaccuracy,
Inactualcase,theaccuracycouldunder
goexpansionby11.8%ofthestatedlimits.

25. Consequently, ISO 10012 part
1:1992 states that
“Theerrorattributabletocalibrationshould
beassmallaspossible,inmostareasof
measurement,itshouldbenomorethan
onethirdandpreferablyonetenthofthe
permissibleerroroftheconfirmed
equipmentwheninuse”.

26. On the same subject, ANSI / NCSL
Z540 –1 –1994 states, in part,
“…..Thecollectiveuncertaintyofthe
measurement standardsshallnotexceed
25%oftheacceptabletoleranceforeach
characteristicofthemeasuringandtest
equipmentbeingcalibratedorverified”

27. ISO/IEC17025:1999,Thebasisoflaboratory
accreditationworld-wide,statesunderCL.5.4.6
that
“Acalibrationlaboratory,oratestinglaboratory
performingitsowncalibrations,
Shallhaveandshallapplyaprocedureto
estimatetheuncertaintyofmeasurementforall
calibrationsandtypesofcalibrations”.

28. OntestingISO/IEC17025:1999
statesunderCL.5.4.6that
“Atestinglaboratory,shallhaveand
shallapplyproceduresforestimatingof
measurement”.

29. COMPLAINCE OF CALIBRATION
SHOULD BE GIVEN WHEN
•Calibrationuncertainty1/3
rd
spec.of
UUC
•IndicatedvaluesoftheUUC,expanded
bytheuncertainty,orwithinthespecified
accuracy(tolerance/uncertainty)limits.

30. Inatestsituationwherecomplianceis
tobereportedthetestresultexpanded
bymeasurementuncertaintyshouldlie
withinthespecificationlimits.

31. STANDARD UNCERTAINTY
Eachcomponentofuncertaintythatcontributes
tothemeasurementuncertainty,isrepresented
byanestimatedstandarddeviation,termedas
standarduncertainty,U
i,andisequaltothe
positivesquarerootofthevarianceU
i
2
.

32. COMBINED STANDARD
UNCERTAINTY
Afteridentifyingandestimatingtheindividual
standarduncertaintiescombinedstandard
uncertainty,U
ciscalculatedbytheRSSorthe
squarerootofthesum-of-thesquares,based
onthelawofpropagationofuncertainty.
U
C= U
1+ U
2+ U
3+ ……… + U
N
2

33. EXPANDED UNCERTAINTY
Expanded uncertainty,Uisdeterminedby
multiplyingu
cwithacoveragefactor“K”suchthat
theestimatedtruevalueofameasurementresulty
mayliewithin“y–U
c”and“y+U
c”values,where
“y”isthemeasuredvalueoftheparameters.
Y = y U
Thecoveragefactor“K”isgenerallytakenastwo
whichisequivalenttoaconfidencelevelof95%.
U
E= K * U
C

34. THE CIPM APPROACH
•TYPE “A” EVALUATION
•TYPE “B” EVALUATION
TWO METHODS FOR ESTIMATING
NUMERICAL VALUES OF UNCERTAINTY

35. FOUR IMPORTANT ASPECTS OF
UNCERTAINTY ESTIMATION
•MEASUREMENT EQUATION
•CENTRAL LIMIT THEORM
•DEGREE OF FREEDOM
•CONFIDENCE LEVEL

36. MEASUREMENT UNCERTAINTY
ESTIMATION IS
•NEITHER A ROUTINE CALCULATION
•NOR A PURELY MATHEMATICAL ONE

37. QUALITY OF ESTIMATION OF
MEASUREMENT UNCERTAINTY AND
ITS USAGE IS DEPENDS ON
•DETAILEDKNOWLEDGE OFTHE
MEASUREMENT SYSTEM
•ACCRACY ANDPRECISION OF
THEMEASUREMENTS PERFORMED
•INTEGRITY OFTHEPERSONS
INVOLVEDINMEASUREMENTS AND
CALCULATIONS

38. “Absolutecertaintyistheprivilegeof
uneducatedmindsandfanatics.Itisfor
scientificfolkandunattainableideal”.

39. “ITISCHANGES, CONTINUING
CHANGES,INEVITABLECHANGES,
THATISTHEDOMINATEFACTORIN
THESOCIETYTODAY
NOSENSIBLEDECISIONCANBE
MADE ANYLONGER WITHOUT
TALKING INTOACCOUNT NOT
ONLYTHEWORLDITIS,BUTTHE
WORLDASITWILLBE”.
Issac Assimov, Russian born us author

40. •IFYOUALWAYS DO
WHATYOUALWAYSDID
•THENYOUWILLALWAYS
GETTHERESULT
WHICHYOUALWAYSGOT

41. Thank You!