EVALUATING MEASUREMENT ACCURACY : a practical approach

328 Pages·2017·4.34 MB·English

by  RABINOVICH

Springer Series in Measurement Science and Technology
Semyon G. Rabinovich
Evaluating
Measurement
Accuracy
A Practical Approach
Third Edition
Springer Series in Measurement Science
and Technology
Serieseditors
MarkysG.Cain,ElectrosciencesLtd.,Farnham,Surrey,UnitedKingdom
Giovanni Battista Rossi, DIMEC Laboratorio di Misure, Universita degli Studi di
Genova,Genova,Italy
Jirˇ´ıTesarˇ,CzechMetrologyInstitute,Prague,CzechRepublic
MarijnvanVeghel,VSLDutchMetrologyInstitute,JADelft,TheNetherlands
Kyung-Young Jhang, Sch of Mechanical Engg, Hanyang Univ, Seoul, Korea
(Republicof)
The Springer Series in Measurement Science and Technology comprehensively
covers the science and technology of measurement, addressing all aspects of the
subject from the fundamental physical principlesthrough tothe state-of-the-art in
appliedandindustrialmetrology.Volumespublishedintheseriescovertheoretical
developments, experimental techniques and measurement best practice, devices
and technology, data analysis, uncertainty, and standards, with application to
physics,chemistry,materialsscience,engineeringandthelifesciences.
The series includes textbooks for advanced students and research monographs
forestablishedresearchersneedingtostayuptodatewiththelatestdevelopments
inthefield.
Moreinformationaboutthisseriesathttp://www.springer.com/series/13337
Semyon G. Rabinovich
Evaluating Measurement
Accuracy
A Practical Approach
Third Edition
SemyonG.Rabinovich
ClevelandHts,OH
USA
ISSN2198-7807 ISSN2198-7815 (electronic)
SpringerSeriesinMeasurementScienceandTechnology
ISBN978-3-319-60124-3 ISBN978-3-319-60125-0 (eBook)
DOI10.1007/978-3-319-60125-0
LibraryofCongressControlNumber:2017951601
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Preface to the Third Edition
Thepurposeofthisbookistopresentmethodsforestimatingtheaccuracyofreal
measurements, that is, measurements performed in industry, trade, scientific
research – wherever the production process, quality control decision, or the inter-
pretation of an experiment depends on measurement accuracy. The necessity for
thisbookarisesfromthefactthattheexistingtheoryofmeasurementaccuracy(the
“classical theory”) contains significant gaps. In particular, the current theory
focusesexclusivelyonmultiplemeasurementsandoverlookssinglemeasurements.
Meanwhile, single measurements are the ones most commonly used in practice.
Moreover, the current theory is incomplete even within the scope of multiple
measurements. For example, it does not provide answers to such fundamental
questions as how to translate the inaccuracy of a measuring instrument into the
inaccuracy of a measurement utilizing this instrument, or how to find the full
uncertainty of a measurement result, that is, the uncertainty that reflects both
systematicandrandomerrors.
I devoted many years of research filling these gaps. This book generalizes and
putsintoacoherentwholetheresultsofthiseffort.Itpresentsmethodsofestimat-
ingtheaccuracyofbothsingleandmultiplemeasurements.Moreover,itformulates
thesemethodsinasystematicandunifiedwaybyformulatingandutilizinganew
perspective that single measurements are the basic type of measurements and
multiple measurements represent a series of repeated single measurements. This
new approach, besides being logical and intuitive, makes accounting for the
measuring instruments inaccuracy an inherent part of the calculations of the
inaccuracy of the measurement. This book offers well-grounded and practical
methods to combine the limits of elementary systematic errors and estimate the
overall measurement uncertainty accounting for both the systematic and random
errors.
Aspartofthegeneraltheoryofmeasurements,thisbookdevelopsthetheoryof
indirectmeasurements.Forindirectmeasurementswithdependentarguments,this
bookproposesthemethodofreductioninplaceofthetraditionalmethodbasedon
the Taylor series. This method is more accurate, simpler, and most importantly
v
vi PrefacetotheThirdEdition
allows one to calculate the confidence limits of the inaccuracy of these measure-
ments, rather than just standard deviation of the measurement result as in the
traditional methods. At the same time, it removes the need to account for the
correlationcoefficient,whichhadbeenathornyissueinthisarea.Thisbookfurther
includes a discussion of the applicability of the Bayes’ theorem and Monte Carlo
methods in measurement data processing, the topics that are being actively
discussednowinthemetrologicalresearchcommunity.
This book can serve as a comprehensive reference for data processing of all
types of measurements, including single and multiple measurements, dependent
andindependentindirectmeasurements,andcombinedandsimultaneousmeasure-
ments.Itincludesmanyconcreteexamplesthatillustratetypicalproblemsencoun-
tered in measurement practice. Thus, this book encompasses the entire area of
measurementdataprocessing,fromgeneraltheorytopracticalapplications.
This book is intended for anyone who is concerned with measurements in any
field of science or technology, who design technological processes and choose
instrumentswithappropriateaccuracyaspartoftheirdesign,andwhodesignand
testnewmeasuringdevices.Itshouldalsobeusefultouniversitystudentspursuing
science and engineering degrees. Indeed, measurements are of such fundamental
importanceformodernscienceandengineeringthateveryoneinthesefieldsmust
knowthebasicsofthetheoryofmeasurementsandespeciallyhowtoevaluatetheir
accuracy.
This monograph first appeared in 2010. The emergence of the method of
enumeration,whichprovidesasolutionformeasurementdataprocessinginindirect
multiple measurements with independent arguments, was the impetus for the
second edition, published in 2013. A number of further additions and corrections
developed afterwards have led to the present third edition. The most important
changesincludethefollowing:
• A new chapter Step-by-Step Guide to Evaluating Measurement Accuracy has
been added. It is a practical guide that distills solutions to most common
measurementdataprocessingtasksintoeasy-to-followstep-by-stepinstructions.
This guide can be used as a stand-alone reference by those who want to apply
properdataprocessingmethodsbutmaynotwanttostudyallthetheorybehind
them.ItcanalsoserveasthebasisforarevisiontoGuidetotheExpressionof
UncertaintyinMeasurement(GUM) [2];theneed forsucharevisionhasbeen
widely recognized and planned for almost 10 years, but there has been little
progresssofar.WediscussthedrawbacksandindeedmistakesintheGUM,as
wellastherelateddocument,VIM[1],indetailinthisbook(Chap.9).
• A variant of the method of enumeration, which I newly developed, has been
added.Thisvariantretainsalladvantagesofthemethodofenumeration(remov-
ingtheneedforlinearizationofthemeasurementequation,requiringnoassump-
tionsaboutthedistributionfunctionsoftheexperimentaldata,andutilizingall
informationthatthesedatacontain),butitismoreintuitiveanddoesnotrelyon
thecentrallimittheoremtoensurethatthesamplemeanisnormallydistributed.
PrefacetotheThirdEdition vii
• The method for evaluating accuracy of single indirect measurement has been
furtherdeveloped.
• Thesystematicerrorinmultiplemeasurementsisdescribedwithnewdetails;the
calculations of such errors in different types of multiple measurements are
shown.
• The chapters devoted to the accuracy of multiple direct and indirect measure-
ments(Chaps.4and5)arefullyrewritten.
• Theadditionmadetothemethodofreductionnowallowstheuseofthismethod
formeasurementshavingseveralmeasurandsinsteadofonlyone.
• The method of transformation has been eliminated because the method of
numerationisbetterandsimpler.
• Thesectiondevotedtotheaccuracyofmeasurementsperformedwithachainof
measuringinstrumentshasbeenrewritten.
• Thestructureofthisbookhasbeenimproved.
• Besidesthesechanges,thiseditionalsocorrectsanumberoftypographicaland
othererrorsthroughoutthisbook.
In conclusion, I would like to express my special gratitude to my son,
Dr. Michael Rabinovich, Professor at Case Western Reserve University. He pro-
videdsupportandassistancethroughoutmyworkonthisbookincludingeditingthe
proposal for publication, discussing new results and the presentation, and editing
thewholebook.Thisbookwouldnotbepossiblewithouthishelp.
Cleveland,OH SemyonG.Rabinovich
USA
Contents
1 GeneralConceptsintheTheoryofMeasurements. . . . . . . . . . . . . 1
1.1 BasicConceptsandTerms. . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 TheBasicMetrologicalProblems. . . . . . . . . . . . . . . . . . . . . . 4
1.3 NewFormsofInternationalCooperationinMetrology. . . . . . . 10
1.4 PostulatesoftheTheoryofMeasurements. . . . . . . . . . . . . . . . 12
1.5 ClassificationofMeasurements. . . . . . . . . . . . . . . . . . . . . . . . 18
1.6 ClassificationofMeasurementErrors. . . . . . . . . . . . . . . . . . . . 23
1.7 GeneralApproachtoEvaluationofMeasurement
Inaccuracy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
1.8 PresentationofMeasurementResults. . . . . . . . . . . . . . . . . . . . 27
2 MeasuringInstrumentsandTheirProperties. . . . . . . . . . . . . . . . . 31
2.1 TypesofMeasuringInstruments. . . . . . . . . . . . . . . . . . . . . . . 31
2.2 MetrologicalCharacteristicsofMeasuringInstruments. . . . . . . 33
2.3 RatingoftheErrorsofMeasuringInstruments. . . . . . . . . . . . . 36
2.4 DynamicCharacteristicsofMeasuringInstruments. . . . . . . . . . 49
2.5 CalibrationandVerificationofMeasuringInstruments. . . . . . . 54
2.6 DesigningaCalibrationScheme. . . . . . . . . . . . . . . . . . . . . . . 59
2.7 StatisticalAnalysisofMeasuringInstrumentErrors. . . . . . . . . 66
3 StatisticalMethodsforExperimentalDataProcessing. . . . . . . . . . 71
3.1 MethodsforDescribingRandomQuantities. . . . . . . . . . . . . . . 71
3.2 RequirementsforStatisticalEstimates. . . . . . . . . . . . . . . . . . . 75
3.3 EvaluationoftheParametersoftheNormalDistribution. . . . . . 77
3.4 EliminationofOutlyingData. . . . . . . . . . . . . . . . . . . . . . . . . 81
3.5 ConstructionofConfidenceIntervals. . . . . . . . . . . . . . . . . . . . 83
3.6 ReliabilityofEstimationoftheVarianceofaSample
fromaNormalDistribution. . . . . . . . . . . . . . . . . . . . . . . . . . . 88
3.7 ReliabilityofEstimationoftheStandardDeviationof
theMeanofaSamplefromaNormalDistribution. . . . . . . . . . 89
ix
x Contents
3.8 TestingHypothesesAbouttheFormofthe
DistributionFunction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
3.9 TestingforHomogeneityofSamples. . . . . . . . . . . . . . . . . . . . 93
3.10 RobustEstimates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
3.11 BootstrapConstructionofConfidenceIntervals. . . . . . . . . . . . 103
3.12 ApplicationoftheBayes’Theorem. . . . . . . . . . . . . . . . . . . . . 104
4 DirectMeasurements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
4.1 RelationBetweenSingleandMultipleMeasurements. . . . . . . . 107
4.2 ClassificationofElementaryErrors. . . . . . . . . . . . . . . . . . . . . 110
4.3 ModelingofElementaryErrors. . . . . . . . . . . . . . . . . . . . . . . . 115
4.3.1 AbsolutelyConstantErrors. . . . . . . . . . . . . . . . . . . . . 115
4.3.2 ConditionallyConstantErrors. . . . . . . . . . . . . . . . . . . 117
4.3.3 PurelyRandomErrors. . . . . . . . . . . . . . . . . . . . . . . . 118
4.3.4 QuasirandomErrors. . . . . . . . . . . . . . . . . . . . . . . . . . 118
4.4 CompositionofUniformDistributions. . . . . . . . . . . . . . . . . . . 119
4.5 MethodsforPreciseMeasurements. . . . . . . . . . . . . . . . . . . . . 125
4.6 AccuracyofSingleMeasurementsUsinga
MeasuringInstrumentUnderReferenceConditions. . . . . . . . . 127
4.7 AccuracyofSingleMeasurementsUsinga
MeasuringInstrumentUnderRatedConditions.. . . . .. . . . . .. 130
4.8 ComparisonofStandardDeviationandConfidence
IntervalasMeasurementAccuracyIndicators. . . . . . . . . . . . . . 136
4.9 AccuracyofMultipleDirectMeasurements. . . . . . . . . . . . . . . 139
4.10 UniversalMethodforSummationofRandomand
SystematicErrors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
4.11 AnalysisoftheAccuracyoftheUniversalMethod
forSummationofSystematicandRandomErrors. . . . . . . . . . . 146
4.12 ComparisonofDifferentMethodsforCombining
SystematicandRandomErrors. . . . . . . . . . . . . . . . . . . . . . . . 149
5 IndirectMeasurements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
5.1 TerminologyandClassification. . . . . . . . . . . . . . . . . . . . . . . . 155
5.2 CorrelationCoefficientandItsCalculation. . . . . . . . . . . . . . . . 157
5.3 ConstructingtheCompositionofHistograms. . . . . . . . . . . . . . 159
5.4 TraditionalMethodofMeasurementDataProcessing. . . . . . . . 168
5.5 ShortcomingsoftheTraditionalMethod. . . . . . . . . . . . . . . . . 173
5.6 MethodofReduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
5.7 MethodofEnumeration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
5.8 AccuracyofSingleIndirectMeasurementsUnder
ReferenceConditionsforInstrumentsInvolved. . . . . . . . . . . . 183
5.9 AccuracyofSingleIndirectMeasurementsUnder
RatedConditionsforInstrumentsInvolved. . . . . . . . . . . . . . . . 185
5.10 AccuracyofaSingleMeasurementwitha
ChainofInstruments. . . . . . .. . . . . . . . . . .. . . . . . . . . . .. . . 186
5.11 TheMonteCarloMethod. . . . . . . . . . . . . . . . . . . . . . . . . . . . 188