Introduction to Statistics in Metrology PDF
Preview Introduction to Statistics in Metrology
Stephen Crowder Collin Delker Eric Forrest Nevin Martin Introduction to Statistics in Metrology Introduction to Statistics in Metrology (cid:129) (cid:129) Stephen Crowder Collin Delker Eric Forrest Nevin Martin Introduction to Statistics in Metrology StephenCrowder CollinDelker SandiaNationalLaboratories SandiaNationalLaboratories Albuquerque,NM,USA Albuquerque,NM,USA EricForrest NevinMartin SandiaNationalLaboratories SandiaNationalLaboratories Albuquerque,NM,USA Albuquerque,NM,USA ISBN978-3-030-53328-1 ISBN978-3-030-53329-8 (eBook) https://doi.org/10.1007/978-3-030-53329-8 ©SpringerNatureSwitzerlandAG2020 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartofthe materialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. The publisher, the authors, and the editorsare safeto assume that the adviceand informationin this bookarebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsor theeditorsgiveawarranty,expressedorimplied,withrespecttothematerialcontainedhereinorforany errorsoromissionsthatmayhavebeenmade.Thepublisherremainsneutralwithregardtojurisdictional claimsinpublishedmapsandinstitutionalaffiliations. ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSwitzerlandAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland To Lee, Leah, Stephen, Colleen, and Anna—S.V.C. To Kim, David, and Shawn—C.J.D. To Lisa, Cari, and Lyla—E.C.F. To Zane, Andy, and Josie—N.S.M. Preface ThisbookistheresultofmanyyearsofcollaborationbetweenthePrimaryStandards LaboratoryandtheStatisticalSciencesDepartmentatSandiaNationalLaboratories. Projectworktogether,publications,andmanydiscussionsregardinghowtobestuse statisticsinmetrologyhaveculminatedinthismanuscript.Withthisbook,wewish to present statistical best practices to both students and practitioners of metrology. Thebookbringstogetherinoneplacemanyofthebasicstatisticalmethodsthathave been applied to problems in metrology, plus much more. It not only includes methods presented in the JCGM 100 “Guide to the Expression of Uncertainty in Measurement” (aka, the GUM), but also presents topics in metrology seldom covered elsewhere. These topics include the design of experiments and statistical process control in metrology, uncertainties in curve fitting, assessment of binary measurement systems, and sample size determination in metrology studies. The book is not intended as a replacement for the GUM or other guiding documents from metrology bodies. Rather, it is intended as a companion resource for the student, technologist, engineer, or scientist involved in measurement studies. The chapterswerechosentoprovideablendoftopicsthatwillbothinformandchallenge studentsandpractitionersofmetrology. As a textbook, it is intended for junior or senior level college students studying engineering,statistics,ormetrologywithinaspecificdiscipline.Itcanalsobeusedat thegraduatelevelforstudentsininstrumentationandmeasurementclasseswhoare learning the basics of metrology and the statistical methods behind uncertainty analyses.Asaprerequisite,readersshouldhaveabasicknowledgeofcalculusand probabilityandstatistics.Relatedreadingsthatgobeyondthescopeofthebookare includedineachchapter.Wehavealsoincludedexercisesattheendofeachchapter tofurtherillustrateandemphasizematerialinthebodyofthebook. Statistical techniques are emphasized throughout, with appropriate engineering and physics background provided as needed. Most of the methods covered in the book are illustrated with case studies from our work in the Nuclear Security Enterprise. The case studies should provide the reader with a solid foundation for vii viii Preface applying the techniques to a wide variety of metrology problems. Many end-of- chapterexercisesalsorelyonthesecasestudies. The statistical topics in metrology are presented by first introducing the basic theory and models necessary to complete an uncertainty analysis. These topics are thenfollowedbycasestudiesillustratingtheapproach. Noteworthyhighlightsofthebookinclude: (cid:129) Measurementuncertaintyasapartofeverydaylife. (cid:129) Basicmeasurementterminologyandtypesofmeasurement. (cid:129) Roleofmeasurementuncertaintyindecision-making. (cid:129) Directandindirectmeasurementmodels. (cid:129) Analyticalmethodsforthepropagationofuncertainties. (cid:129) Designofexperimentsinmetrology. (cid:129) Uncertaintiesincurvefitting. (cid:129) Statisticalprocesscontrolinmetrology. (cid:129) Evaluationofbinarymeasurementsystems. (cid:129) Samplesizedeterminationandallocationinmetrologyexperiments. (cid:129) R-CodeandPythonUncertaintyCalculatorusedinmetrologystudies. Ofcourse,wehavenotcoveredallpossibletopicsinvolvingstatisticsinmetrol- ogy. For example, we have chosen not to cover interlaboratory comparisons or proficiency tests, as these topics are more relevant for calibration laboratories and arewell-coveredinothersourcessuchastheNCSLI’sRP-15.Wehavealsochosen not to cover in detail the metrology of system-level measurements. Asystem-level approach would include a broader understanding of topics such as frequency responses, sampling rates, aliasing, sensor placement and mounting, cables, and connectors.Thesetopicsarewell-coveredinvariousbooksandshortcourses.Other fieldssuchashealthcareandanalyticalchemistrywillhavespecializedextensionsof statisticsinmetrologythatarebeyondthescopeofthisbook.Themanyintricaciesof discipline-specificmetrologypracticessuchasthesearelearnedonlythroughyears oftrainingandhands-onexperience. Chapter 1ofthebookincludes abriefhistoryofmeasurementandthedevelop- ment of measurement science and technology. In Chap. 2, we introduce measure- ment terminology, types of measurement, and sources of uncertainty. Chapter 3 covers the International System of Units (SI), traceability, and calibrations. The SI baseunitsandderivedunitsarepresented,alongwiththenotionofunitrealization. Measurementstandardsandvariousaspectsofcalibrationarealsopresented.These three chapters areincluded toestablish the background andlanguage of metrology usedthroughoutthebook. An introduction to probability and statistics is given in Chap. 4. Topics include typesofdata,summarystatistics,graphicaldisplaysofdata,andanintroductionto theprobabilitydistributionsmostoftenusedinmetrology.InChap.5,weprovidean overview of measurement uncertainty in decision-making, including risk, error probabilities,testuncertaintyratios,andguardbanding. Chapter6developsbothdirectandindirectmeasurementmodelsandtheirroles in an uncertainty analysis. Type A and Type B uncertainty evaluations, standard Preface ix uncertainties, combined standard uncertainties, and expanded uncertainties are introduced here. The GUM approach to quantifying uncertainty is presented, and themethodsareillustratedwithanuncertaintyanalysisofaneutronyieldmeasure- ment. Chapter 7 presents the analytical methods used to propagate uncertainties throughanindirectmeasurementmodel,includingbothfirst-orderandhigherorder models, with both uncorrelated and correlated inputs. Measurement examples are givenforeachcase. Chapter8introducestheMonteCarlomethodforuncertaintyanalysis,beginning with a discussion of random number generation followed by a discussion of the techniques found in the JCGM 101 (aka, the GUM Supplement 1). Measurement examplesandacasestudyareusedtoillustratethisapproach.Chapter9presentsthe basic experimental designs that can be used in the evaluation of uncertainty. Emphasis is on full factorial, fractional factorial, and ANOVA-based designs. A step-by-stepapproachtodesigninganexperimentisgiven,alongwithcasestudiesto illustratethedesignandanalysistechniques. InChap.10,wepresentthemethodsfordetermininguncertaintiesinfittedcurves, including both linear and nonlinear least squares. The Monte Carlo method is also applied to curve fitting, and examples are given for each approach. Finally, in Chap. 11, we cover special topics in metrology that have been important in our work. These topics include statistical process control applied to a measurement process,evaluationofbinarymeasurementsystems,samplesizedeterminationand allocation in metrology experiments, and an introduction to Bayesian analysis in metrology. Throughout this book, R-Code is provided alongside many of the examples to givethereaderanimportanttoolthatcanbeusedtoperformuncertaintyanalyses.R isanopen-sourceprogramminglanguagewhosepopularitystemsprimarilyfromthe number of packages that are available for a wide range of statistical methods, including Monte Carlo sampling, linear and nonlinear regression, ANOVA, and more.RcanbedownloadedfromtheComprehensiveRArchiveNetwork(CRAN) atwww.r-project.organditisavailableforWindows,Unix-Like,andMacoperating systems. The Sandia Uncertainty Calculator (SUNCAL) is also being made available as open-sourcesoftware.ItwasdevelopedbythePrimaryStandardsLabatSandiato perform propagation of uncertainty analyses and other statistical techniques in metrology. It computes uncertainties using both the GUM and Monte Carlo methods. Partial derivatives are solved symbolically to provide the analytical for- mulas used in the calculations. The calculator can handle units conversion and unlimited input variables and uncertainty components. In addition to uncertainty propagation, SUNCAL provides calculations for curve fitting uncertainty, analysis of variance, and false accept/reject risk. SUNCAL was written in Python, a multipurpose language popular among engineers because of its ability to perform dataanalysisalongwithtaskssuchascommunicatingwithmeasurementequipment, interfacingwithdatabases,andaccessingtheinternet.SUNCALcanbeusedthrough a graphical user interface available for Windows and Mac, or as an importable x Preface Python package for programmers. It is released under the GNU General Public License,withsourcecodeandexecutablesavailableathttps://sandiapsl.github.io. Appendix A covers common acronyms and abbreviations used in metrology, followedinAppendixBbyguidelinesforvalidmeasurements.AppendixCincludes atraceabilitychainanduncertaintybudgetcasestudy,presentedinmoredetailthan thoseinthebodyofthebook.AppendixDincludesaquickreferencefortheGUM propagationofuncertaintytechniqueandatableofreferencesforcommontopicsin metrology.Finally,AppendixEprovidesinformationregardingtheinstallationofR softwareandexistingRpackagesusedinmetrology. TheacknowledgmentsaregiventothosefromthePrimaryStandardsLaboratory and the Statistical Sciences Department who have contributed their expertise and case studies in this collaborative effort. Our former and present colleagues in this workincludeStuartKupferman,TomWunsch,BudBurns,LisaBuntingBaca,Greg Guidarelli,AndrewMackrory,DavidSanchez,EdwardO0 Brien,JesseWhitehead, Mark Benner, Meghan Shilling, Donavon Gerty, Stefan Cular, Harold Parks, Eliz- abeth Auden, Ricky Sandoval, Otis Solomon, Roger Burton, Hy Tran, Raegan Johnson, Allie Wichhart, Andrew Wofford, Lauren Wilson, and Dan Campbell. SpecialthankstoDavidWalshforprovidingtheleadprobecasestudyandtoElbara Ziade for providing the CMM case study. Finally, this book would not have been possiblewithoutthesupportofJustinNewcomerandAdeleDoser,Managersofthe StatisticalSciencesDepartment,MeaghanCarpenter,SeniorManagerofthePrimary StandardsLab,andMarceyHoover,DirectorofQualityAssuranceatSandia. Albuquerque,NM,USA StephenCrowder Albuquerque,NM,USA CollinDelker Albuquerque,NM,USA EricForrest Albuquerque,NM,USA NevinMartin A false balance is an abomination to the LORD, but a just weight is his delight Proverbs 11:1
The list of books you might like
