ebook img

Miller & Freund’s Probability and Statistics for Engineers PDF

546 Pages·2017·2.826 MB·english
Save to my drive
Quick download
Download
Most books are stored in the elastic cloud where traffic is expensive. For this reason, we have a limit on daily download.

Preview Miller & Freund’s Probability and Statistics for Engineers

MILLER & FREUND’S PROBABILITY AND STATISTICS FOR ENGINEERS NINTH EDITION Global Edition Richard A. Johnson University of Wisconsin–Madison ©PearsonEducationLimited2018 AuthorizedadaptationfromtheUnitedStatesedition,entitledMiller&Freund’sProbabilityandStatisticsforEngineers,9thEdition, ISBN978-0-321-98624-5,byRichardA.JohnsonpublishedbyPearsonEducation©2017. BritishLibraryCataloguing-in-PublicationData AcataloguerecordforthisbookisavailablefromtheBritishLibrary 10987654321 TypesetbyiEnergizerAptaraLimited ISBN10:1-292-17601-6 ISBN13:978-1-292-17601-7 PrintedandboundinMalaysia. Contents Preface 7 Chapter 1 Introduction 11 1.1 WhyStudyStatistics? 11 1.6 TwoBasicConcepts—Population andSample 15 1.2 ModernStatistics 12 ReviewExercises 20 1.3 StatisticsandEngineering 12 KeyTerms 21 1.4 TheRoleoftheScientistandEngineerin QualityImprovement 13 1.5 ACaseStudy:VisuallyInspectingDatato ImproveProductQuality 13 Chapter 2 Organization and Description of Data 22 2.1 ParetoDiagramsandDotDiagrams 22 2.7 TheCalculationofxands 44 2.2 FrequencyDistributions 24 2.8 ACaseStudy:Problemswith AggregatingData 49 2.3 GraphsofFrequencyDistributions 27 ReviewExercises 52 2.4 Stem-and-LeafDisplays 31 KeyTerms 54 2.5 DescriptiveMeasures 34 2.6 QuartilesandPercentiles 39 Chapter 3 Probability 56 3.1 SampleSpacesandEvents 56 3.6 ConditionalProbability 78 3.2 Counting 60 3.7 Bayes’Theorem 84 3.3 Probability 67 ReviewExercises 91 3.4 TheAxiomsofProbability 69 KeyTerms 93 3.5 SomeElementaryTheorems 72 Chapter 4 Probability Distributions 94 4.1 RandomVariables 94 4.7 PoissonProcesses 122 4.2 TheBinomialDistribution 98 4.8 TheGeometricandNegative 4.3 TheHypergeometricDistribution 103 BinomialDistribution 124 4.4 TheMeanandtheVarianceofa 4.9 TheMultinomialDistribution 127 ProbabilityDistribution 107 4.10 Simulation 128 4.5 Chebyshev’sTheorem 114 ReviewExercises 132 4.6 ThePoissonDistributionand KeyTerms 133 RareEvents 118 3 Chapter 5 Probability Densities 134 5.1 ContinuousRandomVariables 134 5.10 JointDistributions—Discrete 5.2 TheNormalDistribution 140 andContinuous 161 5.3 TheNormalApproximationtothe 5.11 MomentGeneratingFunctions 174 BinomialDistribution 148 5.12 CheckingIftheDataAreNormal 180 5.4 OtherProbabilityDensities 151 5.13 TransformingObservationstoNear 5.5 TheUniformDistribution 151 Normality 182 5.6 TheLog-NormalDistribution 152 5.14 Simulation 184 5.7 TheGammaDistribution 155 ReviewExercises 188 5.8 TheBetaDistribution 157 KeyTerms 190 5.9 TheWeibullDistribution 158 Chapter 6 Sampling Distributions 193 6.1 PopulationsandSamples 193 6.6 TheMomentGeneratingFunction MethodtoObtainDistributions 213 6.2 TheSamplingDistributionoftheMean (σ known) 197 6.7 TransformationMethodstoObtain Distributions 215 6.3 TheSamplingDistributionoftheMean (σ unknown) 205 ReviewExercises 221 6.4 TheSamplingDistributionofthe KeyTerms 222 Variance 207 6.5 RepresentationsoftheNormal TheoryDistributions 210 Chapter 7 Inferences Concerning a Mean 223 7.1 StatisticalApproachestoMaking 7.7 HypothesesConcerningOneMean 249 Generalizations 223 7.8 TheRelationbetweenTestsand 7.2 PointEstimation 224 ConfidenceIntervals 256 7.3 IntervalEstimation 229 7.9 Power,SampleSize,andOperating CharacteristicCurves 257 7.4 MaximumLikelihoodEstimation 236 ReviewExercises 263 7.5 TestsofHypotheses 242 KeyTerms 265 7.6 NullHypothesesandTestsof Hypotheses 244 Chapter 8 Comparing Two Treatments 266 8.1 ExperimentalDesignsforComparing 8.4 MatchedPairsComparisons 280 TwoTreatments 266 8.5 DesignIssues—Randomization 8.2 Comparisons—TwoIndependent andPairing 285 LargeSamples 267 ReviewExercises 287 8.3 Comparisons—TwoIndependent KeyTerms 288 SmallSamples 272 Chapter 9 Inferences Concerning Variances 290 9.1 TheEstimationofVariances 290 ReviewExercises 299 9.2 HypothesesConcerning KeyTerms 310 OneVariance 293 9.3 HypothesesConcerning TwoVariances 295 Chapter 10 Inferences Concerning Proportions 301 10.1 EstimationofProportions 301 10.4 Analysisofr×cTables 318 10.2 HypothesesConcerningOne 10.5 GoodnessofFit 322 Proportion 308 ReviewExercises 325 10.3 HypothesesConcerningSeveral KeyTerms 326 Proportions 310 Chapter 11 Regression Analysis 327 11.1 TheMethodofLeastSquares 327 11.6 Correlation 366 11.2 InferencesBasedontheLeast 11.7 MultipleLinearRegression SquaresEstimators 336 (MatrixNotation) 377 11.3 CurvilinearRegression 350 ReviewExercises 382 11.4 MultipleRegression 356 KeyTerms 385 11.5 CheckingtheAdequacyoftheModel 361 Chapter 12 Analysis of Variance 386 12.1 SomeGeneralPrinciples 386 12.5 AnalysisofCovariance 415 12.2 CompletelyRandomizedDesigns 389 ReviewExercises 422 12.3 Randomized-BlockDesigns 402 KeyTerms 424 12.4 MultipleComparisons 410 Chapter 13 Factorial Experimentation 425 13.1 Two-FactorExperiments 425 13.4 ResponseSurfaceAnalysis 456 13.2 MultifactorExperiments 432 ReviewExercises 459 13.3 TheGraphicPresentationof22 and23 KeyTerms 463 Experiments 441 Chapter 14 Nonparametric Tests 464 14.1 Introduction 464 14.6 TheKolmogorov-Smirnovand 14.2 TheSignTest 464 Anderson-DarlingTests 475 14.3 Rank-SumTests 466 ReviewExercises 478 14.4 CorrelationBasedonRanks 469 KeyTerms 479 14.5 TestsofRandomness 472 Chapter 15 The Statistical Content of Quality-Improvement Programs 480 15.1 Quality-ImprovementPrograms 480 15.5 ControlChartsforMeasurements 488 15.2 StartingaQuality-Improvement 15.6 ControlChartsforAttributes 493 Program 482 15.7 ToleranceLimits 499 15.3 ExperimentalDesignsforQuality 484 ReviewExercises 501 15.4 QualityControl 486 KeyTerms 503 Chapter 16 Application to Reliability and Life Testing 504 16.1 Reliability 504 16.4 TheWeibullModelinLifeTesting 513 16.2 Failure-TimeDistribution 506 ReviewExercises 518 16.3 TheExponentialModelinLife KeyTerms 519 Testing 510 AppendixA Bibliography 521 AppendixB StatisticalTables 522 AppendixC UsingtheRSoftwareProgram 529 IntroductiontoR 529 EnteringData 529 ArithmeticOperations 530 DescriptiveStatistics 530 ProbabilityDistributions 531 NormalProbabilityCalculations 531 SamplingDistributions 531 ConfidenceIntervalsandTestsof Means 532 InferenceaboutProportions 532 Regression 532 One-WayAnalysisof Variance(ANOVA) 533 AppendixD AnswerstoOdd-NumberedExercises 534 Index 541 Preface This bookintroducesprobabilityandstatisticstostudentsofengineeringand the physical sciences. It is primarily applications focused but it contains optionalenrichmentmaterial.Eachchapterbeginswithanintroductorystate- ment and concludes with a set of statistical guidelines for correctly applying statisticalproceduresandavoidingcommonpitfalls.TheseDo’sandDon’tsarethen followed by a checklist of key terms. Important formulas, theorems, and rules are setoutfromthetextinboxes. Theexpositionoftheconceptsandstatisticalmethodsisespeciallyclear.Itin- cludesacarefulintroductiontoprobabilityandsomebasicdistributions.Itcontinues byplacingemphasisonunderstandingthemeaningofconfidenceintervalsandthe logic of testing statistical hypotheses. Confidence intervals are stressed as the ma- jor procedure for making inferences. Their properties are carefully described and their interpretation is reviewed in the examples. The steps for hypothesis testing are clearly and consistently delineated in each application. The interpretation and calculationoftheP-valueisreinforcedwithmanyexamples. In this ninth edition, we have continued to build on the strengths of the previ- ouseditionsbyaddingseveralmoredatasetsandexamplesshowingapplicationof statisticsinscientificinvestigations. Thenewdatasets,likemanyofthosealready inthetext,aroseintheauthor’sconsultingactivitiesorindiscussionswithscientists andengineersabouttheirstatisticalproblems.Datafromsomecompanieshavebeen disguised,buttheystillretainallofthefeaturesnecessarytoillustratethestatistical methodsandthereasoningrequiredtomakegeneralizationsfromdatacollectedin anexperiment. Thetimehasarrivedwhensoftwarecomputationshavereplacedtablelookups forpercentilesandprobabilitiesaswellasperformingthecalculationsforastatisti- calanalysis.Today’swidespreadavailabilityofstatisticalsoftwarepackagesmakes itimperativethatstudentsnowbecomeacquaintedwithatleastoneofthem.Wesug- gestusingsoftwareforperformingsomeanalysiswithlarger samplesandforper- formingregressionanalysis.Besideshavingseveralexistingexercisesdescribingthe useofMINITAB,wenowgivetheRcommandswithinmanyoftheexamples.This newmaterialaugmentsthebasicsofthefreewareRthatarealreadyinAppendixC. NEWFEATURESOFTHENINTHEDITIONINCLUDE: Largenumberofnewexamples.Manynewexamplesareincluded.Mostarebased on important current engineering or scientific data. The many contexts further strengthentheorientationtowardsanapplications-basedintroductiontostatistics. More emphasis on P-values. New graphs illustrating P-values appear in several examplesalongwithaninterpretation. MoredetailsaboutusingR.Throughoutthebook,Rcommandsareincludedina number of examples. This makes it easy for students to check the calculations, on theirownlaptoportablet,whilereadinganexample. Stressonkeyformulasanddownplayofcalculationformulas.Generally,com- putationformulasnowappearonlyattheendofsectionswheretheycaneasilybe skipped.Thisisaccomplishedbysettingkeyformulasinthecontextofanapplica- tionwhichonlyrequiresall,ormostlyall,integerarithmetic.Thestudentcanthen checktheirresultswiththeirchoiceofsoftware. 7 8 Preface Visual presentation of 22 and 23 designs. Two-level factorial designs have a 50-year tradition in the teaching of engineering statistics at the University of Wisconsin. It is critical that engineering students become acquainted with the key ideas of (i) systematically varying several input variables at a time and (ii) how to interpretinteractions.MajorrevisionshaveproducedSection13.3thatisnowself- contained. Instructors cancover this materialintwoor three lecturesattheendof course. Newdatabasedexercises.Alargenumberofexerciseshavebeenchangedtofea- ture real applications. These contexts help both stimulate interest and strengthen a student’sappreciationoftheroleofstatisticsinengineeringapplications. Examples and now numbered. All examples are now numbered within each chapter. Thistexthasbeentestedextensivelyincoursesforuniversitystudentsaswellas byin-planttrainingofengineers.Thewholebookcanbecoveredinatwo-semester or three-quarter course consisting of three lectures a week. The book also makes an excellent basis for a one-semester course where the lecturer can choose topics toemphasizetheoryorapplication.Theauthorcoversmostofthefirstsevenchap- ters,straight-lineregression,andthegraphicpresentationoffactorialdesignsinone semester(seethebasicapplicationssyllabusbelowforthedetails). Togivestudentsanearlypreviewofstatistics,descriptivestatisticsarecovered in Chapter 2. Chapters 3 through 6 provide a brief, though rigorous, introduction tothebasicsofprobability,populardistributionsformodelingpopulationvariation, and sampling distributions. Chapters 7, 8, and 9 form the core material on the key concepts and elementary methods of statistical inference. Chapters 11, 12, and 13 compriseanintroductiontosomeofthestandard,thoughmoreadvanced,topicsof experimental design and regression. Chapter 14 concerns nonparametric tests and goodness-of-fittest.Chapter15stressesthekeyunderlyingstatisticalideasforqual- ity improvement, and Chapter 16 treats the associated ideas of reliability and the fittingoflifelengthmodels. Themathematicalbackgroundexpectedofthereaderisayearcourseincalcu- lus.CalculusisrequiredmainlyforChapter5dealingwithbasicdistributiontheory inthecontinuouscaseandsomesectionsofChapter6. Itisimportant,inaone-semestercourse,tomakesureengineersandscientists becomeacquaintedwiththeleastsquaresmethod,atleastinfittingastraightline.A shortpresentationoftwopredictorvariablesisdesirable,ifthereistime.Also,not to be missed, is the exposure to 2-level factorial designs. Section 13.3 now stands aloneandcanbecoveredintwoorthreelectures. Foranaudiencerequiringmoreexposuretomathematicalstatistics,orifthisis thefirstofatwo-semestercourse,wesuggestacarefuldevelopmentoftheproperties ofexpectation(5.10),representationsofnormaltheorydistributions(6.5),andthen momentgeneratingfunctions(5.11)andtheirroleindistributiontheory(6.6). For each of the two cases, we suggest a syllabus that the instructor can easily modifyaccordingtotheirownpreferences. Preface 9 One-semesterintroductiontoprobabilityand Afirstsemesterintroductionthatdevelops statisticsemphasizingtheunderstandingof thetoolsofprobabilityandsomestatistical basicapplicationsofstatistics. inferences. Chapter1 especially1.6 Chapter1 especially1.6 Chapter2 Chapter2 Chapter3 Chapter3 Chapter4 4.4–4.7 Chapter4 4.4–4.7 4.8(geometric,negative binomial) Chapter5 5.1–5.4,5.6,5.12 Chapter5 5.1–5.4,5.6,5.12 5.10Selectexamplesofjoint 5.5,5.7,5.8(gamma,beta) distribution,independence, 5.10Developjointdistributions, meanandvarianceoflinear independenceexpectationand combinations. momentsoflinearcombinations. Chapter6 6.1–6.4 Chapter6 6.1–6.4 6.5–6.7(Representations, mgf’s,transformation) Chapter7 7.1–7.7 Chapter7 7.1–7.7 Chapter8 Chapter8 Chapter9 (couldskip) Chapter9 (couldskip) Chapter10 10.1–10.4 Chapter10 10.1–10.4 Chapter11 11.1–11.2 11.3and11.4Examples Chapter13 13.322 and23 designs also13.1ifpossible AnytablewhosenumberendsinWcanbedownloadedfromthebook’ssection ofthewebsite http://www.pearsonglobaleditions.com/Johnson We wish to thank MINITAB (State College, Pennsylvania) for permission to includecommandsandoutputfromtheirMINITABsoftwarepackage,theSASin- stitute(Gary,NorthCarolina)forpermissiontoincludeoutputfromtheirSASpack- age and the software package R (R project http://CRAN.R-project.org), which we connecttomanyexamplesanddiscussinAppendixC. Wewishtoheartilythankallofthosewhocontributedthedatasetsthatappear inthisedition.Theyhavegreatlyenrichedthepresentationofstatisticalmethodsby settingeachoftheminthecontextofanimportantengineeringproblem. Thecurrenteditionbenefitedfromtheinputofthereviewers. KamranIqbal,UniversityofArakansasatLittleRock YoungBalMoon,SyracuseUniversity NabinSapkota,UniversityofCentralFlorida KiranBhutani,CatholicUniversityofAmerica XiangguiQu,OaklandUniversity ChristopherChung,UniversityofHouston. AllrevisionsinthiseditionweretheresponsibilityofRichard.A.Johnson. RichardA.Johnson 1 I NTRODUCTION Everything dealingwiththecollection,processing,analysis,andinterpretationof nu- CHAPTER OUTLINE mericaldatabelongstothedomainof statistics.Inengineering,thisincludessuch diversifiedtasksascalculatingtheaveragelengthof computerdowntimes,collect- 1.1 WhyStudy ingandpresentingdataonthenumbersof personsattendingseminarsonsolarenergy, Statistics? 11 evaluatingtheeffectivenessof commercialproducts,predictingthereliabilityof alaunch 1.2 ModernStatistics 12 vehicle,andstudyingthevibrationsof airplanewings. 1.3 Statisticsand In Sections 1.2, 1.3, 1.4, and 1.5 we discuss the recent growth of statistics and its Engineering 12 applicationstoproblemsof engineering.Statisticsplaysamajorroleintheimprovement 1.4 TheRoleof the of qualityof anyproductorservice.Anengineerusingthetechniquesdescribedinthis ScientistandEngineer bookcanbecomemuchmoreeffectiveinallphasesof workrelatingtoresearch,devel- inQuality opment,orproduction.InSection1.6webeginourintroductiontostatisticalconcepts Improvement 13 byemphasizingthedistinctionbetweenapopulationandasample. 1.5 ACaseStudy:Visually InspectingData toImproveProduct 1.1 Why Study Statistics? Quality 13 1.6 TwoBasicConcepts— Answers provided by statistical analysis can provide the basis for making better Populationand decisions and choices of actions. For example, city officials might want to know Sample 15 whetherthelevelofleadinthewatersupplyiswithinsafetystandards.Becausenot all of the water can be checked, answers must be based on the partial information ReviewExercises 20 from samples of water that are collected for this purpose. As another example, an KeyTerms 21 engineer must determine the strength of supports for generators at a power plant. First, loading a few supports to failure, she obtains their strengths. These values provide a basis for assessing the strength of all the other supports that were not tested. Wheninformationissought,statisticalideassuggestatypicalcollectionprocess withfourcrucialsteps. 1. Setclearlydefinedgoalsfortheinvestigation. 2. Makeaplanofwhatdatatocollectandhowtocollectit. 3. Applyappropriatestatisticalmethodstoefficientlyextractinformation fromthedata. 4. Interprettheinformationanddrawconclusions. These indispensable steps will provide a frame of reference throughout as we develop the key ideas of statistics. Statistical reasoning and methods can help you becomeefficientatobtaininginformationandmakingusefulconclusions.

See more

The list of books you might like

Most books are stored in the elastic cloud where traffic is expensive. For this reason, we have a limit on daily download.