Miller & Freund’s Probability and Statistics for Engineers

546 Pages·2017·2.826 MB·english

by  Richard A. Johnson

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.