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Produktbild: Using the Weibull Distribution

Using the Weibull Distribution Reliability, Modeling, and Inference

Aus der Reihe Wiley Series in Probability and Statistics

158,99 €

inkl. gesetzl. MwSt., Versandkostenfrei

Beschreibung

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

28.08.2012

Verlag

John Wiley & Sons

Seitenzahl

366

Maße (L/B/H)

24/16,1/2,4 cm

Gewicht

718 g

Auflage

1. Auflage

Sprache

Englisch

ISBN

978-1-118-21798-6

Beschreibung

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

28.08.2012

Verlag

John Wiley & Sons

Seitenzahl

366

Maße (L/B/H)

24/16,1/2,4 cm

Gewicht

718 g

Auflage

1. Auflage

Sprache

Englisch

ISBN

978-1-118-21798-6

Herstelleradresse

Libri GmbH
Europaallee 1
36244 Bad Hersfeld
DE

Email: gpsr@libri.de

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  • Produktbild: Using the Weibull Distribution

  • Preface xiii

    1. Probability 1

    1.1 Sample Spaces and Events 2

    1.2 Mutually Exclusive Events 2

    1.3 Venn Diagrams 3

    1.4 Unions of Events and Joint Probability 4

    1.5 Conditional Probability 6

    1.6 Independence 8

    1.7 Partitions and the Law of Total Probability 9

    1.8 Reliability 12

    1.9 Series Systems 12

    1.10 Parallel Systems 13

    1.11 Complex Systems 15

    1.12 Crosslinked Systems 16

    1.13 Reliability Importance 19

    References 20

    Exercises 21

    2. Discrete and Continuous Random Variables 23

    2.1 Probability Distributions 24

    2.2 Functions of a Random Variable 26

    2.3 Jointly Distributed Discrete Random Variables 28

    2.4 Conditional Expectation 32

    2.5 The Binomial Distribution 34

    2.6 The Poisson Distribution 39

    2.7 The Geometric Distribution 41

    2.8 Continuous Random Variables 42

    2.9 Jointly Distributed Continuous Random Variables 51

    2.10 Simulating Samples from Continuous Distributions 52

    2.11 The Normal Distribution 54

    2.12 Distribution of the Sample Mean 60

    2.13 The Lognormal Distribution 66

    2.14 Simple Linear Regression 67

    References 69

    Exercises 69

    3. Properties of the Weibull Distribution 73

    3.1 The Weibull Cumulative Distribution Function (CDF) Percentiles Moments and Hazard Function 73

    3.2 The Minima of Weibull Samples 82

    3.3 Transformations 83

    3.4 The Conditional Weibull Distribution 86

    3.5 Quantiles for Order Statistics of a Weibull Sample 89

    3.6 Simulating Weibull Samples 92

    References 94

    Exercises 95

    4. Weibull Probability Models 97

    4.1 System Reliability 97

    4.2 Weibull Mixtures 103

    4.3 P(Y < X) 105

    4.4 Radial Error 108

    4.5 Pro Rata Warranty 110

    4.6 Optimum Age Replacement 112

    4.7 Renewal Theory 119

    4.8 Optimum Bidding 123

    4.9 Optimum Burn-In 124

    4.10 Spare Parts Provisioning 126

    References 127

    Exercises 128

    5. Estimation in Single Samples 130

    5.1 Point and Interval Estimation 130

    5.2 Censoring 130

    5.3 Estimation Methods 132

    5.4 Graphical Estimation of Weibull Parameters 136

    5.5 Maximum Likelihood Estimation 145

    5.6 ML Estimation for the Weibull Distribution 154

    References 177

    Exercises 179

    6. Sample Size Selection Hypothesis Testing and Goodness of Fit 180

    6.1 Precision Measure for Maximum Likelihood (ML) Estimates 180

    6.2 Interval Estimates from Menon's Method of Estimation 182

    6.3 Hypothesis Testing-Single Samples 184

    6.4 Operating Characteristic (OC) Curves for One-Sided Tests of the Weibull Shape Parameter 188

    6.5 OC Curves for One-Sided Tests on a Weibull Percentile 191

    6.6 Goodness of Fit 195

    6.7 Lognormal versus Weibull 204

    References 210

    Exercises 212

    7. The Program Pivotal.exe 213

    7.1 Relationship among Quantiles 216

    7.2 Series Systems 217

    7.3 Confidence Limits on Reliability 218

    7.4 Using Pivotal.exe for OC Curve Calculations 221

    7.5 Prediction Intervals 224

    7.6 Sudden Death Tests 226

    7.7 Design of Optimal Sudden Death Tests 230

    References 233

    Exercises 234

    8. Inference from Multiple Samples 235

    8.1 Multiple Weibull Samples 235

    8.2 Testing the Homogeneity of Shape Parameters 236

    8.3 Estimating the Common Shape Parameter 238

    8.4 Interval Estimation of a Percentile 244

    8.5 Testing Whether the Scale Parameters Are Equal 249

    8.6 Multiple Comparison Tests for Differences in Scale Parameters 257

    8.7 An Alternative Multiple Comparison Test for Percentiles 259

    8.8 The Program Multi-Weibull.exe 261

    8.9 Inference on P (Y < X) 266

    References 274

    Exercises 274

    9. Weibull Regression 276

    9.1 The Power Law Model 276

    9.2 ML Estimation 278

    9.3 Example 279

    9.4 Pivotal Functions 280

    9.5 Confidence Intervals 281

    9.6 Testing the Power Law Model 281

    9.7 Monte Carlo Results 282

    9.8 Example Concluded 285

    9.9 Approximating u* at Other Stress Levels 287

    9.10 Precision 289

    9.11 Stress Levels in Different Proportions Than Tabulated 289

    9.12 Discussion 291

    9.13 The Disk Operating System (DOS) Program REGEST 291

    References 296

    Exercises 296

    10. The Three-Parameter Weibull Distribution 298

    10.1 The Model 298

    10.2 Estimation and Inference for the Weibull Location Parameter 300

    10.3 Testing the Two- versus Three-Parameter Weibull Distribution 301

    10.4 Power of the Test 302

    10.5 Interval Estimation 302

    10.6 Input and Output Screens of LOCEST.exe 307

    10.7 The Program LocationPivotal.exe 309

    10.8 Simulated Example 311

    References 311

    Exercises 312

    11 Factorial Experiments with Weibull Response 313

    11.1 Introduction 313

    11.2 The Multiplicative Model 314

    11.3 Data 317

    11.4 Estimation 317

    11.5 Test for the Appropriate Model 319

    11.6 Monte Carlo Results 320

    11.7 The DOS Program TWOWAY 320

    11.8 Illustration of the Influence of Factor Effects on the Shape Parameter Estimates 320

    11.9 Numerical Examples 327

    References 331

    Exercises 332

    Index 333