Weibull Models

A comprehensive perspective on Weibull models

The literature on Weibull models is vast, disjointed, andscattered across many different journals. Weibull Models is acomprehensive guide that integrates all the different facets ofWeibull models in a single volume.

This book will be of great help to practitioners in reliabilityand other disciplines in the context of modeling data sets usingWeibull models. For researchers interested in these modelingtechniques, exercises at the end of each chapter define potentialtopics for future research.

Organized into seven distinct parts, Weibull Models:

• Covers model analysis, parameter estimation, model validation,and application

• Serves as both a handbook and a research monograph. As ahandbook, it classifies the different models and presents theirproperties. As a research monograph, it unifies the literature andpresents the results in an integrated manner

• Intertwines theory and application

• Focuses on model identification prior to model parameterestimation

• Discusses the usefulness of the Weibull Probability plot (WPP)in the model selection to model a given data set

• Highlights the use of Weibull models in reliability theory

Filled with in-depth analysis, Weibull Models pulls together themost relevant information on this topic to give everyone fromreliability engineers to applied statisticians involved withreliability and survival analysis a clear look at what Weibullmodels can offer.

Autorentext
D. N. PRABHAKAR MURTHY, PhD, is a Professor of Engineering andOperations Management at the University of Queensland in Brisbane,Australia. He received his PhD in applied mathematics from HarvardUniversity.

MIN XIE, PhD, is an Associate Professor of Industrial andSystems Engineering at the National University of Singapore in KentRidge Crescent, Singapore. He received his PhD in qualitytechnology from Linkoping University in Linkoping, Sweden.

RENYAN JIANG, PhD, is a Professor of Engineering at the ChangshaUniversity of Science and Technology and is also affiliated withthe Department of Mechanical Industrial Engineering at theUniversity of Toronto in Toronto, Ontario, Canada. He received hisPhD in mechanical engineering from the University ofQueensland.

Zusammenfassung
A comprehensive perspective on Weibull models

The literature on Weibull models is vast, disjointed, andscattered across many different journals. Weibull Models is acomprehensive guide that integrates all the different facets ofWeibull models in a single volume.

This book will be of great help to practitioners in reliabilityand other disciplines in the context of modeling data sets usingWeibull models. For researchers interested in these modelingtechniques, exercises at the end of each chapter define potentialtopics for future research.

Organized into seven distinct parts, Weibull Models:

• Covers model analysis, parameter estimation, model validation,and application
• Serves as both a handbook and a research monograph. As ahandbook, it classifies the different models and presents theirproperties. As a research monograph, it unifies the literature andpresents the results in an integrated manner
• Intertwines theory and application
• Focuses on model identification prior to model parameterestimation
• Discusses the usefulness of the Weibull Probability plot (WPP)in the model selection to model a given data set

• Highlights the use of Weibull models in reliability theory

  Filled with in-depth analysis, Weibull Models pulls together themost relevant information on this topic to give everyone fromreliability engineers to applied statisticians involved withreliability and survival analysis a clear look at what Weibullmodels can offer.

Inhalt

Preface xiii

PART A OVERVIEW 1

Chapter 1 Overview 3

1.1 Introduction 3

1.2 Illustrative Problems 5

1.3 Empirical Modeling Methodology 7

1.4 Weibull Models 9

1.5 Weibull Model Selection 11

1.6 Applications of Weibull Models 12

1.7 Outline of the Book 15

1.8 Notes 16

Exercises 16

Chapter 2 Taxonomy for Weibull Models 18

2.1 Introduction 18

2.2 Taxonomy for Weibull Models 18

2.3 Type I Models: Transformation of Weibull Variable 21

2.4 Type II Models: Modification/Generalization of Weibull Distribution 23

2.5 Type III Models: Models Involving Two or More Distributions 28

2.6 Type IV Models: Weibull Models with Varying Parameters 30

2.7 Type V Models: Discrete Weibull Models 33

2.8 Type VI Models: Multivariate Weibull Models 34

2.9 Type VII Models: Stochastic Point Process Models 37

Exercises 39

PART B BASIC WEIBULL MODEL 43

Chapter 3 Model Analysis 45

3.1 Introduction 45

3.2 Basic Concepts 45

3.3 Standard Weibull Model 50

3.4 Three-Parameter Weibull Model 54

3.5 Notes 55

Exercises 56

Chapter 4 Parameter Estimation 58

4.1 Introduction 58

4.2 Data Types 58

4.3 Estimation: An Overview 60

4.4 Estimation Methods and Estimators 61

4.5 Two-Parameter Weibull Model: Graphical Methods 65

4.6 Standard Weibull Model: Statistical Methods 67

4.7 Three-Parameter Weibull Model 74

Exercises 82

Chapter 5 Model Selection and Validation 85

5.1 Introduction 85

5.2 Graphical Methods 86

5.3 Goodness-of-Fit Tests 89

5.4 Model Discrimination 93

5.5 Model Validation 94

5.6 Two-Parameter Weibull Model 95

5.7 Three-Parameter Weibull Model 99

Exercises 100

PART C TYPES I AND II MODELS 103

Chapter 6 Type I Weibull Models 105

6.1 Introduction 105

6.2 Model I(a)-3: Reflected Weibull Distribution 106

6.3 Model I(a)-4: Double Weibull Distribution 108

6.4 Model I(b)-1: Power Law Transformation 109

6.5 Model I(b)-2: Log Weibull Transformation 111

6.6 Model I(b)-3: Inverse Weibull Distribution 114

Exercises 119

Chapter 7 Type II Weibull Models 121

7.1 Introduction 121

7.2 Model II(a)-1: Pseudo-Weibull Distribution 122

7.3 Model II(a)-2: StacyMihram Model 124

7.4 Model II(b)-1: Extended Weibull Distribution 125

7.5 Model II(b)-2: Exponentiated Weibull Distribution 127

7.6 Model II(b)-3: Modified Weibull Distribution 134

7.7 Models II(b)46: Generalized Weibull Family 138

7.8 Model II(b)-7: Three-Parameter Generalized Gamma 140

7.9 Model II(b)-8: Extended Generalized Gamma 143

7.10 Models II(b)910: Four- and Five-Parameter Weibulls 145

7.11 Model II(b)-11: Truncated Weibull Distribution 146

7.12 Model II(b)-12: SlymenLachenbruch Distributions 148

7.13 Model II(b)-13: Weibull Extension 151

Exercises 154

PART D TYPE III MODELS 157

Chapter 8 Type III(a) Weibull Models 159

8.1 Introduction 159

8.2 Model III(a)-1: Weibull Mixture Model 160

8.3 Model III(a)-2: Inverse Weibull Mixture Model 176

8.4 Model III(a)-3: Hybrid Weibull Mixture Models 179

8.5 Notes 179

Exercises 180

Chapter 9 Type III(b) Weibull Models 182

9.1 Introduction 182

9.2 Model III(b)-1: Weibull Competing Risk Model 183

9.3 Model III(b)-2: Inverse Weibull Competing Risk Model 190 9.4 Model III(b)-3: Hybrid Weibull Competing Risk Model 1...