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.
Table of Contents:
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: Stacy–Mihram 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)4–6: 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)9–10: Four- and Five-Parameter Weibulls 145
7.11 Model II(b)-11: Truncated Weibull Distribution 146
7.12 Model II(b)-12: Slymen–Lachenbruch 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 191
9.5 Model III(b)-4: Generalized Competing Risk Model 192
Exercises 195
Chapter 10 Type III(c) Weibull Models 197
10.1 Introduction 197
10.2 Model III(c)-1: Multiplicative Weibull Model 198
10.3 Model III(c)-2: Inverse Weibull Multiplicative Model 203
Exercises 206
Chapter 11 Type III(d) Weibull Models 208
11.1 Introduction 208
11.2 Analysis of Weibull Sectional Models 210
11.3 Parameter Estimation 216
11.4 Modeling Data Set 219
11.5 Applications 219
Exercises 220
PART E TYPES IV TO VII MODELS 221
Chapter 12 Type IV Weibull Models 223
12.1 Introduction 223
12.2 Type IV(a) Models 224
12.3 Type IV(b) Models: Accelerated Failure Time (AFT) Models 225
12.4 Type IV(c) Models: Proportional Hazard (PH) Models 229
12.5 Model IV(d)-1 231
12.6 Type IV(e) Models: Random Parameters 232
12.7 Bayesian Approach to Parameter Estimation 236
Exercises 236
Chapter 13 Type V Weibull Models 238
13.1 Introduction 238
13.2 Concepts and Notation 238
13.3 Model V-1 239
13.4 Model V-2 242
13.5 Model V-3 243
13.6 Model V-4 244
Exercises 245
Chapter 14 Type VI Weibull Models (Multivariate Models) 247
14.1 Introduction 247
14.2 Some Preliminaries and Model Classification 248
14.3 Bivariate Models 250
14.4 Multivariate Models 256
14.5 Other Models 258
Exercises 258
Chapter 15 Type VII Weibull Models 261
15.1 Introduction 261
15.2 Model Formulations 261
15.3 Model VII(a)-1: Power Law Process 265
15.4 Model VII(a)-2: Modulated Power Law Process 272
15.5 Model VII(a)-3: Proportional Intensity Model 273
15.6 Model VII(b)-1: Ordinary Weibull Renewal Process 274
15.7 Model VII(b)-2: Delayed Renewal Process 277
15.8 Model VII(b)-3: Alternating Renewal Process 278
15.9 Model VII(c): Power Law–Weibull Renewal Process 278
Exercises 278
PART F WEIBULL MODELING OF DATA 281
Chapter 16 Weibull Modeling of Data 283
16.1 Introduction 283
16.2 Data-Related Issues 284
16.3 Preliminary Model Selection and Parameter Estimation 285
16.4 Final Model Selection Parameter Estimation and Model Validation 287
16.5 Case Studies 290
16.6 Conclusions 299
Exercises 299
PART G APPLICATIONS IN RELIABILITY 301
Chapter 17 Modeling Product Failures 303
17.1 Introduction 303
17.2 Some Basic Concepts 304
17.3 Product Structure 306
17.4 Modeling Failures 306
17.5 Component-Level Modeling (Black-Box Approach) 306
17.6 Component-Level Modeling (White-Box Approach) 308
17.7 Component-Level Modeling (Gray-Box Approach) 312
17.8 System-Level Modeling (Black-Box Approach) 313
17.9 System-Level Modeling (White-Box Approach) 316
Chapter 18 Product Reliability and Weibull Models 324
18.1 Introduction 324
18.2 Premanufacturing Phase 325
18.3 Manufacturing Phase 332
18.4 Postsale Phase 336
18.5 Decision Models Involving Weibull Failure Models 341
References 348
Index 377
About the Author :
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.
Review :
"...valuable to readers seeking an overview of Weibull modelsand...a valuable contribution to libraries..." (Journalof the American Statistical Association, September 2005)
"...may serve as a handbook in research andteaching..." (Zentralblatt Math, Vol.1047, No.22,2004)
"The book is generally well written and easy to read. It couldserve as a useful reference to practitioners...andresearchers." (Technometrics, November 2004)
"The literature of Weibull models is vast, disjointed, andscattered across many different journals. There are a couple ofbooks devoted solely to the Weibull distribution, but these areoriented toward training and/or consulting purposes. There is nobook that deals with the different Weibull models in an integratedmanner. This book fills that gap." (Mathematical Reviews,Issue 2004h)
