Covers model analysis, parameter estimation, model validation, and application. This work also classifies the different models and their properties; intertwines theory and application; and focuses on model identification prior to model parameter estimation.

Preface xiiiPART A OVERVIEW 1Chapter 1 Overview 31.1 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

A comprehensive perspective on Weibull models The literature on Weibull models is vast, disjointed, and scattered across many different journals. Weibull Models is a comprehensive guide that integrates all the different facets of Weibull models in a single volume. This book will be of great help to practitioners in reliability and other disciplines in the context of modeling data sets using Weibull models. For researchers interested in these modeling techniques, exercises at the end of each chapter define potential topics for future research. Organized into seven distinct parts, Weibull Models: Covers model analysis, parameter estimation, model validation, and applicationServes as both a handbook and a research monograph. As a handbook, it classifies the different models and presents their properties. As a research monograph, it unifies the literature and presents the results in an integrated mannerIntertwines theory and applicationFocuses on model identification prior to model parameter estimationDiscusses the usefulness of the Weibull Probability plot (WPP) in the model selection to model a given data setHighlights the use of Weibull models in reliability theory Filled with in-depth analysis, Weibull Models pulls together the most relevant information on this topic to give everyone from reliability engineers to applied statisticians involved with reliability and survival analysis a clear look at what Weibull models can offer.

"...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)