Intro
Preface
Acknowledgments
Contents
Acronyms
1 Introduction and Preliminaries
1.1 Overall Introduction
1.1.1 Early Origins of Fiber Bundles Model
1.1.2 Organization of This Book
1.2 Preliminaries
1.2.1 Elements of Probability
1.2.1.1 Sample Space and Events
1.2.1.2 Axioms of Probability
1.2.1.3 Conditional Probability and Independence
1.2.2 Random Variables
1.2.2.1 Expectation of a Random Variable
1.2.2.2 Variance, Covariance, and Correlation of Random Variables
1.2.2.3 Moments of a Random Variable
1.2.2.4 Survival Function

1.2.2.5 Hazard Function
1.2.2.6 Quantile Function
1.2.2.7 Distributions of Minimum and Maximum
1.2.3 Some Commonly Used Discrete Distributions
1.2.3.1 Binomial Distribution
1.2.3.2 Poisson Distribution
1.2.4 Some Commonly Used Continuous Distributions
1.2.4.1 Uniform Distribution
1.2.4.2 Normal Distribution
1.2.4.3 Exponential Distribution
1.2.4.4 Weibull Distribution
1.2.4.5 Other Log-Location-Scale Distributions
1.2.4.6 Other Lifetime Distributions
1.2.5 Likelihood Inference
1.2.5.1 Likelihood and Fisher Information Matrices

1.2.5.2 General Maximum Likelihood Theory
1.2.6 Statistical Inference
1.2.7 Model Selection Criteria
1.2.8 Regression
1.2.8.1 Simple Regression Analysis
1.2.8.2 Parametric Lifetime Regression Models (Weibull Regression, Exponential Regression)
1.2.8.3 Semiparametric Regression Model (Cox Proportional Hazards Model)
1.2.9 Censoring
1.2.10 Kaplan-Meier Estimator of cdf
Part I Physical Aspects of Fiber Bundle Models
2 Electrical Circuits of Ordinary Capacitors
2.1 Electrical Laws for Circuits of Capacitors
2.2 Conservation Laws for Series and Parallel Circuits

2.2.1 Conservation Laws for Series and Parallel Circuits
2.2.2 Consequences of the Conservation Laws: The Capacitor Laws
2.2.3 Parallel and Series Circuits of Capacitors with the Same Capacitance
2.2.4 Behavior of the Charge and Voltage Load Distributions for Series Circuits of Capacitors
3 Breakdown of Thin-Film Dielectrics
3.1 Quantum Theory of Electron States in Solids
3.2 The Two Dielectric Materials Being Examined
3.2.1 Structure of Silicon Dioxide Thin Films
3.2.2 Structure of Hafnium Oxide Thin Films
3.3 Mechanisms of Conduction Through Dielectrics

3.3.1 Electrode-Limited Conduction Mechanisms
3.3.2 Bulk-Limited Conduction Mechanisms
3.4 Breakdown in Silicon Dioxide Dielectrics
3.5 Breakdown in Hafnium Oxide Dielectrics
4 Cell Models for Dielectrics
Part II Statistical Aspects of Fiber Bundle Models
5 Electrical Breakdown and the Breakdown Formalism
5.1 The Breakdown Formalism
5.2 Time-to-Breakdown (TBD) Formalism: Static Loads
5.2.1 TBD Formalism: Dynamic Loads
6 Statistical Properties of a Load-Sharing Bundle
6.1 Load-Sharing Rules
6.2 The Bundle Strength Distribution as an Affine Mixture