Accelerated Life Models: Modeling and Statistical Analysis
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Summary
The authors of this monograph have developed a large and important class of survival analysis models that generalize most of the existing models. In a unified, systematic presentation, this monograph fully details those models and explores areas of accelerated life testing usually only touched upon in the literature.
Accelerated Life Models: Modeling and Statistical Analysis presents models, methods of data collection, and statistical analysis for failure-time regression data in accelerated life testing and for degradation data with explanatory variables. In addition to the classical results, the authors devote considerable attention to models with time-varying explanatory variables and to methods of semiparametric estimation. They also examine the simultaneous analysis of degradation and failure-time data when the intensities of failure in different modes depend on the level of degradation and the values of explanatory variables.
The authors avoid technical details by explaining the ideas and referring to resources where thorough analysis can be found. Whether used for teaching, research or general reference, Accelerated Life Models: Modeling and Statistical Analysis provides new and known models and modern methods of accelerated life data analysis.
Table of Contents
Failure Time Distributions
Introduction
Parametric Classes of Failure Time Distributions
Accelerated Life Models
Introduction
Generalized Sedyakin's Model
Accelerated Failure Time Model
Proportional Hazards Model
Generalized Proportional Hazards Models
Generalized Additive and Additive-Multiplicative Hazards Models
Changing Shape and Scale Models
Generalizations
Models Including Switch-Up and Cycling Effects
Heredity Hypothesis
Summary
Accelerated Degradation Models
Introduction
Degradation Models
Modeling the Influence of Explanatory Variables on Degradation
Modeling the Traumatic Event Process
Maximum Likelihood Estimation for FTR Data
Censored Failure Time Data
Parametric Likelihood Function for Right Censored FTR Data
Score Function
Asymptotic Properties of the Maximum Likelihood Estimators
Approximate Confidence Intervals
Some Remarks on Semi-Parametric Estimation
AFT Model: Parametric FTR and ALT Data Analysis
Parametrization of the AFT Model
Interpretation of the Regression Coefficients
FTR Data Analysis: Scale-Shape Families of Distributions
FTR Data Analysis: Generalized Weibull Distribution
FTR Data Analysis: Exponential Distribution
Plans of Experiments in Accelerated Life Testing
Parametric Estimation in ALT Under the AFT Model
AFT Models: Semi-Parametric FTR and AFT Data Analysis
FTR Data Analysis
Semi-Parametric Estimation in ALT
PH Model: Semi-Parametric FTR Data Analysis
Introduction
Parametrization of the PH Model
Interpretation of the Regression Coefficients
Semi-Parametric FTR Data Analysis for the PH Model
GPH Models: FTR Analysis
Introduction
Semi-Parametric FTR Data Analysis for the GPH1 Models
Semi-Parametric FTR Data Analysis: Intersecting Hazards
Changing Scale and Shape Model
Parametric FTR Data Analysis
Semi-Parametric FTR Data Analysis
Semi-Parametric Estimation in ALT
GAH and GAMH Model: Semi-Parametric FTR and ALT Data Analysis
GAH Model
GAMH Model
AAR Model
PPAR Model
Estimation When a Process of Production in Unstable
Application of the AFT Model
Application of the GPH1 Model
Goodness-of-Fit for Accelerated Life Models
Goodness-of-Fit for the GS Model
Goodness-of-Fit for the Model with Absence of Memory
Goodness-of-Fit for the AFT Model
Goodness-of-Fit for the PH Model
Goodness-of-Fit for the GPH Models
Goodness-of-Fit for the Parametric Regression Models
Estimation in Degradation Models with Explanatory Variables
Introduction
Linear Path Models
Gamma and Shock Processes
Some Results from Stochastic Process Theory
Stochastic Process. Filtration
Counting Process
Stochastic Integral
Conditional Expectation
Martingale
Predictable Process and Doob-Meyer Decomposition
Predictable Variation and Predictable Covariation
Stochastic Integrals with Respect to Martingales
Localization
Stochastic Integrals with Respect to Martingales (continuation)
Weak Convergence
Central Limit Theorem for Martingales
Non-Parametric Estimators of the Cumulative Hazard and the Survival Function
Product-Integral
Delta Method
References
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