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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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