Accelerated Life Models: Modeling and Statistical Analysis, 1st Edition (Hardback) book cover

Accelerated Life Models

Modeling and Statistical Analysis, 1st Edition

By Vilijandas Bagdonavicius, Mikhail Nikulin

Chapman and Hall/CRC

360 pages | 20 B/W Illus.

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Hardback: 9781584881865
pub: 2001-11-28
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Description

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

About the Series

Chapman & Hall/CRC Monographs on Statistics and Applied Probability

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Subject Categories

BISAC Subject Codes/Headings:
BUS053000
BUSINESS & ECONOMICS / Quality Control
MAT029000
MATHEMATICS / Probability & Statistics / General
TEC032000
TECHNOLOGY & ENGINEERING / Quality Control