Accelerated life models: modeling and statistical analysis.

*(English)*Zbl 1001.62035
Monographs on Statistics and Applied Probability. 94. Boca Raton, FL: CRC Press. xix, 334 p. (2002).

This interesting book presents models and methods suitable for the statistical analysis of failure time regression (FTR) data, accelerated life testing (ALT) data and degradation data with explanatory variables. Only classes of univariate models are considered. The most used FTR and ALT models are the parametric accelerated failure time and semiparametric proportional hazard models. Nevertheless, they are quite restrictive and do not always agree well with real data. So a number of models, which are alternatives or generalizations of them, are presented using a unified approach to their formulation, giving the possibility to formulate new models and to see relations between them.

For most models, estimation procedures from FTR data censored by time varying and constant explanatory variables are given. In particular, plans of experiments and estimation methods from ALT data are considered. Methods for analysis of ALT data when the production process is unstable are also given. At last, but not at least, for most important models formal goodness-of-fit tests are given.

The book is intended especially for mathematicians. For engineers and more practically oriented people it can be difficult to read due to the fact that real numerical examples and diagnostic plots are not included.

Contents: Failure time distributions; Accelerated life models; Accelerated degradation models; Maximum likelihood estimation for FTR data; Parametric AFT model; Semiparametric AFT model; The Cox or PH model; GHP models: FTR analysis; Changing scale and shape model; GAH and GAHM models; Estimation when a process of production is unstable; Goodness-of-fit for accelerated life models; Estimation in degradation models; Some results from stochastic process theory.

For most models, estimation procedures from FTR data censored by time varying and constant explanatory variables are given. In particular, plans of experiments and estimation methods from ALT data are considered. Methods for analysis of ALT data when the production process is unstable are also given. At last, but not at least, for most important models formal goodness-of-fit tests are given.

The book is intended especially for mathematicians. For engineers and more practically oriented people it can be difficult to read due to the fact that real numerical examples and diagnostic plots are not included.

Contents: Failure time distributions; Accelerated life models; Accelerated degradation models; Maximum likelihood estimation for FTR data; Parametric AFT model; Semiparametric AFT model; The Cox or PH model; GHP models: FTR analysis; Changing scale and shape model; GAH and GAHM models; Estimation when a process of production is unstable; Goodness-of-fit for accelerated life models; Estimation in degradation models; Some results from stochastic process theory.

Reviewer: Jaromir Antoch (Praha)

##### MSC:

62N05 | Reliability and life testing |

62-02 | Research exposition (monographs, survey articles) pertaining to statistics |