ABSTRACT
In this chapter, a few reliability or survival analysis models involving latent variables are presented. Latent variable models are generally proposed to consider missing information, heterogeneity of observations, measurement errors, dependency, etc. On one hand, the statistical models described are mainly devoted to the study of duration data, and on the other hand, a large number of estimation methods are shown for use to estimate parametrically, semi-parametrically, or nonparametrically the unknown parameters of these models. In the parametric setup, when the maximum likelihood principle is too complex to be handled, an EM or stochastic EM algorithm may be useful. In the nonparametric setup, combining empirical processes are shown with the functional delta-method allowing the derivation of the asymptotic properties of estimators. Some examples are based on Gamma processes to model degradation data and may involve time-dependent latent variables.
