Abstract : For a given system, either biological or technological, survival and reliability analysis study the waiting time X for an event to occur (death, recovery, failure of a component) or else the successive
sojourn times in successive states (of health or of functioning)
are functions of factors called covariates in the medical field and stresses in the technological field.
Various regression models have been developed in order to represent how the durations depend on the
stresses / covariates, whose properties are those required by the final objective of the experimenter.
Three major features are different in survival as compared to reliability. One is the phenomenon of
censoring and truncation which is much more present in survival analysis. The second is the treatment
of asymptotics, which usually relies on the number of patients tending to infinity in survival analysis,
while in reliability it may be the observation time of a unique technological system that tends to infinity.
And the third aspect which is different is the control : when testing the reliability of systems, one
can control the stresses and thus accelerate the wear while in the biomedical field, covariates are observed
except in clinical trials when two treatments are compared. The models most frequently used
are hazard based models, like Cox model and its extensions and accelerated models. A competitor of
those models is a latent variable model : the Threshold Regression (TR) model. This latter model has
the advantage of allowing to treat the factors under consideration in three different ways, according
to their role in the waiting time of the onset of the event, whether it is intrinsic, evolving in time, or
acting like a catalyst accelerating the process. An example of such an application is proposed.