Some recent results on accelerated failure time models with time-varying stresses, by L.Gerville-Reache and M.Nikulin

Failure of highly reliable units are rare and it may be not possible to gather the failure time data needed for reliability estimation. One way of obtaining failures during the time given for experiments is to apply methods of accelerated life testing (ALT). In ALT units are tested at higher than usual stress conditions. As a result, failures which in normal conditions would occur only after a long testing, can be observed and the size of data can be enlarged. Using failure time data from accelerated experiments, statistical inference about item reliability under normal stress must be done. To solve this statistical problem the so-called accelerated life models are used to model the relationship between failure time data and covariate data like internal degradation and external environmental processes. A number of such models was proposed by engineers who considered physics of failure formation process of certain products or by statisticians