Level crossing problems and drift reliability

Reliability of products is often determined by special technical or physical drift parameters. Suitable stochastic processes are applied to model such drift processes. A failure can be observed when the drift process leaves a given region at the first time. Then the lifetime is the random time to first exit. Applying the first exit theory it is possible to find the type of lifetime distribution. Further, the parameters of the lifetime distribution are to be estimated by observations of realisations of the underlying drift process.