An age-wear dependent model of failure

A failure model is treated that describes the cumulative damage (wear) of a component by a Markov process and assumes an arbitrary functional dependence between the probability of failure and the process of damage. In particular, the rate-limited case of the failure model in which the increments of damage occur at the time instances of a Poisson process and the case of a continuation process of damage are considered. Equations that completely describe the process of failure are presented and solved. Expressions are derived for the distribution of the time to failure and related measures. The applicability of the model is briefly discussed.