An Age-Wear Dependent Model of Failure

A failure model describes, by a Markov process, the cumulative damage (wear) of a component 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 where the increments of damage occur at the time instances of a Poisson process as well as the case of a continuous process of damage are considered. Equations which 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 material is briefly discussed.