An age-wear-dependent model of failure and its description by cut-off Markov processes

An arbitrary functional dependence between the probability of failure on the one hand and the age and wear of a component on the other is assumed. The wear is assumed measurable and is described by cut-off Markov processes. Expressions are presented for the distribution of the failure time as well as for the failure rate. The application of the failure model is demonstrated by examples. The results of numerical computations are figured.