System reliability based on system wear

This paper describes methods for formulating and estimating system reliability in settings where failure results from wear of system parts reaching a critical threshold. We propose a model concerned with the stochastic behavior of wear in which a right-continuous non-decreasing wear process is composed of "continuous and "jump parts. Several properties of our proposed model are presented, bounds are obtained for the reliability function, and the unknown parameters are estimated by the method of maximum likelihood. From these an estimate of the reliability function is obtained. In this part, contrary to common practice, we do not assume availability of failure data.