Some Stochastic Properties of a Compound-Renewal Damage Model

The compound-renewal process is investigated as a model of cumulative damage. The component is assumed to function until the cumulative wear exceeds some critical threshold, in general a random variable, at which time the component is assumed useless. It is this first passage time until breakdown which is of prime interest. Rather than focusing the attention on a certain selected compound-renewal process governed by mathematically convenient distributions, a class of compound-renewal processes involving the nonparametric, physically appealing assumption of a monotone failure rate is studied. Since the assumptions are nonparametric, the results for the most part manifest themselves in the form of useful bounds.