Traditional shock models view system failure time as a first passage problem. Yeh Lam proposed a new class of models called δ-shock models in which failure was dependent on the frequency of shocks. The present work generalizes Yeh Lam's results for renewal shock arrivals and random threshold. Several special cases and an optimal replacement problem are also discussed.
Availability function which forms an important part of reliability analysis is expressed in terms of an integral equation. The analytical solution of such an equation is possible only in very simple cases and hence approximations are the only tools available; very few such approximations are available in the literature. This paper proposes three useful approximations, two of which are based only on the first few moments of the underlying distributions and do not require their functional forms. The third approximation uses the Riemannian sum to approximate the integral equation. Numerical illustrations based on test cases are provided to show the efficacy of the approximations. As an application, the problem of an opportunistic channel access scheme in a communication network is used to test the approximations.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.