A translated renewal model with cost optimization applications

In this paper, a general model is developed to account for the cost accumulated in systems the dynamic behavior of which depends on underlying translated renewal processes. In particular, we consider translated renewal processes with excess-time displacements which are those displacements each exceeding in duration some constant length of time s>0. Application of the model is demonstrated in examples of insurance claim/premium and product warranty models, where cost optimization analysis is performed under plausible sufficient conditions.