In this paper we study models for cumulative damage of a component caused by shocks occurring randomly in time, following a historical approach. The damage caused by a shock, is also of random nature. A very well-known model is the compound renewal process, with the compound Poisson process as a special case. These models play an important role in maintenance analysis and cost calculations. In these models the times at which shocks occur and the damage caused by the shock are assumed to be independent. But very often this is not realistic, the damage will depend on the time since the last shock, in some engineering applications it is even a deterministic function of the time since the last shock. Also, the results are often asymptotic. We will develop a model which allows dependence between damage and time since the last shock. We will calculate Laplace transforms of the interesting quantities and show how these can be inverted to get probability distributions for finite time horizons.