Realistic variation of shock models

The standard assumptions in shock models are that the failure (of a system) is related either to the cumulative effect of a (large) number of shocks or that failure is caused by a shock that exceeds a certain critical level. The present paper is devoted to both types but with variation of the scheme. We consider that a shock can partly harm the system which implies a lower critical boundary for the following shocks to be fatal. For the cumulative model we deal with the case that only the sum of the most recent shocks implies a system failure. In addition, we consider the combination of both models with some link functions.