Realistic variation of shock models

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On new classes of extreme shock models and some generalizations (2011, background): “Note that, e.g. Gut and Hüsler (2005) considered the case of the renewal process of shocks (and constant probability p), but even for this simplest history of the shock process, only asymptotic results (as t → ∞) could be obtained.”
On a Terminating Shock Process with Independent Wear Increments (2009, background): “…to in the literature as an extreme shock model, as only the impact of the current, possibly fatal shock is taken into account, whereas in cumulative shock models (see later) the impact of all shocks is accumulated (see Sumita and Shanthikumar (1985) and Gut and Husler (2005), among others).”