On history-dependent shock models

The crucial assumption in extreme shock models is that the survival/failure probability of system does not depend on the corresponding histories of the shock process and the system operation. By weakening this restrictive assumption, more 'realistic' and 'useful' models that describe various cumulative effects can be developed. However, a careful probabilistic reasoning should be employed for performing this operation. By considering the histories of the processes involved, we suggest a new theoretical insight for shock modeling and analysis.