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.
Bibliographical noteFunding Information:
The authors would like to thank the referee for very profound and detailed suggestions on the presentation of this paper. This work was supported by a National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (No. 2011-0017338 ). The work of the second author was supported by the NRF (National Research Foundation of South Africa) grant FA2006040700002 .
- Conditional failure rate
- History-dependent point process
- Operational history
- Shock model
- Shock process