# A dynamic stress–strength model with stochastically decreasing strength

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## Abstract

We consider a dynamic stress–strength model under external shocks. The strength of the system decreases with time and the failure occurs when the strength finally vanishes. Furthermore, there is another cause of the system failure induced by an external shock process. Each shock is characterized by the corresponding stress. If the magnitude of the stress exceeds the current strength, then the system also fails. We assume that the initial strength of the system and its decreasing drift pattern are random. We derive the survival function of the system and interpret the time-dependent dynamic changes of the random quantities which govern the reliability performance of the system.

## Keywords

Stress–strength model External shock process Nonhomogeneous Poisson process Multivariate stochastic order## Notes

### Acknowledgments

The authors would like to thank the editor and the referee for very careful and helpful comments, which have improved and clarified the presentation of our paper. The work of the first author was supported by the National Research Foundation of Korea (NRF) Grant funded by the Korea government (MEST) (No. 2011-0017338). The work of the first author was also supported by Priority Research Centers Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2009-0093827). The work of the second author was supported by the NRF (National Research Foundation of South Africa) Grant FA2006040700002.

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