Stochastic failure models for systems under randomly variable environment (dynamic environment) are often described using hazard rate process. In this paper, we consider hazard rate processes induced by external shocks affecting a system that follow the nonhomogeneous Poisson process. The sample paths of these processes monotonically increase. However, the failure rate of a system can have completely different shapes and follow, e.g., the upside-down bathtub pattern. We describe and study various 'conditional properties' of the models that help to analyze and interpret the shape of the failure rate and other relevant characteristics.
Bibliographical noteFunding Information:
The authors would like to thank the Editor and reviewer for helpful comments and suggestions, which have improved the presentation of the 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 IFR2011040500026 .
- Failure rate
- Hazard rate process
- Nonhomogeneous Poisson process