Abstract
At many practical instances, the initiating point events (e.g., shocks) affect an object not immediately, but after some random delay. These models were studied in the literature only for the case when an initial shock process is Poisson. In our paper, we generalize these results to a meaningful case of the generalized Polya process (GPP) of initial shocks that was recently introduced in the literature. Distinct from the Poisson process, the GPP possesses the property of dependent increments, which makes it much more attractive in applications. We derive the distribution of the time to failure for a system subject to the GPP with delays. Our main focus, however, is on analysis of the corresponding residual lifetime distribution that depends now on the full history (information) of the initiating shock process.
| Original language | English |
|---|---|
| Pages (from-to) | 209-216 |
| Number of pages | 8 |
| Journal | Statistics and Probability Letters |
| Volume | 137 |
| DOIs | |
| State | Published - Jun 2018 |
Bibliographical note
Funding Information:The authors would like to thank the referees for careful review, helpful comments and valuable suggestions. The work of the first author was 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 first author was also supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2016R1A2B2014211 ). The work of the second author was supported by the NRF (National Research Foundation of South Africa) grant IFR2011040500026 .
Publisher Copyright:
© 2018 Elsevier B.V.
Keywords
- Delayed failure
- Generalized Polya process
- Poisson process
- Residual lifetime
- Shocks