Abstract
We consider shocks modeling in a 'natural' scale which is a discrete scale of natural numbers. A system is subject to the shock process and its survival probability and other relevant characteristics are studied in this scale. It turns out that all relations for the probabilities of interest become much easier in the new scale as compared with the conventional chronological time scale. Furthermore, it does not matter what type of the point process of shocks is considered. The shock processes with delays and the analog of a shot-noise process are discussed. Another example of the application of this concept is presented for systems with finite number of components described by signatures.
| Original language | English |
|---|---|
| Pages (from-to) | 104-110 |
| Number of pages | 7 |
| Journal | Reliability Engineering and System Safety |
| Volume | 145 |
| DOIs | |
| State | Published - 1 Jan 2016 |
Bibliographical note
Funding Information:The authors would like to thank the Associate Editor and referees for valuable comments and suggestions. 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 National Research Foundation of South Africa (NRF) Grant IFR2011040500026 .
Publisher Copyright:
© 2015 Published by Elsevier Ltd.
Keywords
- Discrete distribution
- Poisson process
- Renewal process
- Shock process
- Shot-noise process
- Signature