Abstract
In this paper, we stochastically model positively dependent multivariate reliability distributions based on stochastically dependent dynamic shock models. In the first part, we consider a shock model with delayed failures. This shock model will be used to construct a class of absolutely continuous multivariate reliability distributions. Explicit parametric forms for the multivariate reliability functions are suggested. Multivariate ageing properties and dependence structures of the class are discussed as well. In the second part, we obtain two types of absolutely continuous multivariate exponential distributions based on further generalized shock models.
| Original language | English |
|---|---|
| Pages (from-to) | 199-216 |
| Number of pages | 18 |
| Journal | Applied Mathematical Modelling |
| Volume | 51 |
| DOIs | |
| State | Published - Nov 2017 |
Bibliographical note
Funding Information:The authors would like to thank the referees for helpful comments and constructive 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 second author has been supported by Spanish government under research projects MTM2012-36603-C02-02 and MTM2015-63978-P.
Publisher Copyright:
© 2017 Elsevier Inc.
Keywords
- Common shock
- Multivariate IFR
- Nonhomogeneous Poisson process
- Positive upper orthant dependent
- Shock models