In reliability and survival analysis, the shot-noise processes have been intensively employed as a useful tool for modeling the impact of a dynamic environment (in the form of the point process of stresses) on survival characteristics of systems and organisms. However, the studies on the shot-noise processes have been mostly focused on the univariate analysis. In this paper, we develop a class of multivariate stochastic failure models based on a dynamic shock model induced by multiple shot-noise processes and study its properties. Explicit parametric forms for the multivariate survival functions are suggested. Multivariate ageing properties and dependence structures of the class are discussed as well.
Bibliographical noteFunding Information:
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).
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- Common shock model
- Dependence ordering
- Dependence structure
- Multiple shot-noise processes
- Multivariate ageing property