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Bivariate shock models driven by the geometric counting process
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DOI：10.1017/jpr.2025.10061.png)
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Abstract
En 中文
We consider shock models governed by the bivariate geometric counting process. By assuming the competing risks framework, failures are due to one of two mutually exclusive causes (shocks). We obtain and study some relevant functions, such as failure densities, survival functions, probability of the cause of failure, and moments of the failure time conditioned on a specific cause. Such functions are specified by assuming that systems or living organisms fail at the first instant in which a random threshold is reached by the sum of received shocks. Under this failure scheme, various cases arising for suitable choices of the random threshold are provided too.
Keywords:
Shock model
geometric counting process
competing risks
failure distribution
random lifetime
hazard rate
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