Bivariate shock models driven by the geometric counting process
Abstract
Abstract 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.
Fields of Study & Subjects
Reliability and Maintenance Optimization
Probability and Statistical Research
Statistical Distribution Estimation and Applications
Publication details
- Journal / source
- Journal of Applied Probability
- Volume
- 63
- Issue
- 2
- Pages
- 849–863
- Publication date
- 12 February 2026
- Language
- EN