turkmath.org

In traditional Marshall-Olkin type shock models and their modifications, there are three type of shocks that arrive at random times. These shocks destroy the components of a system which has two or more components. In this study, we assume that if the magnitude of the shock exceeds some predefined threshold, then the corresponding component is destroyed; otherwise it continues to survive. It is obvious that, this approach is different from classical Marshall-Olkin type shock models. More precisely, we assume that the shock time and the magnitude of the shock are dependent random variables with given bivariate distribution. For different examples of underlying bivariate distributions of lifetimes and shock magnitudes, the joint distributions of lifetimes of the components were investigated. The multivariate extension of the proposed model is also discussed.