Competing risks within shock models

We consider a competing risks model, in which system failures are due to one out of two mutually exclusive causes, formulated within the framework of shock models driven by bivariate Poisson process. We obtain the failure densities and the survival functions as well as other related quantities under three different schemes. Namely, system failures are assumed to occur at the first instant in which a random constant threshold is reached by (a) the sum of received shocks, (b) the minimum of shocks, (c) the maximum of shocks.