  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.
