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.