  In this paper we explore the functional correlation approach to operational
risk. We consider networks with heterogeneous a-priori conditional and
unconditional failure probability. In the limit of sparse connectivity,
self-consistent expressions for the dynamical evolution of order parameters are
obtained. Under equilibrium conditions, expressions for the stationary states
are also obtained. The consequences of the analytical theory developed are
analyzed using phase diagrams. We find co-existence of operational and
non-operational phases, much as in liquid-gas systems. Such systems are
susceptible to discontinuous phase transitions from the operational to
non-operational phase via catastrophic breakdown. We find this feature to be
robust against variation of the microscopic modelling assumptions.
