  We propose a new network reliability measure for some particular kind of
service networks, which we refer to as domination reliability. We relate this
new reliability measure to the domination polynomial of a graph and the
coverage probability of a hypergraph. We derive explicit and recursive formulae
for domination reliability and its associated domination reliability
polynomial, deduce an analogue of Whitney's broken circuit theorem, and prove
that computing domination reliability is NP-hard.
