  This paper proves a new general K-network constrained energy reliability
global factorization theorem. As in the unconstrained case, beside its
theoretical mathematical importance the theorem shows how to do parallel
processing in exact network constrained energy reliability calculations in
order to reduce the processing time of this NP-hard problem. Followed by a new
simple factorization formula for its calculation, we propose a new definition
of constrained energy network reliability motivated by the factorization
theorem and the accomplishment of parallel processing, something impossible
with the original definition.
