  The property of preserving the convexity and concavity of the Bernstein
polynomial and of the B\'{e}zier curves is used to generate a method of
approximating the reliability polynomial of a hammock network. The mutual
behaviour of the reliability polynomials of two dual hammock networks is used
to generate a system of constraints since the initial information is not enough
for using a classical approximation scheme. A cubic spline function is
constructed to generate approximations of the coefficients of the two
reliability polynomials. As consequence, an approximation algorithm is
described and tested through simulations on hammocks with known reliability,
comparing the results with the results of approximations attempts from
literature.
