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The property of preserving the convexity and concavity of the Bernsteinpolynomial and of the B\'{e}zier curves is used to generate a method ofapproximating the reliability polynomial of a hammock network. The mutualbehaviour of the reliability polynomials of two dual hammock networks is usedto generate a system of constraints since the initial information is not enoughfor using a classical approximation scheme. A cubic spline function isconstructed to generate approximations of the coefficients of the tworeliability polynomials. As consequence, an approximation algorithm isdescribed and tested through simulations on hammocks with known reliability,comparing the results with the results of approximations attempts fromliterature.

Cubic spline approximation of the reliability polynomials of two dual hammock networks