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

TL;DR

This paper introduces a cubic spline approximation method for reliability polynomials of dual hammock networks, leveraging convexity properties and mutual polynomial behavior to improve accuracy over existing methods.

Contribution

It presents a novel cubic spline-based approximation algorithm that utilizes dual network properties to estimate reliability polynomials more effectively.

Findings

The method accurately approximates reliability polynomials in simulations.

Compared to literature, the approach shows improved approximation quality.

The algorithm is validated on networks with known reliability values.

Abstract

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.