Geometry of reliability models of electrical system used inside spacecraft

This paper, introduces the minimal path method in order to solve the network model, which represents an electric system used inside spacecraft, and its reliability polynomial have been obtained. Factually, this polynomial has big number of terms, which makes it difficult to deal with in order to obtain useful information. For that reason, another technique, called the Reduction technique was introduced, for a simplified reliability polynomial. This technique transforms a complex network to its equivalent series and parallel form. Geometrically, a diffeomorphism has been used to change the initial reliability polynomial into a simplified form. Due to this original outcome, we formulate and prove some original results, regarding the “reliability”(1) hypersurface for a given network model, and to find the critical points of the reliability polynomial, which proved the nontrivial compatibility of the system. In addition, we had analyzed and computed the Hessian Matrix of reliability polynomial, and try to algebraically interpret the manner in which the reliability polynomial had been convex or concave, which reveals that the reliability of the system is increased or decreased. Most of the calculations and figures made in this paper have used Mathematica software.