New properties of the equivalent reliability polynomial through the geometric representation

This paper utilizes the geometric interpretations that were used to analyze the reliability of an electrical system that is used inside a spacecraft. Several new ideas have been addressed; (i) geodesics for equivalent simplified reliability polynomial; (ii) the mean time to failure (MTTF), the failure rates, and the steady state failure rates for the system have been studied based on their geometric properties; (iii) investigating all the exponential curves of decay included in the hypersurface of reliability. An extension of the standard definition of reliability has been considered by assuming the reliability component to be defined over the whole domain of the real axis.