Generalized S-Shapedness of Reliability Functions

Reliability functions have the property that if they intersect the diagonal y = x it is done in an S-shaped form (Moore and Shannon).

In this paper a wider class of polynomials is presented, the members of which form a dense grid on the unit square. The S-shapedness intersection property holds whenever a reliability function intersects a polynomial in this set.

The members of this set are all reliability polynomials. The diagonal y = x is also a member of this set, thus a generalization of Moore-Shannon result is achieved.