The Roots of the Reliability Polynomials of Circular Consecutive-k-out-of-n:F Systems

The zeros of the reliability polynomials of circular consecutive-k-out-of-n:F systems are studied. We prove that, for any fixed k≥2, the set of the roots of all the reliability polynomials (for all n≥k) is unbounded in the complex plane. In the particular case k=2, we show that all the nonzero roots are real, distinct numbers and find the closure of the set of roots. For every n≥k, the expressions of the minimum root and the maximum root are given, both for circular as well as for linear systems.