Reliability polynomials of consecutive‐k‐out‐of‐n:Fsystems have unbounded roots

This article studies the roots of the reliability polynomials of linear consecutive‐ k ‐out‐of‐ n : F systems. We prove that these roots are unbounded in the complex plane, for any fixed . In the particular case , we show that the reliability polynomials have only real roots and highlight the closure of these roots by establishing their explicit formulas. We also point out that in this case, for any fixed n , the nonzero roots of the reliability polynomial are distinct numbers.