  In this paper we compute the coefficients of the reliability polynomial of a
consecutive-$k$-out-of-$n$:$F$ system, in Bernstein basis, using the
generalized Pascal coefficients. Based on well-known combinatorial properties
of the generalized Pascal triangle we determine simple closed formulae for the
reliability polynomial of a consecutive system for particular ranges of $k$.
Moreover, for the remaining ranges of $k$ (where we were not able to determine
simple closed formulae), we establish easy to calculate sharp bounds for the
reliability polynomial of a consecutive system.
