Tight Bounds on the Coeffcients of Consecutive k-out-of-n:F Systems
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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.
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