Economical Design of Large Consecutive-k-out-of-n:F Systems

We first employ the concept of taboo probability to find a general closed-form formula for the reliability of a consecutive-k-out-of n:F system. We prove that for 1 ≤ k ≤ 4, the lim Rk,n= exp(-nqk)n→∞ where q is the component failure probability, and nqk is bounded. The limit formulas are used to design a large system where tradeoffs of costs can be considered.