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An O(k3·log(n/k)) algorithm for the consecutive-k-out-of-n:F system

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2 Author(s)
Hwang, F.K. ; AT&T Bell Labs., Murray Hill, NJ, USA ; Wright, P.E.

The fastest generally-recognized algorithms for computing the reliability of consecutive-k-out-of-n:F systems require O(n) time, for both the linear and circular systems. The authors' new algorithm requires O(k3·log(n/k)) time. The algorithm can be extended to yield an O(n·max{k3·log(n/k), log(n))} total time procedure for solving the combinatorial problem of counting the number of working states, with w working and n-w failed components, w=1,2,...,n

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Reliability, IEEE Transactions on  (Volume:44 ,  Issue: 1 )