A Minimal-Automaton-Based Algorithm for the Reliability of Con(d, k, n) Systems

Jen-Chun Chang (), Rong-Jaye Chen () and Frank K. Hwang ()
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Jen-Chun Chang: Ming Hsin Institute of Technology
Rong-Jaye Chen: National Chiao Tung University
Frank K. Hwang: National Chiao Tung University

Methodology and Computing in Applied Probability, 2001, vol. 3, issue 4, 379-386

Abstract: Abstract A d-within-consecutive-k-out-of-n system, abbreviated as Con(d, k, n), is a linear system of n components in a line which fails if and only if there exists a set of k consecutive components containing at least d failed ones. So far the fastest algorithm to compute the reliability of Con(d, k, n) is Hwang and Wright's $$O\left( {\left| L \right|^3 n} \right)$$ algorithm published in 1997, where $$\left| L \right| = O\left( {2^k } \right)$$ . In this paper we use automata theory to reduce $$\left| L \right|$$ to $$\left( {\begin{array}{*{20}c} k \\ {d - 1} \\ \end{array} } \right) + 1$$ . For d small or close to k, we have reduced $$\left| L \right|$$ from exponentially many (in k) to polynomially many. The computational complexity of our final algorithm is $$O\left( {\left| L \right|^2 + \left| L \right|n} \right)$$ , where $$\left| L \right| = \left( {\begin{array}{*{20}c} k \\ {d - 1} \\ \end{array} } \right) + 1$$ .

Keywords: consecutive system; Con(d; k; n) system; reliability; algorithm; complexity (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1023/A:1015464119846

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