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An Efficient Algorithm for the Reliability of

Consecutive-

**Jen-Chun Chang, Rong-Jaye Chen ^{*} and Frank K. Hwang^{+}**

Ming Hsin Institute of Technology

Hsinchu, 304 Taiwan

E-mail: jimmy@mis.mhit.edu.tw

National Chiao Tung Univeristy

Hsinchu, 300 Taiwan

E-mail: rjchen@csie.nctu.edu.tw

E-mail: fhwang@math.nctu.edu.tw

A consecutive-*k-n* network is a generalization of the well-known consecutive-*k*-out-of-*n* system, and has many practical applications. This network consists of *n* + 2 nodes (node 0, the source, nodes 1, 2, ¡K, *n*, and node *n* + 1, the target) and directed links from node i to node j (0 < *i* < *j* < *n* + 1, *j* - i
< *k*). Because all nodes except the source and target, and all links are fallible, the network works if and only if there exists a working path from the source to the target. For the *k* = 2 case, based on identical node reliabilities and some assumptions on link reliabilities, Chen, Hwang and Li (1993) gave a recursive algorithm for the reliability of the consecutive-2-*n* network. In this paper we give a closed form equation for the reliability of the general consecutive-*k-n* network by means of a novel Markov chain method. Based on the equation, we propose an algorithm which is more efficient than other published ones for the reliability of the consecutive-*k-n* network.

* Keywords:* consecutive-

Retrieve PDF document (**200301_09.pdf**)

Received February 15, 2000; revised July 15, 2000; accepted July 31, 2000.

Communicated by Gen-Huey Chen.