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A generalized class of consecutive-*k*-out-of-*n*:G systems, referred to as Con/*k*^{*}/*n*:G systems, is studied. A Con/*k*^{*}/*n*:G system has *n* ordered components and is good if and only if *k*_{i} good consecutive components that originate at component *i* are all good, where *k*_{i} is a function of *i*. Theorem 1 gives an *O*(*n*) time equation to compute the reliability of a linear system and Theorem 2 gives an *O*(*n*^{2}) time equation for a circular system. A distributed computing system with a linear (ring) topology is an example of such system. This application is very important, since for other classes of topologies, such as general graphs, planar graphs, series-parallel graphs, tree graphs, and star graphs, this problem has been proven to be *NP*-hard.

- Publication
- IEICE TRANSACTIONS on Information Vol.E83-D No.6 pp.1309-1313

- Publication Date
- 2000/06/25

- Publicized

- Online ISSN

- DOI

- Type of Manuscript
- LETTER

- Category
- Fault Tolerance

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Min-Sheng LIN, Ming-Sang CHANG, Deng-Jyi CHEN, "A Generalization of Consecutive k-out-of-n:G Systems" in IEICE TRANSACTIONS on Information,
vol. E83-D, no. 6, pp. 1309-1313, June 2000, doi: .

Abstract: A generalized class of consecutive-*k*-out-of-*n*:G systems, referred to as Con/*k*^{*}/*n*:G systems, is studied. A Con/*k*^{*}/*n*:G system has *n* ordered components and is good if and only if *k*_{i} good consecutive components that originate at component *i* are all good, where *k*_{i} is a function of *i*. Theorem 1 gives an *O*(*n*) time equation to compute the reliability of a linear system and Theorem 2 gives an *O*(*n*^{2}) time equation for a circular system. A distributed computing system with a linear (ring) topology is an example of such system. This application is very important, since for other classes of topologies, such as general graphs, planar graphs, series-parallel graphs, tree graphs, and star graphs, this problem has been proven to be *NP*-hard.

URL: https://global.ieice.org/en_transactions/information/10.1587/e83-d_6_1309/_p

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@ARTICLE{e83-d_6_1309,

author={Min-Sheng LIN, Ming-Sang CHANG, Deng-Jyi CHEN, },

journal={IEICE TRANSACTIONS on Information},

title={A Generalization of Consecutive k-out-of-n:G Systems},

year={2000},

volume={E83-D},

number={6},

pages={1309-1313},

abstract={A generalized class of consecutive-*k*-out-of-*n*:G systems, referred to as Con/*k*^{*}/*n*:G systems, is studied. A Con/*k*^{*}/*n*:G system has *n* ordered components and is good if and only if *k*_{i} good consecutive components that originate at component *i* are all good, where *k*_{i} is a function of *i*. Theorem 1 gives an *O*(*n*) time equation to compute the reliability of a linear system and Theorem 2 gives an *O*(*n*^{2}) time equation for a circular system. A distributed computing system with a linear (ring) topology is an example of such system. This application is very important, since for other classes of topologies, such as general graphs, planar graphs, series-parallel graphs, tree graphs, and star graphs, this problem has been proven to be *NP*-hard.},

keywords={},

doi={},

ISSN={},

month={June},}

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TY - JOUR

TI - A Generalization of Consecutive k-out-of-n:G Systems

T2 - IEICE TRANSACTIONS on Information

SP - 1309

EP - 1313

AU - Min-Sheng LIN

AU - Ming-Sang CHANG

AU - Deng-Jyi CHEN

PY - 2000

DO -

JO - IEICE TRANSACTIONS on Information

SN -

VL - E83-D

IS - 6

JA - IEICE TRANSACTIONS on Information

Y1 - June 2000

AB - A generalized class of consecutive-*k*-out-of-*n*:G systems, referred to as Con/*k*^{*}/*n*:G systems, is studied. A Con/*k*^{*}/*n*:G system has *n* ordered components and is good if and only if *k*_{i} good consecutive components that originate at component *i* are all good, where *k*_{i} is a function of *i*. Theorem 1 gives an *O*(*n*) time equation to compute the reliability of a linear system and Theorem 2 gives an *O*(*n*^{2}) time equation for a circular system. A distributed computing system with a linear (ring) topology is an example of such system. This application is very important, since for other classes of topologies, such as general graphs, planar graphs, series-parallel graphs, tree graphs, and star graphs, this problem has been proven to be *NP*-hard.

ER -