Efficient Algorithm for the Reliability of a 2-Dimensional Cylindrical k-within-Consecutive-(r, s)-out-of-(m, n):F System

Hisashi YAMAMOTO; Tomoaki AKIBA

Efficient Algorithm for the Reliability of a 2-Dimensional Cylindrical k-within-Consecutive-(r, s)-out-of-(m, n):F System

Hisashi YAMAMOTO, Tomoaki AKIBA

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A 2-dimensional cylindrical k-within-consecutive-(r, s)-out-of-(m, n):F system consists of m n components arranged on a cylindrical grid. Each of m circles has n components, and this system fails if and only if there exists a grid of size r s within which at least k components are failed. This system may be used into reliability models of "Feelers for measuring temperature on reaction chamber," "TFT Liquid Crystal Display system with 360 degree wide area" and others. In this paper, first, we propose an efficient algorithm for the reliability of a 2-dimensional cylindrical k-within-consecutive-(r, s)-out-of-(m, n):F system. The feature of this algorithm is calculating their system reliabilities with shorter computing time and smaller memory size than Akiba and Yamamoto. Next, we show some numerical examples so that our proposed algorithm is more effective than Akiba and Yamamoto for systems with large n.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E87-A No.5 pp.1251-1257

Publication Date: 2004/05/01

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Type of Manuscript: PAPER

Category: Reliability, Maintainability and Safety Analysis

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Hisashi YAMAMOTO, Tomoaki AKIBA, "Efficient Algorithm for the Reliability of a 2-Dimensional Cylindrical k-within-Consecutive-(r, s)-out-of-(m, n):F System" in IEICE TRANSACTIONS on Fundamentals, vol. E87-A, no. 5, pp. 1251-1257, May 2004, doi: .
Abstract: A 2-dimensional cylindrical k-within-consecutive-(r, s)-out-of-(m, n):F system consists of m n components arranged on a cylindrical grid. Each of m circles has n components, and this system fails if and only if there exists a grid of size r s within which at least k components are failed. This system may be used into reliability models of "Feelers for measuring temperature on reaction chamber," "TFT Liquid Crystal Display system with 360 degree wide area" and others. In this paper, first, we propose an efficient algorithm for the reliability of a 2-dimensional cylindrical k-within-consecutive-(r, s)-out-of-(m, n):F system. The feature of this algorithm is calculating their system reliabilities with shorter computing time and smaller memory size than Akiba and Yamamoto. Next, we show some numerical examples so that our proposed algorithm is more effective than Akiba and Yamamoto for systems with large n.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e87-a_5_1251/_p

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@ARTICLE{e87-a_5_1251,
author={Hisashi YAMAMOTO, Tomoaki AKIBA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Efficient Algorithm for the Reliability of a 2-Dimensional Cylindrical k-within-Consecutive-(r, s)-out-of-(m, n):F System},
year={2004},
volume={E87-A},
number={5},
pages={1251-1257},
abstract={A 2-dimensional cylindrical k-within-consecutive-(r, s)-out-of-(m, n):F system consists of m n components arranged on a cylindrical grid. Each of m circles has n components, and this system fails if and only if there exists a grid of size r s within which at least k components are failed. This system may be used into reliability models of "Feelers for measuring temperature on reaction chamber," "TFT Liquid Crystal Display system with 360 degree wide area" and others. In this paper, first, we propose an efficient algorithm for the reliability of a 2-dimensional cylindrical k-within-consecutive-(r, s)-out-of-(m, n):F system. The feature of this algorithm is calculating their system reliabilities with shorter computing time and smaller memory size than Akiba and Yamamoto. Next, we show some numerical examples so that our proposed algorithm is more effective than Akiba and Yamamoto for systems with large n.},
keywords={},
doi={},
ISSN={},
month={May},}

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TY - JOUR
TI - Efficient Algorithm for the Reliability of a 2-Dimensional Cylindrical k-within-Consecutive-(r, s)-out-of-(m, n):F System
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1251
EP - 1257
AU - Hisashi YAMAMOTO
AU - Tomoaki AKIBA
PY - 2004
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E87-A
IS - 5
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - May 2004
AB - A 2-dimensional cylindrical k-within-consecutive-(r, s)-out-of-(m, n):F system consists of m n components arranged on a cylindrical grid. Each of m circles has n components, and this system fails if and only if there exists a grid of size r s within which at least k components are failed. This system may be used into reliability models of "Feelers for measuring temperature on reaction chamber," "TFT Liquid Crystal Display system with 360 degree wide area" and others. In this paper, first, we propose an efficient algorithm for the reliability of a 2-dimensional cylindrical k-within-consecutive-(r, s)-out-of-(m, n):F system. The feature of this algorithm is calculating their system reliabilities with shorter computing time and smaller memory size than Akiba and Yamamoto. Next, we show some numerical examples so that our proposed algorithm is more effective than Akiba and Yamamoto for systems with large n.
ER -