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A linear consecutive-*k*-out-of-*n*: F system is an ordered sequence of *n* components. This system fails if, and only if, *k* or more consecutive components fail. Optimal arrangement is one of the main problems for such kind of system. In this problem, we want to obtain an optimal arrangement of components to maximize system reliability, when all components of the system need not have equal component failure probability and all components are mutually statistically independent. As *n* becomes large, however, the amount of calculation would be too much to solve within a reasonable computing time even by using a high-performance computer. Hanafusa and Yamamoto proposed applying Genetic Algorithm (GA) to obtain quasi optimal arrangement in a linear consecutive-*k*-out-of-*n*: F system. GA is known as a powerful tool for solving many optimization problems. They also proposed ordinal representation, which produces only arrangements satisfying the necessary conditions for optimal arrangements and eliminates redundant arrangements with same system reliabilities produced by reversal of certain arrangements. In this paper, we propose an efficient GA. We have modified the previous work mentioned above to allocate components with low failure probabilities, that is to say reliable components, at equal intervals, because such arrangements seem to have relatively high system reliabilities. Through the numerical experiments, we observed that our proposed GA with interval *k* provides better solutions than the previous work for the most cases.

- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E92-A No.7 pp.1578-1584

- Publication Date
- 2009/07/01

- Publicized

- Online ISSN
- 1745-1337

- DOI
- 10.1587/transfun.E92.A.1578

- Type of Manuscript
- Special Section PAPER (Special Section on Recent Advances in Technologies for Assessing System Reliability)

- Category

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Koji SHINGYOCHI, Hisashi YAMAMOTO, "Efficient Genetic Algorithm for Optimal Arrangement in a Linear Consecutive-k-out-of-n: F System" in IEICE TRANSACTIONS on Fundamentals,
vol. E92-A, no. 7, pp. 1578-1584, July 2009, doi: 10.1587/transfun.E92.A.1578.

Abstract: A linear consecutive-*k*-out-of-*n*: F system is an ordered sequence of *n* components. This system fails if, and only if, *k* or more consecutive components fail. Optimal arrangement is one of the main problems for such kind of system. In this problem, we want to obtain an optimal arrangement of components to maximize system reliability, when all components of the system need not have equal component failure probability and all components are mutually statistically independent. As *n* becomes large, however, the amount of calculation would be too much to solve within a reasonable computing time even by using a high-performance computer. Hanafusa and Yamamoto proposed applying Genetic Algorithm (GA) to obtain quasi optimal arrangement in a linear consecutive-*k*-out-of-*n*: F system. GA is known as a powerful tool for solving many optimization problems. They also proposed ordinal representation, which produces only arrangements satisfying the necessary conditions for optimal arrangements and eliminates redundant arrangements with same system reliabilities produced by reversal of certain arrangements. In this paper, we propose an efficient GA. We have modified the previous work mentioned above to allocate components with low failure probabilities, that is to say reliable components, at equal intervals, because such arrangements seem to have relatively high system reliabilities. Through the numerical experiments, we observed that our proposed GA with interval *k* provides better solutions than the previous work for the most cases.

URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E92.A.1578/_p

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@ARTICLE{e92-a_7_1578,

author={Koji SHINGYOCHI, Hisashi YAMAMOTO, },

journal={IEICE TRANSACTIONS on Fundamentals},

title={Efficient Genetic Algorithm for Optimal Arrangement in a Linear Consecutive-k-out-of-n: F System},

year={2009},

volume={E92-A},

number={7},

pages={1578-1584},

abstract={A linear consecutive-*k*-out-of-*n*: F system is an ordered sequence of *n* components. This system fails if, and only if, *k* or more consecutive components fail. Optimal arrangement is one of the main problems for such kind of system. In this problem, we want to obtain an optimal arrangement of components to maximize system reliability, when all components of the system need not have equal component failure probability and all components are mutually statistically independent. As *n* becomes large, however, the amount of calculation would be too much to solve within a reasonable computing time even by using a high-performance computer. Hanafusa and Yamamoto proposed applying Genetic Algorithm (GA) to obtain quasi optimal arrangement in a linear consecutive-*k*-out-of-*n*: F system. GA is known as a powerful tool for solving many optimization problems. They also proposed ordinal representation, which produces only arrangements satisfying the necessary conditions for optimal arrangements and eliminates redundant arrangements with same system reliabilities produced by reversal of certain arrangements. In this paper, we propose an efficient GA. We have modified the previous work mentioned above to allocate components with low failure probabilities, that is to say reliable components, at equal intervals, because such arrangements seem to have relatively high system reliabilities. Through the numerical experiments, we observed that our proposed GA with interval *k* provides better solutions than the previous work for the most cases.},

keywords={},

doi={10.1587/transfun.E92.A.1578},

ISSN={1745-1337},

month={July},}

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TY - JOUR

TI - Efficient Genetic Algorithm for Optimal Arrangement in a Linear Consecutive-k-out-of-n: F System

T2 - IEICE TRANSACTIONS on Fundamentals

SP - 1578

EP - 1584

AU - Koji SHINGYOCHI

AU - Hisashi YAMAMOTO

PY - 2009

DO - 10.1587/transfun.E92.A.1578

JO - IEICE TRANSACTIONS on Fundamentals

SN - 1745-1337

VL - E92-A

IS - 7

JA - IEICE TRANSACTIONS on Fundamentals

Y1 - July 2009

AB - A linear consecutive-*k*-out-of-*n*: F system is an ordered sequence of *n* components. This system fails if, and only if, *k* or more consecutive components fail. Optimal arrangement is one of the main problems for such kind of system. In this problem, we want to obtain an optimal arrangement of components to maximize system reliability, when all components of the system need not have equal component failure probability and all components are mutually statistically independent. As *n* becomes large, however, the amount of calculation would be too much to solve within a reasonable computing time even by using a high-performance computer. Hanafusa and Yamamoto proposed applying Genetic Algorithm (GA) to obtain quasi optimal arrangement in a linear consecutive-*k*-out-of-*n*: F system. GA is known as a powerful tool for solving many optimization problems. They also proposed ordinal representation, which produces only arrangements satisfying the necessary conditions for optimal arrangements and eliminates redundant arrangements with same system reliabilities produced by reversal of certain arrangements. In this paper, we propose an efficient GA. We have modified the previous work mentioned above to allocate components with low failure probabilities, that is to say reliable components, at equal intervals, because such arrangements seem to have relatively high system reliabilities. Through the numerical experiments, we observed that our proposed GA with interval *k* provides better solutions than the previous work for the most cases.

ER -