Algorithm for Obtaining Optimal Arrangement of a Connected-(r,s)-out-of-(m,n): F System — The Case of m=r and s=2 —

Toru OMURA  Tomoaki AKIBA  Xiao XIAO  Hisashi YAMAMOTO  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E98-A   No.10   pp.2018-2024
Publication Date: 2015/10/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E98.A.2018
Type of Manuscript: Special Section PAPER (Special Section on Recent Developments on Reliability, Maintainability and Dependability)
2 dimensional consecutive-k system,  optimal arrangement,  branch and bound,  

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A connected-(r,s)-out-of-(m,n): F system is a kind of the connected-X-out-of-(m,n): F system defined by Boehme et al. [2]. A connected-(r,s)-out-of-(m,n): F system consists of m×n components arranged in (m,n)-matrix. This system fails if and only if there exists a grid of size r×s in which all components are failed. When m=r, this system can be regarded as a consecutive-s-out-of-n: F system, and then the optimal arrangement of this system satisfies theorem which stated by Malon [9] in the case of s=2. In this study, we proposed a new algorithm for obtaining optimal arrangement of the connected-(r,2)-out-of-(m,n): F system based on the above mentioned idea. We performed numerical experiments in order to compare the proposed algorithm with the algorithm of enumeration method, and calculated the order of the computation time of these two algorithms. The numerical experiments showed that the proposed algorithm was more efficiently than the algorithm of enumeration method.