A Recursive Algorithm for the Reliability of a Circular Connected-(r,s)-out-of-(m,n):F Lattice System with a Large Number of Rays

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  • 放射数が大きい場合の円筒型(r,s)-out-of-(m,n):F格子システムの信頼度計算方法
  • ホウシャスウ ガ オオキイ バアイ ノ エントウケイ r s out of m n F ゴウシ システム ノ シンライド ケイサン ホウホウ

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Abstract

A circular connected-(r,s)-out-of-(m,n):F lattice system is a two-dimensional version of a circular consecutive-k-out-of-n:F system. This system consists of m×n components arranged in a cylindrical grid. Each of the m circles has n components, and this system fails if and only if there exists a grid of size r×s with all failed components. A circular connected-(r,s)-out-of-(m,n):F lattice system may be used in reliability models of "feelers for measuring temperature on reaction chamber" and "TFT (thin film transistor) liquid crystal display systems with 360° wide area." Malinowski and Preuss (1995) and Yamamoto and Miyakawa (1996) independently proposed recursive algorithms for the reliability of a circular connected-(r,s)-out-of-(m,n):F lattice system based on the same idea. Recursive algorithms are effective when the system size is small or moderate, much more computing time and memory capacity are needed as the system size, especially n, becomes larger. Therefore, an efficient algorithm is needed for the reliability of a circular connected-(r,s)-out-of-(m,n):F lattice system when the system size, especially n, becomes large. In this study, we propose a new recursive algorithm for the reliability of a circular connected-(r,s)-out-of-(m,n):F lattice system. For evaluating the proposed algorithm, the orders of computing time and memory capacity are given. Furthermore, we carry out a numerical experiment to compare our proposed algorithm to the preceding algorithm. The results indicate that the proposed algorithm is an effective algorithm for systems with large n.

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