Evaluation and Design Method for Multi-Dimensional Consecutive-k-systems

多维连续k系统的评估与设计方法

• 批准号: 14580483
• 负责人: YAMAMOTO Hisashi
• 金额: $ 1.66万
• 依托单位: Tokyo Metropolitan Institute of Technology
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2002
• 资助国家: 日本
• 起止时间: 2002 至 2004
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-14580483/
• 关键词: Consecutive-k-out-of-n: F system; Multidimensional system; Recursive Algorithm; System Reliability; Upper and Lower Bound; Approximate value; Limit Theorem

Multi-dimensional consecutive-k-systems consist of components arranged in a 2 or 3 dimensional space and fails when many components in a narrow space fail, but this system does not fail even if components fail in wide space. As the 2-dimensional oonsecutive-k-systems, we have connected-(r, s)-out-of-(m, n): F lattice system and 2-dimensional k-within-consecutive-(r, s)-out-of-(m, n) :F system. In this study, we proposed 3 dimensional systems as a type of consecutive-k-systems. These systems are applied to supervisory system for two or three dimensional space and so on.In this study, first, we proposed efficient algorithm for optimal arrangement of components in consecutive-k-out-of-n: F system, based on genetic algorithm or branch and bound algorithm. For multidimensional systems with medium size, recursive formulas for the reliabilities of some consecutive-k-systems were proposed and the efficiency of these algorithms were proven by the order of algorithm and the results of numerical experiments. For large systems, we proposed upper and lower bounds or approximate values of system reliabilities based on limit theorems. And we confirm the good fitness of these bounds or approximate values by numerical experiments. Furthermore, by using the above basic idea, we proposed recursive algorithm for performance index or reliability of network system.As the future works, we need to study more complex systems, for example, multi-states consecutive-k-systems, in order to research more systems in the real world.

多维的连续K系统由在2或3维空间中排列的组件组成，并且当狭窄空间中的许多组件失败时会失败，但是即使组件在较宽的空间中失败，该系统也不会失败。作为二维Oonsectection-K系统，我们已连接 - （r，s） - out-（m，n）：f晶格系统和二维k-Within-conseconesectectectect-（r，s） - （s） - out-（m，m，n）：f System：f System。在这项研究中，我们提出了3个维系统作为连续的K系统。这些系统适用于两个或三维空间的监督系统，等等。在这项研究中，首先，我们提出了基于基因算法或分支和绑定算法的N：F系统中组件的最佳布置的有效算法。对于具有中等大小的多维系统，提出了一些连续K-Systems的可靠性的递归公式，并通过算法顺序证明了这些算法的效率和数值实验的结果。对于大型系统，我们提出了基于极限定理的上限和下限或系统可靠性的近似值。我们通过数值实验证实了这些边界或近似值的良好适合度。此外，通过使用上述基本思想，我们提出了用于性能指数或网络系统可靠性的递归算法。在未来的工作中，我们需要研究更多复杂的系统，例如，多态连续系统，以研究更多的现实世界中的系统。

项目成果

T.Akiba, H.Yamamoto: "Approximate values of reliability of the 2-dimensional rectangular k-within-consecutive-(r, s)-out-of-(m, n):F system"the proceeding of Mathematical Methods in Reliability 2002. 23-26 (2002)

T.Akiba、H.Yamamoto：“二维矩形 k-within-consecutive-(r, s)-out-of-(m, n):F 系统的可靠性近似值”数学方法进展

Reliability of A 3-Dimensional Adjacent Triangle:F Triangular Lattice System

三维邻接三角形的可靠性：F三角晶格系统

• 发表时间: 2004
• 期刊: the proceeding of APIEMS'04 (CD-ROM)
• 作者: T.Akiba;H.Yamamoto;Y.Kainuma
• 通讯作者: Y.Kainuma

Evaluating methods for the reliability of a 2-dimensional cylindrical k-within-consecutive-(r,s)-out-of-(m,n):F system

二维圆柱k-连续-(r,s)-out-of-(m,n):F系统可靠性评估方法

• 发表时间: 2004
• 期刊: The Institute of Electronics, Information and Communication Engineering Vol.E87-A,No.5
• 作者: Hisashi Yamamoto;Tomoaki Akiba
• 通讯作者: Tomoaki Akiba

The ordinal representation for optimal arrangement problem in a circular consecutive-k-out-of-n: F system

循环连续 k-out-of-n: F 系统中最优排列问题的序数表示

• 发表时间: 2003
• 期刊: Multiconference on Systemics, Cybernetics and Informatics PROCEEDINGS, Volume XIV (Florida, USA)
• 作者: Hanafusa;Taku;Yamamoto;Hisashi;Kubo;Syun-Ichiro;Tsujimura;Yasuhiro
• 通讯作者: Yasuhiro

Approximate values of reliability of the 2-dimensional rectangular k-within-consecutive-(r, s)-out-of-(m, n) : F system

二维矩形 k-within-consecutive-(r, s)-out-of-(m, n) 的可靠性近似值：F 系统

• 发表时间: 2002
• 期刊: the proceeding of Mathematical Methods in Reliability 2002
• 作者: Akiba;Tomoaki;Yamamoto;Hisashi
• 通讯作者: Hisashi