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.

多维召唤-k-系统由排列在2维或3维空间中的组件组成，当狭窄空间中的许多组件失效时，该系统失效，但即使组件在宽空间中失效，该系统也不会失效。作为二维连续k-系统，我们给出了（r，s）-out-of-（m，n）：F格系统和二维k-within-continuous-（r，s）-out-of-（m，n）：F系统。在这项研究中，我们提出了3维系统作为一类召唤-k-系统。这些系统可应用于二维或三维空间的监控系统等。在本研究中，首先，我们提出了一种基于遗传算法或分支定界算法的n中取k：F召唤系统中元件优化排列的有效算法。对于中等规模的多维系统，给出了某些召唤k-系统可靠度的递推公式，并通过算法的阶数和数值实验结果证明了算法的有效性.对于大系统，基于极限定理给出了系统可靠度的上、下界或近似值。并通过数值实验证实了这些界或近似值的良好拟合性。进一步，利用上述基本思想，我们提出了网络系统性能指标或可靠性的递推算法。作为未来的工作，我们需要研究更复杂的系统，例如多状态的召唤-k-系统，以便研究真实的世界中更多的系统。

项目成果

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

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

(m,n)外圆连通(r,s)可靠性的递推算法:F大量射线格子系统

• 发表时间: 2004
• 期刊: Journal of Japan Industrial Management Association, (in Japanese) Vol.55, No. 3
• 作者: Yamamoto;Hisashi;Akiba;Tomoaki
• 通讯作者: Tomoaki

秋葉 知昭, 山本 久志: "システムサイズが大きい場合の円筒型k-within-(r,s)-out-of-(m,n) : Fシステムの信頼度評価方法"日本信頼性学会誌. Vol.25, No.5. 485-496 (2003)

Tomoaki Akiba、Hisashi Yamamoto：“系统规模较大时的圆柱 k-within-(r,s)-out-of-(m,n)：F 系统的可靠性评估方法”日本可靠性学会杂志，第 1 卷。 .25，第5号485-496（2003）

Evaluating methods for the reliability of a 3-Dimensional k-within-Consecutive-(r1, r2, r3)-out-of-(n1, n2, n3) : F System

评估 3 维 k-within-Consecutive-(r1, r2, r3)-out-of-(n1, n2, n3) 可靠性的方法：F 系统

• 发表时间: 2005
• 期刊: Journal of Quality in Maintenance Engineering (to appear)
• 作者: Akiba;Tomoaki;Yamamoto;Hisashi;Tsujimura;Yasuhiro
• 通讯作者: Yasuhiro

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