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In the field of reliability engineering, many studies on the relationship of reliability between components and the entire system have been conducted since the 1960s. Various properties of large-scale systems can be studied by limit theorems. In addition, the limit theorem can provide an approximate system reliability. Existing studies have established the limit theorems of a connected-(*r*, *s*)-out-of-(*m*, *n*):F lattice system consisting of components with the same reliability. However, the existing limit theorems are constrained in terms of (a) the system shape and (b) the condition under which the theorem can be applied. Therefore, this study generalizes the existing limit theorems along the two aforementioned directions. The limit theorem established in this paper can be useful for revealing the properties of the reliability of a large-scale connected-(*r*, *s*)-out-of-(*m*, *n*):F lattice system.

- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E105-A No.3 pp.562-570

- Publication Date
- 2022/03/01

- Publicized
- 2021/09/13

- Online ISSN
- 1745-1337

- DOI
- 10.1587/transfun.2020EAP1145

- Type of Manuscript
- PAPER

- Category
- Reliability, Maintainability and Safety Analysis

Koki YAMADA

Tokyo Metropolitan University

Taishin NAKAMURA

Tokai University

Hisashi YAMAMOTO

Tokyo Metropolitan University

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Koki YAMADA, Taishin NAKAMURA, Hisashi YAMAMOTO, "Generalization of Limit Theorems for Connected-(r, s)-out-of- (m, n):F Lattice Systems" in IEICE TRANSACTIONS on Fundamentals,
vol. E105-A, no. 3, pp. 562-570, March 2022, doi: 10.1587/transfun.2020EAP1145.

Abstract: In the field of reliability engineering, many studies on the relationship of reliability between components and the entire system have been conducted since the 1960s. Various properties of large-scale systems can be studied by limit theorems. In addition, the limit theorem can provide an approximate system reliability. Existing studies have established the limit theorems of a connected-(*r*, *s*)-out-of-(*m*, *n*):F lattice system consisting of components with the same reliability. However, the existing limit theorems are constrained in terms of (a) the system shape and (b) the condition under which the theorem can be applied. Therefore, this study generalizes the existing limit theorems along the two aforementioned directions. The limit theorem established in this paper can be useful for revealing the properties of the reliability of a large-scale connected-(*r*, *s*)-out-of-(*m*, *n*):F lattice system.

URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2020EAP1145/_p

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@ARTICLE{e105-a_3_562,

author={Koki YAMADA, Taishin NAKAMURA, Hisashi YAMAMOTO, },

journal={IEICE TRANSACTIONS on Fundamentals},

title={Generalization of Limit Theorems for Connected-(r, s)-out-of- (m, n):F Lattice Systems},

year={2022},

volume={E105-A},

number={3},

pages={562-570},

abstract={In the field of reliability engineering, many studies on the relationship of reliability between components and the entire system have been conducted since the 1960s. Various properties of large-scale systems can be studied by limit theorems. In addition, the limit theorem can provide an approximate system reliability. Existing studies have established the limit theorems of a connected-(*r*, *s*)-out-of-(*m*, *n*):F lattice system consisting of components with the same reliability. However, the existing limit theorems are constrained in terms of (a) the system shape and (b) the condition under which the theorem can be applied. Therefore, this study generalizes the existing limit theorems along the two aforementioned directions. The limit theorem established in this paper can be useful for revealing the properties of the reliability of a large-scale connected-(*r*, *s*)-out-of-(*m*, *n*):F lattice system.},

keywords={},

doi={10.1587/transfun.2020EAP1145},

ISSN={1745-1337},

month={March},}

Copy

TY - JOUR

TI - Generalization of Limit Theorems for Connected-(r, s)-out-of- (m, n):F Lattice Systems

T2 - IEICE TRANSACTIONS on Fundamentals

SP - 562

EP - 570

AU - Koki YAMADA

AU - Taishin NAKAMURA

AU - Hisashi YAMAMOTO

PY - 2022

DO - 10.1587/transfun.2020EAP1145

JO - IEICE TRANSACTIONS on Fundamentals

SN - 1745-1337

VL - E105-A

IS - 3

JA - IEICE TRANSACTIONS on Fundamentals

Y1 - March 2022

AB - In the field of reliability engineering, many studies on the relationship of reliability between components and the entire system have been conducted since the 1960s. Various properties of large-scale systems can be studied by limit theorems. In addition, the limit theorem can provide an approximate system reliability. Existing studies have established the limit theorems of a connected-(*r*, *s*)-out-of-(*m*, *n*):F lattice system consisting of components with the same reliability. However, the existing limit theorems are constrained in terms of (a) the system shape and (b) the condition under which the theorem can be applied. Therefore, this study generalizes the existing limit theorems along the two aforementioned directions. The limit theorem established in this paper can be useful for revealing the properties of the reliability of a large-scale connected-(*r*, *s*)-out-of-(*m*, *n*):F lattice system.

ER -