Two-dimensional consecutive-k-out-of-n:F models

Salvia, Anthony A.; Lasher, William C.

doi:10.1109/24.103023

Cited by 97 publications

(35 citation statements)

References 4 publications

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“…The two-dimensional consecutive-k-out-of-n: F system, which was introduced by Salvia and Lasher [17] (see also [8, ll]), consists of n2 components arranged on a square grid of size n and fails, if and only if there exists at least one square grid of size k (2 5 k 5 n -1) that contains all failed components. Any square grid of size k is a minimal cut set, and applying Theorem 2.4, we immediately obtain the following: 2.2).…”

Section: Applicationsmentioning

confidence: 99%

Note: Pairwise rearrangements in reliability structures

Koutras

Papadopoulos

Papastavridis

1994

Naval Research Logistics

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Boland, Proschan, and Tong [2] used the notion of criticality of nodes in a coherent system to study the optimal component arrangement of reliability structures. They also provided a sufficient minimal cut (path) based criterion for verifying the criticality ordering of two nodes. We develop a necessary and sufficient condition for two nodes to be comparable and provide specific examples illustrating our result's applicability. As a corollary, certain optimal arrangement properties of well‐known systems are derived. © 1994 John Wiley & Sons, Inc.

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Section: Applicationsmentioning

confidence: 99%

Note: Pairwise rearrangements in reliability structures

Koutras

Papadopoulos

Papastavridis

1994

Naval Research Logistics

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“…In Tables 1-5 we present, for a variety of choices of n 1 , n 2 , k 1 , k 2 , p ij , the values of the bounds described in formulae (16), (17), (18), (20), (21), (23), (24) (they have been labeled as…”

Section: Applicationmentioning

confidence: 99%

“…It was first introduced by Salvia and Lasher (1990) who also discussed several practical applications of the system to real life problems.…”

Section: Applicationmentioning

confidence: 99%

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Generalized reliability bounds for coherent structures

Boutsikas

Koutras

2000

J. Appl. Probab.

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In this article we introduce generalizations of several well known reliability bounds. These bounds are based on arbitrary partitions of the family of minimal path or cut sets of the system and can be used for approximating the reliability of any coherent structure with iid components. An illustration is also given of how the general results can be applied for a specific reliability structure (two-dimensional consecutive-k 1 × k 2 -out-of-n 1 × n 2 system) along with extensive numerical calculations revealing that, in most cases, the generalized bounds perform better than other available bounds in the literature for this system.

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“…Various extensions of the system have been studied. For example, Salvia and Lasher (1990) proposed 2-dimensional consecutive-k-out-ofn:F models in which occurrences of patterns are investigated. Further, some kinds of linear and circular lattice systems were studied by Boehme et al (1992).…”

Section: Introductionmentioning

confidence: 99%

Exact Distributions of the Number of Pattern Occurrences in Undirected Graphical Models

Aki

Inoue

2012

JJSS

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The method of probability generating functions is extended for obtaining exact distributions of the number of occurrences of a discrete pattern in undirected graphical models. General results for deriving the distributions are given with illustrative examples. Further, a device for reducing calculations is proposed. It works effectively when the graphical model is relatively simple. An algorithm for obtaining the distributions including the device is also given. In order to show the feasibility of our method, exact distributions of the number of occurrences of a "1"-run are derived in two undirected graphical models whose vertices are allocated on a sphere and a torus, respectively. As an application of our results, the exact reliabilities of consecutive-k-out-of-n:F systems corresponding to the undirected graphical models are obtained.

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Two-dimensional consecutive-k-out-of-n:F models

Cited by 97 publications

References 4 publications

Note: Pairwise rearrangements in reliability structures

Note: Pairwise rearrangements in reliability structures

Generalized reliability bounds for coherent structures

Exact Distributions of the Number of Pattern Occurrences in Undirected Graphical Models

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