Generalized reliability bounds for coherent structures

Boutsikas, Michael V.; Koutras, Markos V.

doi:10.1017/s0021900200015990

Cited by 7 publications

(13 citation statements)

References 20 publications

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“…Since C ij , i = 1, 2, ..., N 1 , j = 1, 2, ..., N 2 are disjoint and satisfy (9), they form a partition of the family C of system's minimal cut sets. As Boutsikas and Koutras [3] have proven (cf. Theorem 2) the quantity…”

Section: Propositionmentioning

confidence: 73%

“…Recalling once more the partition described in the proof of Proposition 2 and applying Corollary 1 of Boutsikas and Koutras [3] (the optimum choice of the required binary functions a s should be invoked) we readily obtain the upper bound…”

Section: Propositionmentioning

confidence: 99%

“…A substantially better upper bound is provided by the next proposition which makes use of the generalized Fu and Koutras upper bound given in Boutsikas and Koutras [3].…”

Section: Propositionmentioning

confidence: 99%

“…The key tool for the construction of this bound is a general result given by Boutsikas and Koutras [3]; since the latter involves covariances of appropriate discrete random variables, the resulting upper bound will be referred as covariance bound. To start with, let us denote by B ab the set of all components (i, j) such that (i, j) < (a, b) (use lexicographic ordering) and…”

Section: Covariance Boundsmentioning

confidence: 99%

“…More specifically, Boutsikas and Koutras [3] introduced several generalizations of well-known reliability bounds based on arbitrary partitions of the family of minimal path or cut sets of a coherent structure. After the introduction of the necessary definitions and notations (Section 2) we proceed at the establishment of product-type upper and lower bounds for the cumulative distribution function of the scan statistic (Section 3).…”

Section: Introductionmentioning

confidence: 99%

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Bounds for the Distribution of Two-Dimensional Binary Scan Statistics

Boutsikas

Koutras

2003

Prob. Eng. Inf. Sci.

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In the present article we develop some efficient bounds for the distribution function of a two dimensional scan statistic defined on a (double) sequence of iid binary trials. The methodology employed here takes advantage of the connection between the scan statistic problem and a equivalent reliability structure and exploits appropriate techniques of reliability theory to establish tractable bounds for the distribution of the statistic of interest. An asymptotic result is established and a numerical study is carried out to investigate the efficiency of the suggested bounds.

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Section: Propositionmentioning

confidence: 73%

Section: Propositionmentioning

confidence: 99%

“…A substantially better upper bound is provided by the next proposition which makes use of the generalized Fu and Koutras upper bound given in Boutsikas and Koutras [3].…”

Section: Propositionmentioning

confidence: 99%

Section: Covariance Boundsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Bounds for the Distribution of Two-Dimensional Binary Scan Statistics

Boutsikas

Koutras

2003

Prob. Eng. Inf. Sci.

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Scan Statistics

Glaz¹

2007

Encyclopedia of Statistics in Quality and Reliability

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Scan statistics have been used extensively in several areas of science and technology to test for the occurrence of clusters of rare events. In this article we present a survey of results in the area of scan statistics that are applicable to quality control and reliability theory. In quality control, scan statistics have been used in the design and analysis of acceptance sampling schemes. We survey results that are useful in evaluating the operating characteristics of such sampling schemes. In reliability theory, scan statistics have been used in the analysis and design of a k ‐within‐consecutive‐ m ‐out‐of‐ n : F system of n components arranged in a linear or circular fashion. This system fails if k components fail within any segment of m consecutive components. In this article, we survey results for approximations and bounds for the system reliability of such systems. Two‐dimensional scan statistics have been used in the analysis and design of a k ‐within‐consecutive‐( m 1 , m 2 )‐out‐of‐( n 1 , n 2 ): F system of n 1 n 2 components arranged in an n 1 by n 2 rectangular or cylindrical lattice. This system fails if k components fail within an m 1 by m 2 rectangular subregion in the n 1 by n 2 lattice. We survey results for the approximations and bounds for system reliability of these systems. In material science, reliability of certain materials can be compromised by the appearance of a large number of microcracks in a small area or volume. We present a survey of two‐ and three‐dimensional scan statistics that have been used in analyzing the occurrences of such microcracks.

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On a class of multiple failure mode systems

Boutsikas

Koutras

2002

Naval Research Logistics

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The primary objective of this work is to introduce and perform a detailed study of a class of multistate reliability structures in which no ordering in the levels of components' performances is necessary. In particular, the present paper develops the basic theory (exact reliability formulae, reliability bounds, asymptotic results) that will make it feasible to investigate systems whose components are allowed to experience m ≥ 2 kinds of failure (failure modes) and their breakdown is described by different families of cut sets in each mode. For illustration purposes, two classical (binary) systems are extended to analogous multiple failure mode structures and their reliability performance (bounds and asymptotic behaviour) is investigated by numerical experimentation.

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Generalized reliability bounds for coherent structures

Cited by 7 publications

References 20 publications

Bounds for the Distribution of Two-Dimensional Binary Scan Statistics

Bounds for the Distribution of Two-Dimensional Binary Scan Statistics

Scan Statistics

On a class of multiple failure mode systems

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