Bounds on Reliability of Larger Systems by Linear Programming with Delayed Column Generation

Byun, Ji-Eun; Song, Junho

doi:10.1061/(asce)em.1943-7889.0001717

Cited by 29 publications

(3 citation statements)

References 28 publications

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“…Next, these are used as the constraints for the LP problem defined for the target system event. Byun and Song (2020) proposed an LP bounds Computational time is not significantly affected by the level of the probability and modestly increases with the number of components and the correlation between the random variables.…”

Section: Methods For General Systemsmentioning

confidence: 99%

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Structural System Reliability: Overview of Theories and Applications to Optimization

Song

Kang

Lee

et al. 2021

ASCE-ASME J. Risk Uncertainty Eng. Syst., Part A: Civ. Eng.

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This paper provides an overview of theories and applications of structural system reliability (SSR). The paper defines SSR problems and discusses the growing needs for SSR analysis and technical challenges. Detailed literature reviews are provided for three subtopics: SSR methods for Boolean system events, SSR methods for sequential failures, and SSR-based design/topology optimization. Discussions of each subtopic define the target problem using mathematical formulations and categorize existing SSR methods in terms of the characteristics of the problems and approaches. The paper summarizes SSR methods that are considered critical in the history and have introduced notable technological developments in recent years. In each subtopic or category, the reviewed methods are compared with each other in terms of accuracy, computational efficiency, and implementation issues to allow identifying apposite methods for SSR applications. The paper concludes with remarks on future research needs and opportunities.

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Section: Methods For General Systemsmentioning

confidence: 99%

“…LP bounds method (Song and Der Kiureghian 2003;Der Kiureghian and Song 2008;Byun and Song 2020) Method provides the narrowest possible bounds for the given joint probability information.…”

Section: Time-variant System Reliability Analysis Methodsmentioning

confidence: 99%

Structural System Reliability: Overview of Theories and Applications to Optimization

Song

Kang

Lee

et al. 2021

ASCE-ASME J. Risk Uncertainty Eng. Syst., Part A: Civ. Eng.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Chang and Mori [46] developed a relaxed linear programming (RLP) bounds method while Chang et al [47] derived bounds on failure probability of k-out-of-n systems with the help of universal generating function and LP. Byun and Song [48] applied binary integer programming to tackle the problem of exponential rise in the number of variables in LP with system size. A recent overview of all these structural reliability estimation methods is available in Song, Kang, Lee and Chun [49].…”

Section: Introductionmentioning

confidence: 99%