research-article

Static Network Reliability Estimation under the Marshall-Olkin Copula

Authors:

Zdravko I. Botev,

Pierre L'Ecuyer,

Richard Simard,

Bruno TuffinAuthors Info & Claims

ACM Transactions on Modeling and Computer Simulation (TOMACS), Volume 26, Issue 2

Article No.: 14, Pages 1 - 28

https://doi.org/10.1145/2775106

Published: 13 January 2016 Publication History

Abstract

In a static network reliability model, one typically assumes that the failures of the components of the network are independent. This simplifying assumption makes it possible to estimate the network reliability efficiently via specialized Monte Carlo algorithms. Hence, a natural question to consider is whether this independence assumption can be relaxed while still attaining an elegant and tractable model that permits an efficient Monte Carlo algorithm for unreliability estimation. In this article, we provide one possible answer by considering a static network reliability model with dependent link failures, based on a Marshall-Olkin copula, which models the dependence via shocks that take down subsets of components at exponential times, and propose a collection of adapted versions of permutation Monte Carlo (PMC, a conditional Monte Carlo method), its refinement called the turnip method, and generalized splitting (GS) methods to estimate very small unreliabilities accurately under this model. The PMC and turnip estimators have bounded relative error when the network topology is fixed while the link failure probabilities converge to 0, whereas GS does not have this property. But when the size of the network (or the number of shocks) increases, PMC and turnip eventually fail, whereas GS works nicely (empirically) for very large networks, with over 5,000 shocks in our examples.

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Cited By

Cancela HMurray LRubino G(2024)Robust Implementation of Permutation Monte Carlo for Network Reliability Estimation2024 L Latin American Computer Conference (CLEI)10.1109/CLEI64178.2024.10700448(1-8)Online publication date: 12-Aug-2024
https://doi.org/10.1109/CLEI64178.2024.10700448
Lagos GBarrera JRomero PValencia J(2024)Limiting Behavior of Mixed Coherent Systems With Lévy‐Frailty Marshall–Olkin Failure TimesApplied Stochastic Models in Business and Industry10.1002/asmb.289340:5(1229-1244)Online publication date: 8-Oct-2024
https://doi.org/10.1002/asmb.2893
Mai JBlagoeva AScherer M(2023)A Stochastic gradient descent algorithm to maximize power utility of large credit portfolios under Marshall–Olkin dependenceFrontiers of Mathematical Finance10.3934/fmf.2023020(0-0)Online publication date: 2023
https://doi.org/10.3934/fmf.2023020
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Index Terms

Static Network Reliability Estimation under the Marshall-Olkin Copula
1. Computing methodologies
  1. Modeling and simulation
2. Mathematics of computing
  1. Probability and statistics

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Published In

cover image ACM Transactions on Modeling and Computer Simulation

ACM Transactions on Modeling and Computer Simulation Volume 26, Issue 2

January 2016

152 pages

ISSN:1049-3301

EISSN:1558-1195

DOI:10.1145/2875131

Editor:
Adelinde M. Uhrmacher
University of Rostock, Germany

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Copyright © 2016 ACM.

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Association for Computing Machinery

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Publication History

Published: 13 January 2016

Accepted: 01 May 2015

Revised: 01 April 2015

Received: 01 December 2014

Published in TOMACS Volume 26, Issue 2

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Australian Research Council
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NSERC-Canada Discovery Grant
Faculty of Science Visiting Researcher Award at UNSW

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Cited By

Cancela HMurray LRubino G(2024)Robust Implementation of Permutation Monte Carlo for Network Reliability Estimation2024 L Latin American Computer Conference (CLEI)10.1109/CLEI64178.2024.10700448(1-8)Online publication date: 12-Aug-2024
https://doi.org/10.1109/CLEI64178.2024.10700448
Lagos GBarrera JRomero PValencia J(2024)Limiting Behavior of Mixed Coherent Systems With Lévy‐Frailty Marshall–Olkin Failure TimesApplied Stochastic Models in Business and Industry10.1002/asmb.289340:5(1229-1244)Online publication date: 8-Oct-2024
https://doi.org/10.1002/asmb.2893
Mai JBlagoeva AScherer M(2023)A Stochastic gradient descent algorithm to maximize power utility of large credit portfolios under Marshall–Olkin dependenceFrontiers of Mathematical Finance10.3934/fmf.2023020(0-0)Online publication date: 2023
https://doi.org/10.3934/fmf.2023020
Cancela HMurray LRubino G(2023)Reliability Estimation for Stochastic Flow Networks With Dependent ArcsIEEE Transactions on Reliability10.1109/TR.2022.317841372:2(622-636)Online publication date: Jun-2023
https://doi.org/10.1109/TR.2022.3178413
Gibson LKroese D(2022)Rare-Event Simulation via Neural NetworksAdvances in Modeling and Simulation10.1007/978-3-031-10193-9_8(151-168)Online publication date: 1-Dec-2022
https://doi.org/10.1007/978-3-031-10193-9_8
Größer JOkhrin O(2022)CopulaeWIREs Computational Statistics10.1002/wics.155714:3Online publication date: 12-May-2022
https://dl.acm.org/doi/10.1002/wics.1557
Barrera JMoreno EMuñoz GRomero P(2022)Exact reliability optimization for series‐parallel graphs using convex envelopesNetworks10.1002/net.2208980:2(235-248)Online publication date: 27-Jan-2022
https://doi.org/10.1002/net.22089
Cancela HMurray LRobledo FRomero PSartor P(2021)On the reliability estimation of stochastic binary systemsInternational Transactions in Operational Research10.1111/itor.1303429:3(1688-1722)Online publication date: 28-Jul-2021
https://doi.org/10.1111/itor.13034
Barrera JLagos G(2020)Limit distributions of the upper order statistics for the Lévy-frailty Marshall-Olkin distributionExtremes10.1007/s10687-020-00386-zOnline publication date: 7-Aug-2020
https://doi.org/10.1007/s10687-020-00386-z
Cancela HMurray LRubino G(2019)Efficient Estimation of Stochastic Flow Network ReliabilityIEEE Transactions on Reliability10.1109/TR.2019.289732268:3(954-970)Online publication date: Sep-2019
https://doi.org/10.1109/TR.2019.2897322
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