Improved sampling plans for combinatorial invariants of coherent systems

Vaisman, Radislav, Kroese, Dirk P. and Gertsbakh, Ilya B. (2016) Improved sampling plans for combinatorial invariants of coherent systems. IEEE Transactions on Reliability, 65 1: 410-424. doi:10.1109/TR.2015.2446471


Author Vaisman, Radislav
Kroese, Dirk P.
Gertsbakh, Ilya B.
Title Improved sampling plans for combinatorial invariants of coherent systems
Journal name IEEE Transactions on Reliability   Check publisher's open access policy
ISSN 0018-9529
1558-1721
Publication date 2016-03
Sub-type Article (original research)
DOI 10.1109/TR.2015.2446471
Open Access Status Not Open Access
Volume 65
Issue 1
Start page 410
End page 424
Total pages 15
Place of publication Piscataway, NJ United States
Publisher Institute of Electrical and Electronics Engineers Inc.
Collection year 2017
Language eng
Abstract Terminal network reliability problems appear in many real-life applications, such as transportation grids, social and computer networks, communication systems, etc. In this paper, we focus on monotone binary systems with identical component reliabilities. The reliability of such systems depends only on the number of failure sets of all possible sizes, which is an essential system invariant. For large problems, no analytical solution for calculating this invariant in a reasonable time is known to exist, and one has to rely on different approximation techniques. An example of such a method is Permutation Monte Carlo. It is known that this simple plan is not sufficient for adequate estimation of network reliability due to the rare-event problem. As an alternative, we propose a different sampling strategy that is based on the recently pioneered Stochastic Enumeration algorithm for tree cost estimation. We show that, thanks to its built-in splitting mechanism, this method is able to deliver accurate results while employing a relatively modest sample size. Moreover, our numerical results indicate that the proposed sampling scheme is capable of solving problems that are far beyond the reach of the simple Permutation Monte Carlo approach.
Keyword System structure function
Network reliability
Permutation Monte Carlo
Rare events
Splitting
Stochastic enumeration
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
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Created: Sun, 17 Apr 2016, 00:15:50 EST by System User on behalf of School of Mathematics & Physics