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Network reliability evaluation

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Abstract This article, beyond presenting a spectrum of network reliability methods studied in the past decades, describes a scalable innovative ‘overlap technique’ to tackle large complex networks' reliability evaluation difficulties, which cannot be handled by straightforward reliability block diagramming (RBD) techniques used for the simple parallel‐series topologies. Examples are shown on how to apply the overlap algorithm to compute the ingress‐egress reliability. Monte Carlo simulations demonstrate the methods discussed. (1) Static (time independent), (2) dynamic (time dependent) using a versatile Weibull distribution to represent the multiple stages of network components from infancy to useful life period and to wear‐out, and (3) multistate versions to include derated behavior beyond conventional working and nonworking states, are illustrated for calculating the directional source‐target (s‐t) reliability of complex networks by using the Java software ERBDC: Exact Reliability Block Diagramming Calculator. Copyright © 2010 John Wiley & Sons, Inc. This article is categorized under: Statistical and Graphical Methods of Data Analysis > Reliability, Survivability, and Quality Control

Example 1: five‐node/two‐path static network.

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Fifty‐two node Weibull results graphical comparison.

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Example 14: 52‐node Weibull network, s = 1, t = 52.

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Nineteen‐node Weibull results for graphical comparison.

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Linear graph for 1/α.

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Linear graph for β.

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Exponential graph for β.

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Example 13: 19‐node Weibull network.

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Weibull reliability distributions.

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Example 12: implementation of multistate overlap reliability to 52‐node network in 18 s. Solution (s = 1, t = 52): full reliability = 0.05, derated reliability = 0.51, full unreliability = 0.44.

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Example 11: implementation of multistate overlap reliability to 19‐node network in 1.26 s. Solution (s = 1, t = 19): full reliability = 0.36, derated reliability = 0.43, full unreliability = 0.21.

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Example 10: power plant with four multiple derated turbines (nodes 1 to 4) in parallel and a transformer (egress node 5) in series, and node 0 (as an ingress dummy node with full reliability).

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Example 9: active parallel–series system with doubly derated states for 2 and 3.

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Example 8: a simple parallel–series system with single derated states.

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Example 7: active parallel system with IN(1) and OUT(4) full reliability; others(2,3) are derated.

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Example 6: simple series system with a derated state.

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Example 5: Simulation for (s = 1, t = 52) with 72 links is 0.558 in 17,119 s. The faster analytical result is 0.556 in 18.034 s in 0.1% of the much longer simulation time. The more simulation runs are conducted, the closer the analytical and simulation results will converge to each other.

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Example 4: 19‐node (s = 1, t = 19) complex network with Monte Carlo simulation (83 s) and analytical results (50 s), both 0.784 with simulation taking 33 s more.

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Example 3: eight‐node/nine‐path static network with s = 7, t = 8.

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Example 2: six‐node network without including link reliabilities ( = 1.0) and (s=1, t=6) solution.

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Statistical and Graphical Methods of Data Analysis > Reliability, Survivability, and Quality Control

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