Bayesian Importance Measure-Based Approach for Optimal Redundancy Assignment

Bhattacharya, Debasis; Roychowdhury, Soma

doi:10.1080/01966324.2016.1203850

Cited by 4 publications

(5 citation statements)

References 9 publications

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“…In the context of K-terminal network reliability, applying equations (10) and (12) to equation (16), we have…”

Section: Spectrum Representation For Raw and Rrw Of An Individual Edgementioning

confidence: 99%

“…Hence, the summation for k is from 0 to n 2 2 and B(k + 2, 1 i , 1 j ) will substitute for B(k, 1 i , 1 j ). Moreover, in the context of K-terminal network reliability, by substituting equations (20) and (10) into equation (19), we can write…”

Section: Spectrum Representation For Raw and Rrw With Pair Of Edgesmentioning

confidence: 99%

“…In equation (24), since the state of the pair of edges (i, j) is known and they are down, the summation for k is from 1 to n 2 2. Moreover, by substituting equations (10) and (24) into equation (23), under the context of Kterminal network reliability, we can get RRW(i, j) = =…”

Section: Example 4 Considering the Network Depicted Inmentioning

confidence: 99%

“…The IMs produce numerical indexes to determine which edges are more critical for network failure or more important with respect to network reliability improvement. Many different IMs are proposed and investigated by researchers, including Birnbaum IM, [3][4][5] Fussell-Vesely (FV) IM, [6][7][8] Bayesian IM, 9,10 reliability achievement worth (RAW), 11 and reliability reduction worth (RRW). 12 Furthermore, Page and Perry 13 exploited the reliability polynomial to quantify the importance of individual edge based on its impact on network reliability.…”

Section: Introductionmentioning

confidence: 99%

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Evaluating network importance measures based on the construction spectrum

Pan

et al. 2019

Advances in Mechanical Engineering

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The construction spectrum is a useful tool to investigate the network reliability, which only depends on network structure and is called structure invariant. Importance measures are efficient tools to quantify and rank the impact of edges within a network. This study considers the K-terminal network with n edges and assumes that edges fail with an equal probability. The article focuses on investigating the importance measures of individual edge for the K-terminal network, including reliability achievement worth and reliability reduction worth, via the construction spectrum-based method. Generally, we establish the equations for reliability achievement worth and reliability reduction worth using the construction spectrum and determine the conditions under which the importance rankings generated by reliability achievement worth and reliability reduction worth only depend on the network structure through the construction spectrum. Similar results are obtained with reliability achievement worth and reliability reduction worth for pair of edges. A construction spectrum-based Monte-Carlo simulation is used to estimate reliability achievement worth and reliability reduction worth. Finally, a numerical example is presented to illustrate the application of these measures.

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“…In the context of K-terminal network reliability, applying equations (10) and (12) to equation (16), we have…”

Section: Spectrum Representation For Raw and Rrw Of An Individual Edgementioning

confidence: 99%

Section: Spectrum Representation For Raw and Rrw With Pair Of Edgesmentioning

confidence: 99%

Section: Example 4 Considering the Network Depicted Inmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Evaluating network importance measures based on the construction spectrum

Pan

et al. 2019

Advances in Mechanical Engineering

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show abstract

“…There are many other kinds of importance measures for binary systems such as the Fussell-Vesely importance, 13 the criticality importance, 14 and the Bayesian reliability importance. 15 Among all of the importance measures, the Birnbaum importance (BI) is so essential and widespread that plenty of extensions have been developed based on the importance measure. 16,17 For reconfigurable systems, importance measures are also used to investigate the CAP and find the optimal configuration.…”

Section: Introductionmentioning

confidence: 99%

Maintenance optimization of reconfigurable systems based on multi-objective Birnbaum importance

Wang

Cai

et al. 2020

Proceedings of the Institution of Mechanical Engineers, Part O:

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Reconfigurable systems can meet the changing requirements of system performance by several approaches, such as adjusting the system structure, improving the component performance, and reassigning components. However, it is also challengeable to find a cost-effective maintenance scheme by integrating these maintenance approaches. This article investigates the multi-objective maintenance optimization problem for reconfigurable systems with the consideration of maintenance cost and system reliability. First, the multi-objective maintenance optimization model is established to maximize the system reliability and minimize the total maintenance cost considering the constraints on budget and system performance. Second, a multi-objective Birnbaum importance is proposed to quantify the contribution of the individual component to the system reliability. The multi-objective Birnbaum importance–based non-dominated sorting genetic algorithm II is developed to obtain the optimal maintenance scheme with the maximum system reliability and minimum maintenance cost. Finally, the performance of multi-objective Birnbaum importance–based non-dominated sorting genetic algorithm II is proved by three numerical experiments. Experiment 1 verifies the advantage of multi-objective Birnbaum importance compared with Birnbaum importance to improve the system reliability in direct maintenance. Experiment 2 shows that the effectiveness of multi-objective Birnbaum importance is much better than that of the Birnbaum importance to enhance the performance of non-dominated sorting genetic algorithm II in comprehensive maintenance. Experiment 3 illustrates that the performance of multi-objective Birnbaum importance–based non-dominated sorting genetic algorithm II is better than that of other multi-objective algorithms combining with multi-objective Birnbaum importance.

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Recent advances in system reliability optimization driven by importance measures

Zhao

Cai

et al. 2020

Front. Eng. Manag.

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Bayesian Importance Measure-Based Approach for Optimal Redundancy Assignment

Cited by 4 publications

References 9 publications

Evaluating network importance measures based on the construction spectrum

Evaluating network importance measures based on the construction spectrum

Maintenance optimization of reconfigurable systems based on multi-objective Birnbaum importance

Recent advances in system reliability optimization driven by importance measures

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