Truncation approach with the decomposition method for system reliability analysis

Yevkin, Olexandr

doi:10.1109/rams.2009.4914715

Cited by 8 publications

(9 citation statements)

References 15 publications

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“…For binary tree structures (fault and attack trees), BDD's have been applied to simplify the modeling threats on complex systems [1,4,5,17,18]. The common approach to determine probabilities on binary tree structures is to apply probability equations, such as those described in [6].…”

Section: Determining System Output Probabilitiesmentioning

confidence: 99%

Using Multiple-Valued Logic Decision Diagrams to Model System Threat Probabilities

Manikas

Thornton

Feinstein³

2011

2011 41st IEEE International Symposium on Multiple-Valued Logic

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Abstract-System security continues to be of increasing importance. To effectively address both natural and intentional threats to large systems, the threats must be cataloged and analyzed. Extremely large and complex systems can have an accordingly large number of threat scenarios. Simply listing the threats and devising countermeasures for each is ineffective and not efficient. We describe a threat cataloging methodology whereby a large number of threats can be efficiently cataloged and analyzed for common features. This allows countermeasures to be formulated that address a large number of threats that share common features. The methodology utilizes MultipleValued Logic for describing the state of a large system and a multiple-valued decision diagram (MDD) for the threat catalog and analysis.Large System Security, Threat cataloging, MDD

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Section: Determining System Output Probabilitiesmentioning

confidence: 99%

Using Multiple-Valued Logic Decision Diagrams to Model System Threat Probabilities

Manikas

Thornton

Feinstein³

2011

2011 41st IEEE International Symposium on Multiple-Valued Logic

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“…Minimal cut sets with higher order are discarded in the so‐called rare event approximation in static FT analysis because their contribution to the top event probability is small. A similar idea is used in the truncation approach in decomposition method . In case of Markov chain method, this approach is more complicated (especially for reparable system) and less efficient because the number of discarded states is much greater than in static FT.…”

Section: Approximate Markov Chain Methodsmentioning

confidence: 99%

An Efficient Approximate Markov Chain Method in Dynamic Fault Tree Analysis

Yevkin

2015

Qual. Reliab. Engng. Int.

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Approximate Markov chain method for dynamic fault tree analysis is suggested for both reparable and non‐reparable systems. The approximation is based on truncation, aggregation and elimination of Markov chain states during the process of dynamic fault tree transformation to corresponding Markov chain. The method is valid for small probabilities. For reparable systems, it is true if mean time to repair is much less than mean time to failure. Several examples are studied. Additional simplification is considered in case the system is in a steady state. Copyright © 2015 John Wiley & Sons, Ltd.

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“…Minimal cut sets with higher order are discarded in so called rare case approximation in static FT analysis because their contribution to the top event probability is neglectably small. Similar idea is used in truncation approach in decomposition method (Yevkin 2009). In case of MC method, this approach is more complicated and less efficient because the number of discarded states is relatively large if normalization of FT to minimal cut sets/sequences is not completed beforehand.…”

Section: Truncating MC Statesmentioning

confidence: 99%

Markov Chain method in dynamic fault tree with reparable components

Yevkin¹

2013

Safety, Reliability and Risk Analysis

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Markov Chain method for Dynamic Fault Tree with reparable components is discussed. The complexity of the problem and definition of dynamic gates is considered. Significant simplification of the method is suggested based on joining and truncation of Markov Chain states. The accuracy of approximation is based on assumption that Mean Time to Repair is much less than Mean Time to Failure. Several examples are studied.The second, joining approach is based on combining together states with the same set of failure events but with different order of their failures. We studied when the second approach is possible to apply without significant loss of accuracy of the calculation result. It is shown that both approximations are applicable if the Mean Time between Failure (MTBF) of the system is much less than Mean Time to Repair (MTTR). Obviously, this is the most important practical case. We illustrated the accuracy and efficiency of the approximate method with several examples. DYNAMIC GATES DEFINITION AND COMPLEXITY OF THE PROBLEMWe use MC method to define DGs with reparable components developing definition introduced earlier for DTF without reparable components (Dugan et al. 1992). We recognize that this approach has its limitations, compared, for example, to Monte Carlo method. In this paper we will be focused mostly on considering several significant simplifications of MC method under reasonable assumptions. Priority and gate (PAND)

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Truncation approach with the decomposition method for system reliability analysis

Cited by 8 publications

References 15 publications

Using Multiple-Valued Logic Decision Diagrams to Model System Threat Probabilities

Using Multiple-Valued Logic Decision Diagrams to Model System Threat Probabilities

An Efficient Approximate Markov Chain Method in Dynamic Fault Tree Analysis

Markov Chain method in dynamic fault tree with reparable components

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