A combinatorial approach to modeling imperfect coverage

Doyle, S.A.; Dugan, J.B.; Patterson-Hine, F. A.

doi:10.1109/24.376525

Cited by 65 publications

(24 citation statements)

References 12 publications

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“…They are often modeled by multi-state systems with multistate components (or simply multi-state systems) in which levels of performance, reliability, safety, efficiency, power consumption, etc. are represented by more than two states [2], [3], [12], [14]- [16].…”

Section: Introductionmentioning

confidence: 99%

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Analysis Methods of Multi-state Systems Partially Having Dependent Components Using Multiple-Valued Decision Diagrams

Nagayama

Sasao

Butler

et al. 2014

2014 IEEE 44th International Symposium on Multiple-Valued Logic

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Abstract-In a large system, such as a water, gas, or electrical distribution system, degraded performance due to failures of components can be modeled as a set of discrete states interconnected by edges with weights that represent conditional probabilities. To establish such a model, we compute the conditional probabilities with multi-valued decision diagrams (MDDs). Since a typical decision diagram is large, the computation time is also large. In this paper, we propose an edge-valued MDD (EVMDD) based method to avoid unnecessary path traversals. The proposed method is a hybrid method of a path traversal method and a bottomup method that visits each node only once. By effectively combining both methods, we achieve a speed-up of the analysis by about 2.3 times for large systems compared to an existing method.Keywords-Multi-state systems with multi-state components; structure functions; system analysis based on decision diagrams; system analysis using conditional probabilities; EVMDDs.

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Section: Introductionmentioning

confidence: 99%

“…This reduces time complexity [2], [3] of the analysis. However, there exist systems, such as medical systems [7], in which states of components occur depending on other components.…”

Section: Introductionmentioning

confidence: 99%

Analysis Methods of Multi-state Systems Partially Having Dependent Components Using Multiple-Valued Decision Diagrams

Nagayama

Sasao

Butler

et al. 2014

2014 IEEE 44th International Symposium on Multiple-Valued Logic

View full text Add to dashboard Cite

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“…Although methods based on the Markov model [5], [8], [9], [19] can deal with probability distributions that depend on time, they are impractical for a large MSS. This is because their time complexity is O(m 3n ), where m is the number of states, and n is the number of components in an MDD [3], [4].…”

Section: Introductionmentioning

confidence: 99%

“…are represented by states. It is widely used to model various fault tolerant systems including computer server systems, telecommunication systems, water, gas, electrical power distribution systems, flight control systems, and nuclear power plant monitoring systems [3]- [5], [16], [19], [21], [23], [24]. To design dependable fault tolerant systems, intensive analysis of MSSs in terms of various assessment measures, such as reliability and availability is needed [16].…”

Section: Introductionmentioning

confidence: 99%

Edge Reduction for EVMDDs to Speed Up Analysis of Multi-state Systems

Nagayama

Sasao

Butler

et al. 2015

2015 IEEE International Symposium on Multiple-Valued Logic

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Abstract-This paper proposes a new reduction rule for edge-valued multi-valued decision diagrams (EVMDDs), which improves the speed of analysis of multi-state systems (MSSs). Existing reduction rules for decision diagrams remove redundant nodes, while the proposed rule removes redundant edges in EVMDDs. Since the time to do an analysis in an MSS depends on the number of edges in the EVMDD, the proposed rule is faster especially when used with edge minimization algorithms based on variable grouping. Experimental results show that the proposed rule reduces the number of edges by up to 30%, and this results in an analysis time that is reduced by up to 30%.

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“…Most of published works use Markov models (non-homogenous Markov or semi-Markov model) to solve multi-state problems [8]. However, it is difficult to find the correct model of a system and there will be a total of N = (m+1) n states if there are n modules in the system and each module has (m+1) states including the imperfect coverage state.…”

Section: Introductionmentioning

confidence: 99%