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Solving dynamic flowgraph methodology models using binary decision diagrams

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  • Bjorkman, Kim

Abstract

Dynamic flowgraph methodology (DFM) is a computationally challenging approach to the reliability analysis of dynamic systems with feedback loops. To improve the computational efficiency of DFM modelling, we propose a new approach, based on binary decision diagrams (BDDs), to solving DFM models. The objective of DFM analysis is to identify the root causes of a postulated top event. The result is a set of prime implicants that represent system faults resulting from diverse combinations of software logic errors, hardware failures, human errors and adverse environmental conditions. Two approaches to solving prime implicants have been implemented in software called YADRAT. The first approach is based on meta-products, and the second on zero-suppressed BDDs (ZBDD). Both approaches have been used previously in fault tree analysis. In this work, the ideas of prime implicant computations are adapted to a dynamic reliability analysis approach combined with multi-valued logic. The computational efforts required for the two approaches are compared by analysing three example systems. The results of the comparison show that BDDs are applicable in DFM computation and that in particular the ZBDD-based approach can solve moderately sized DFM models in a reasonable time.

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  • Bjorkman, Kim, 2013. "Solving dynamic flowgraph methodology models using binary decision diagrams," Reliability Engineering and System Safety, Elsevier, vol. 111(C), pages 206-216.
    • Handle: RePEc:eee:reensy:v:111:y:2013:i:c:p:206-216
    DOI: 10.1016/j.ress.2012.11.009
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    References listed on IDEAS

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    1. Bucci, Paolo & Kirschenbaum, Jason & Mangan, L. Anthony & Aldemir, Tunc & Smith, Curtis & Wood, Ted, 2008. "Construction of event-tree/fault-tree models from a Markov approach to dynamic system reliability," Reliability Engineering and System Safety, Elsevier, vol. 93(11), pages 1616-1627.
    2. R Remenyte-Prescott & J Andrews, 2008. "Analysis of non-coherent fault trees using ternary decision diagrams," Journal of Risk and Reliability, , vol. 222(2), pages 127-138, June.
    3. Kelly, Dana L. & Smith, Curtis L., 2009. "Bayesian inference in probabilistic risk assessment—The current state of the art," Reliability Engineering and System Safety, Elsevier, vol. 94(2), pages 628-643.
    4. A B Rauzy, 2008. "Some disturbing facts about depth-first left-most variable ordering heuristics for binary decision diagrams," Journal of Risk and Reliability, , vol. 222(4), pages 573-582, December.
    5. Doguc, Ozge & Ramirez-Marquez, Jose Emmanuel, 2009. "A generic method for estimating system reliability using Bayesian networks," Reliability Engineering and System Safety, Elsevier, vol. 94(2), pages 542-550.
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    Cited by:

    1. Di Maio, Francesco & Baronchelli, Samuele & Zio, Enrico, 2014. "Hierarchical differential evolution for minimal cut sets identification: Application to nuclear safety systems," European Journal of Operational Research, Elsevier, vol. 238(2), pages 645-652.
    2. McNelles, Phillip & Zeng, Zhao Chang & Renganathan, Guna & Lamarre, Greg & Akl, Yolande & Lu, Lixuan, 2016. "A comparison of Fault Trees and the Dynamic Flowgraph Methodology for the analysis of FPGA-based safety systems Part 1: Reactor trip logic loop reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 153(C), pages 135-150.
    3. McNelles, Phillip & Renganathan, Guna & Zeng, Zhao Chang & Chirila, Marius & Lu, Lixuan, 2019. "A comparison of fault trees and the Dynamic Flowgraph Methodology for the analysis of FPGA-based safety systems part 2: Theoretical investigations," Reliability Engineering and System Safety, Elsevier, vol. 183(C), pages 60-83.
    4. Zaitseva, Elena & Levashenko, Vitaly & Kostolny, Jozef, 2015. "Importance analysis based on logical differential calculus and Binary Decision Diagram," Reliability Engineering and System Safety, Elsevier, vol. 138(C), pages 135-144.
    5. Mo, Yuchang & Xing, Liudong & Amari, Suprasad V. & Bechta Dugan, Joanne, 2015. "Efficient analysis of multi-state k-out-of-n systems," Reliability Engineering and System Safety, Elsevier, vol. 133(C), pages 95-105.
    6. Reed, Sean, 2017. "An efficient algorithm for exact computation of system and survival signatures using binary decision diagrams," Reliability Engineering and System Safety, Elsevier, vol. 165(C), pages 257-267.

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