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Importance analysis based on logical differential calculus and Binary Decision Diagram

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  • Zaitseva, Elena
  • Levashenko, Vitaly
  • Kostolny, Jozef

Abstract

System availability evaluation, sensitivity analysis, Importance Measures, and optimal design are important issues that have become research topics for reliability engineering. There are different mathematical approaches to the development of these topics. The structure function based approach is one of them. Structure function enables one to analyse a system of any complexity. But computational complexity of structure function based methods is time consuming for large-scale networks. We propose to use two mathematical approaches for decision to this problem for system importance analysis. The first of them is Direct Partial Boolean Derivative. New equations for calculating the Importance Measures are developed in terms of these derivatives. The second is Binary Decision Diagram (BDD), that supports efficient manipulation of Boolean algebra. Two algorithms for calculating Direct Partial Boolean Derivative based on BDD of structure function are proposed in this paper. The experimental results show the efficiency of new algorithms for calculating Direct Partial Boolean Derivative and Importance Measures.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:reensy:v:138:y:2015:i:c:p:135-144
    DOI: 10.1016/j.ress.2015.01.009
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    Cited by:

    1. Yeh, Wei-Chang, 2021. "A quick BAT for evaluating the reliability of binary-state networks," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    2. Jintao Liu & Keping Li & Wei Zheng & Jiebei Zhu, 2019. "An importance order analysis method for causes of railway signaling system hazards based on complex networks," Journal of Risk and Reliability, , vol. 233(4), pages 567-579, August.
    3. Aliee, Hananeh & Borgonovo, Emanuele & Glaß, Michael & Teich, Jürgen, 2017. "On the Boolean extension of the Birnbaum importance to non-coherent systems," Reliability Engineering and System Safety, Elsevier, vol. 160(C), pages 191-200.
    4. Kawahara, Jun & Sonoda, Koki & Inoue, Takeru & Kasahara, Shoji, 2019. "Efficient construction of binary decision diagrams for network reliability with imperfect vertices," Reliability Engineering and System Safety, Elsevier, vol. 188(C), pages 142-154.
    5. Nicolae Brînzei & Jean-François Aubry, 2018. "Graphs models and algorithms for reliability assessment of coherent and non-coherent systems," Journal of Risk and Reliability, , vol. 232(2), pages 201-215, April.
    6. Zaitseva, Elena & Levashenko, Vitaly & Sedlacek, Peter & Kvassay, Miroslav & Rabcan, Jan, 2021. "Logical differential calculus for calculation of Birnbaum importance of non-coherent system," Reliability Engineering and System Safety, Elsevier, vol. 215(C).
    7. Elena Zaitseva & Vitaly Levashenko & Ravil Mukhamediev & Nicolae Brinzei & Andriy Kovalenko & Adilkhan Symagulov, 2023. "Review of Reliability Assessment Methods of Drone Swarm (Fleet) and a New Importance Evaluation Based Method of Drone Swarm Structure Analysis," Mathematics, MDPI, vol. 11(11), pages 1-26, June.

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