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A short Boolean derivation of mean failure frequency for any (also non-coherent) system

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  • Schneeweiss, Winfrid G.

Abstract

For stationary repairable systems it is shown that the probabilistic weights for the individual components’ mean failure frequencies (MFFs) that can be added to yield the system's MFF are found easily from the first step of the Boolean fault tree function's Shannon decomposition. This way one finds a general theory of a system's MFF and the case of coherence covered in standard textbooks is shown to be a subcase. Unfortunately, elegant rules for calculating system MFF from any polynomial form of the fault tree's Boolean function are only known for the coherent case, but repeated here, because they are not yet found in many textbooks. An example known from literature is treated extensively with great care.

Suggested Citation

  • Schneeweiss, Winfrid G., 2009. "A short Boolean derivation of mean failure frequency for any (also non-coherent) system," Reliability Engineering and System Safety, Elsevier, vol. 94(8), pages 1363-1367.
    • Handle: RePEc:eee:reensy:v:94:y:2009:i:8:p:1363-1367
    DOI: 10.1016/j.ress.2008.12.001
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    Cited by:

    1. Sedlacek, Peter & Zaitseva, Elena & Levashenko, Vitaly & Kvassay, Miroslav, 2021. "Critical state of non-coherent multi-state system," Reliability Engineering and System Safety, Elsevier, vol. 215(C).
    2. Miroslav Kvassay & Vitaly Levashenko & Elena Zaitseva, 2016. "Analysis of minimal cut and path sets based on direct partial Boolean derivatives," Journal of Risk and Reliability, , vol. 230(2), pages 147-161, April.
    3. 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.
    4. Rusnak, Patrik & Zaitseva, Elena & Levashenko, Vitaly & Bolvashenkov, Igor & Kammermann, Jörg, 2024. "Importance analysis of a system based on survival signature by structural importance measures," Reliability Engineering and System Safety, Elsevier, vol. 243(C).
    5. 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).
    6. 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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