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On the number of failed components in a k-out-of-n system upon system failure when the lifetimes are discretely distributed

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  • Davies, Katherine
  • DembiÅ„ska, Anna

Abstract

In this paper, we examine properties of k-out-of-n systems when the component lifetimes are discretely distributed. The primary focus is the random variable which represents the number of failed components upon system failure. For this variate we derive the probability mass function under the most general setting of possibly dependent and heterogeneous components. We also present conditional probabilities for this variable given some information about the time of system failure. In addition to these results, we show that, in the special case of series systems, this variable exhibits some aging properties, and we establish several characterizations of probability distributions based on such properties. For illustration, we provide three numerical examples.

Suggested Citation

  • Davies, Katherine & DembiÅ„ska, Anna, 2019. "On the number of failed components in a k-out-of-n system upon system failure when the lifetimes are discretely distributed," Reliability Engineering and System Safety, Elsevier, vol. 188(C), pages 47-61.
    • Handle: RePEc:eee:reensy:v:188:y:2019:i:c:p:47-61
    DOI: 10.1016/j.ress.2019.03.008
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    References listed on IDEAS

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    8. Cai, Zhiqiang & Si, Shubin & Sun, Shudong & Li, Caitao, 2016. "Optimization of linear consecutive-k-out-of-n system with a Birnbaum importance-based genetic algorithm," Reliability Engineering and System Safety, Elsevier, vol. 152(C), pages 248-258.
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    Cited by:

    1. Alkaff, Abdullah, 2021. "Discrete time dynamic reliability modeling for systems with multistate components," Reliability Engineering and System Safety, Elsevier, vol. 209(C).
    2. Dembińska, Anna & Eryilmaz, Serkan, 2021. "Discrete time series–parallel system and its optimal configuration," Reliability Engineering and System Safety, Elsevier, vol. 215(C).
    3. Jasiński, Krzysztof, 2020. "Some concept of Markov property of discrete order statistics arising from independent and non-identically distributed variables," Statistics & Probability Letters, Elsevier, vol. 160(C).
    4. Eryilmaz, Serkan & Ozkut, Murat, 2020. "Optimization problems for a parallel system with multiple types of dependent components," Reliability Engineering and System Safety, Elsevier, vol. 199(C).
    5. Eryilmaz, Serkan & Yalcin, Femin, 2022. "The number of failed components upon system failure when the lifetimes are discretely distributed," Reliability Engineering and System Safety, Elsevier, vol. 225(C).
    6. Dong Lyu & Shubin Si & Zhiqiang Cai & Liyang Xie, 2020. "Computational method for importance measure of the k-out-of-n system based on stress–strength interference," Journal of Risk and Reliability, , vol. 234(1), pages 27-40, February.

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