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Hierarchical probability and risk assessment for K-out-of-N system in hierarchy

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  • Ye, Xiong-Fei
  • Zhang, Yi
  • Harutoshi, Ogai
  • Kim, Chul-Woo

Abstract

In this research, the model of hierarchical structure from universe theory is imported into the general probability system which helps logically and subordinately describing, measuring, and evaluating the hierarchical probabilistic system. To clearly classify the hierarchy, “fayer†is proposed as the unit of hierarchy. Then, discussions on the relationship between hierarchy and system-of-systems and the risks caused by the hierarchy are proposed. This paper divides the problems of hierarchical probability mainly into two classes: the problems of surviving ratio and problems of passing ratio, and also, mixed problems of surviving ratio and passing ratio. Simultaneously, the surviving ratio is called as reliability. System reliability is one marked kind of hierarchical probability for the risk assessment of the hierarchical system. This paper introduces a new reliability system, P-out-of-1 system, which is derived from the K-out-of-N systems in hierarchy. The hierarchical reliability calculation of every fayer of the P-out-of-1 system is different from other fayers. Furthermore, the risk assessment of the hierarchical system for decision making of one maintenance manifests many differences by different descriptions in different fayers, even these descriptions concentrate on the same system.

Suggested Citation

  • Ye, Xiong-Fei & Zhang, Yi & Harutoshi, Ogai & Kim, Chul-Woo, 2019. "Hierarchical probability and risk assessment for K-out-of-N system in hierarchy," Reliability Engineering and System Safety, Elsevier, vol. 189(C), pages 242-260.
    • Handle: RePEc:eee:reensy:v:189:y:2019:i:c:p:242-260
    DOI: 10.1016/j.ress.2019.04.026
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    1. Charles J. Kowalski, 1972. "On the Effects of Non‐Normality on the Distribution of the Sample Product‐Moment Correlation Coefficient," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 21(1), pages 1-12, March.
    2. Prashanthi Boddu & Liudong Xing, 2013. "Reliability evaluation and optimization of series–parallel systems with k-out-of-n: G subsystems and mixed redundancy types," Journal of Risk and Reliability, , vol. 227(2), pages 187-198, April.
    3. Coit, David W. & Chatwattanasiri, Nida & Wattanapongsakorn, Naruemon & Konak, Abdullah, 2015. "Dynamic k-out-of-n system reliability with component partnership," Reliability Engineering and System Safety, Elsevier, vol. 138(C), pages 82-92.
    4. Wang, Wenbin & Banjevic, Dragan & Pecht, Michael, 2010. "A multi-component and multi-failure mode inspection model based on the delay time concept," Reliability Engineering and System Safety, Elsevier, vol. 95(8), pages 912-920.
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    Cited by:

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