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Reliability analysis of generalized multi-state k-out-of-n systems

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  • S K Chaturvedi
  • S H Basha
  • S V Amari
  • M J Zuo

Abstract

The recently proposed generalized multi-state k -out-of- n system model provides more flexibility in describing practical systems. In this model, there are n components in the system where each component and the system can be in one of M +  1 possible states: 0, 1, 2, …, M . The system is in below state j if there exists an integer value l , (1  ≤ i ≤ j ) such that at least k l components are in states below l . Although the model has several practical applications, existing methods for computing either the exact or approximate reliability of these systems are computationally inefficient and limited to very small systems. This paper proposes an efficient method and a detailed algorithm to compute the exact reliability of multi-state k -out-of- n systems with independent and identically distributed components. The method is based on conditional probabilities and is applicable for all cases of multi-state k -out-of- n systems with respect to the recent definitions of this system.

Suggested Citation

  • S K Chaturvedi & S H Basha & S V Amari & M J Zuo, 2012. "Reliability analysis of generalized multi-state k-out-of-n systems," Journal of Risk and Reliability, , vol. 226(3), pages 327-336, June.
    • Handle: RePEc:sae:risrel:v:226:y:2012:i:3:p:327-336
    DOI: 10.1177/1748006X11422623
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    References listed on IDEAS

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    1. Zhigang Tian & Ming Zuo & Richard Yam, 2009. "Multi-state systems and their performance evaluation," IISE Transactions, Taylor & Francis Journals, vol. 41(1), pages 32-44.
    2. Richard E. Barlow & Alexander S. Wu, 1978. "Coherent Systems with Multi-State Components," Mathematics of Operations Research, INFORMS, vol. 3(4), pages 275-281, November.
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    1. Faghih-Roohi, Shahrzad & Xie, Min & Ng, Kien Ming & Yam, Richard C.M., 2014. "Dynamic availability assessment and optimal component design of multi-state weighted k-out-of-n systems," Reliability Engineering and System Safety, Elsevier, vol. 123(C), pages 57-62.
    2. 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.
    3. Xiaogang Song & Zhengjun Zhai & Yangming Guo & Peican Zhu & Jie Han, 2017. "Approximate Analysis of Multi-State Weighted k -Out-of- n Systems Applied to Transmission Lines," Energies, MDPI, vol. 10(11), pages 1-16, October.

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