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Availability of a general k-out-of-n:G system with non-identical components considering shut-off rules using quasi-birth–death process

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  • Moghaddass, Ramin
  • Zuo, Ming J.
  • Wang, Wenbin

Abstract

A general repairable k-out-of-n:G system with non-identical components, which is a common form of redundancy, is considered in this paper. The number of repairmen is assumed to be r (1≤r≤n−k+1) while components can have similar or different repair priorities. The objective of this work is to address the problem of efficient evaluation of the system's availability in a way that steady state solutions can be obtained systematically in a reasonable computational time. This problem is modeled as a finite state-dependent non-homogeneous quasi-birth–death (QBD) process. An algorithm is introduced to systematically generate the system state vectors and transition rate matrix and then an iterative method based on the Block Gauss–Seidel method is employed to determine the steady state probabilities. These are the novel contributions made in this paper. An analog Monte Carlo simulation is presented to demonstrate the correctness and the efficiency of the proposed method.

Suggested Citation

  • Moghaddass, Ramin & Zuo, Ming J. & Wang, Wenbin, 2011. "Availability of a general k-out-of-n:G system with non-identical components considering shut-off rules using quasi-birth–death process," Reliability Engineering and System Safety, Elsevier, vol. 96(4), pages 489-496.
    • Handle: RePEc:eee:reensy:v:96:y:2011:i:4:p:489-496
    DOI: 10.1016/j.ress.2010.12.001
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    References listed on IDEAS

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    1. Li, Xiaohu & Zuo, Ming J. & Yam, Richard C.M., 2006. "Reliability analysis of a repairable k-out-of-n system with some components being suspended when the system is down," Reliability Engineering and System Safety, Elsevier, vol. 91(3), pages 305-310.
    2. Bernard Philippe & Youcef Saad & William J. Stewart, 1992. "Numerical Methods in Markov Chain Modeling," Operations Research, INFORMS, vol. 40(6), pages 1156-1179, December.
    3. Xiaohu Li & Jing Chen, 2004. "Aging properties of the residual life length of k‐out‐of‐n systems with independent but non‐identical components," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 20(2), pages 143-153, April.
    4. Ruiz-Castro, Juan Eloy & Pérez-Ocón, Rafael & Fernández-Villodre, Gemma, 2008. "Modelling a reliability system governed by discrete phase-type distributions," Reliability Engineering and System Safety, Elsevier, vol. 93(11), pages 1650-1657.
    5. Khatab, A. & Nahas, N. & Nourelfath, M., 2009. "Availability of K-out-of-N:G systems with non-identical components subject to repair priorities," Reliability Engineering and System Safety, Elsevier, vol. 94(2), pages 142-151.
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    Cited by:

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    4. Aboalkhair, Ahmad M. & Coolen, Frank P.A. & MacPhee, Iain M., 2014. "Nonparametric predictive inference for reliability of a k-out-of-m:G system with multiple component types," Reliability Engineering and System Safety, Elsevier, vol. 131(C), pages 298-304.
    5. Guo, Linhan & Li, Ruiyang & Wang, Yu & Yang, Jun & Liu, Yu & Chen, Yiming & Zhang, Jianguo, 2023. "Availability for multi-component k-out-of-n: G warm-standby system in series with shut-off rule of suspended animation," Reliability Engineering and System Safety, Elsevier, vol. 233(C).
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    7. Moghaddass, Ramin & Zuo, Ming J., 2012. "A parameter estimation method for a condition-monitored device under multi-state deterioration," Reliability Engineering and System Safety, Elsevier, vol. 106(C), pages 94-103.

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