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Dependability estimation for non-Markov consecutive-k-out-of-n: F repairable systems by fast simulation

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  • Xiao, Gang
  • Li, Zhizhong
  • Li, Ting

Abstract

A model of consecutive-k-out-of-n: F repairable system with non-exponential repair time distribution and (k-1)-step Markov dependence is introduced in this paper along with algorithms of three Monte Carlo methods, i.e. importance sampling, conditional expectation estimation and combination of the two methods, to estimate dependability of the non-Markov model including reliability, transient unavailability, MTTF, and MTBF. A numerical example is presented to demonstrate the efficiencies of above methods. The results show that combinational method has the highest efficiency for estimation of unreliability and unavailability, while conditional expectation estimation is the most efficient method for estimation of MTTF and MTBF. Conditional expectation estimation seems to have overall higher speedups in estimating dependability of such systems.

Suggested Citation

  • Xiao, Gang & Li, Zhizhong & Li, Ting, 2007. "Dependability estimation for non-Markov consecutive-k-out-of-n: F repairable systems by fast simulation," Reliability Engineering and System Safety, Elsevier, vol. 92(3), pages 293-299.
    • Handle: RePEc:eee:reensy:v:92:y:2007:i:3:p:293-299
    DOI: 10.1016/j.ress.2006.04.004
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    References listed on IDEAS

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    1. Perwez Shahabuddin, 1994. "Importance Sampling for the Simulation of Highly Reliable Markovian Systems," Management Science, INFORMS, vol. 40(3), pages 333-352, March.
    2. Lam, Yeh & Ng, Hon Keung Tony, 2001. "A general model for consecutive-k-out-of-n: F repairable system with exponential distribution and (k-1)-step Markov dependence," European Journal of Operational Research, Elsevier, vol. 129(3), pages 663-682, March.
    3. Stavros Papastavridis & Markos Koutras, 1992. "Consecutive k-out-of-n systems with maintenance," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 44(4), pages 605-612, December.
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    Cited by:

    1. Levitin, Gregory, 2011. "Linear m-gap-consecutive k-out-of-r-from-n:F systems," Reliability Engineering and System Safety, Elsevier, vol. 96(2), pages 292-298.
    2. Eryılmaz, Serkan, 2009. "Reliability properties of consecutive k-out-of-n systems of arbitrarily dependent components," Reliability Engineering and System Safety, Elsevier, vol. 94(2), pages 350-356.
    3. Villén-Altamirano, José, 2010. "RESTART simulation of non-Markov consecutive-k-out-of-n: F repairable systems," Reliability Engineering and System Safety, Elsevier, vol. 95(3), pages 247-254.
    4. Villén-Altamirano, J., 2014. "Asymptotic optimality of RESTART estimators in highly dependable systems," Reliability Engineering and System Safety, Elsevier, vol. 130(C), pages 115-124.
    5. Zhao, Fei & Peng, Rui & Zhang, Nan, 2023. "Inspection policy optimization for a k-out-of-n/Cl(k′,n′;F) system considering failure dependence: a case study," Reliability Engineering and System Safety, Elsevier, vol. 237(C).
    6. Wang, Yan & Hu, Linmin & Yang, Li & Li, Jing, 2022. "Reliability modeling and analysis for linear consecutive-k-out-of-n: F retrial systems with two maintenance activities," Reliability Engineering and System Safety, Elsevier, vol. 226(C).

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