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RESTART simulation of non-Markov consecutive-k-out-of-n: F repairable systems

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  • Villén-Altamirano, José

Abstract

The reliability of consecutive-k-out-of-n: F repairable systems and (k−1)-step Markov dependence is studied. The model analyzed in this paper is more general than those of previous studies given that repair time and component lifetimes are random variables that follow a general distribution. The system has one repair service which adopts a priority repair rule based on system failure risk. Since crude simulation has proved to be inefficient for highly dependable systems, the RESTART method was used for the estimation of steady-state unavailability, MTBF and unreliability. Probabilities up to the order of 10−16 have been accurately estimated with little computational effort. In this method, a number of simulation retrials are performed when the process enters regions of the state space where the chance of occurrence of a rare event (e.g., a system failure) is higher. The main difficulty for the application of this method is to find a suitable function, called the importance function, to define the regions. Given the simplicity involved in changing some model assumptions with RESTART, the importance function used in this paper could be useful for dependability estimation of many systems.

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  • 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.
    • Handle: RePEc:eee:reensy:v:95:y:2010:i:3:p:247-254
    DOI: 10.1016/j.ress.2009.10.005
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    References listed on IDEAS

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    1. 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.
    2. Eryilmaz, Serkan & Kan, Cihangir & Akici, Fatih, 2009. "Consecutive k-within-m-out-of-n:F system with exchangeable components," MPRA Paper 26838, University Library of Munich, Germany.
    3. Cui, Lirong & Li, Haijun, 2007. "Analytical method for reliability and MTTF assessment of coherent systems with dependent components," Reliability Engineering and System Safety, Elsevier, vol. 92(3), pages 300-307.
    4. Yun, Won-Young & Kim, Gui-Rae & Yamamoto, Hisashi, 2007. "Economic design of a circular consecutive-k-out-of-n:F system with (k-1)-step Markov dependence," Reliability Engineering and System Safety, Elsevier, vol. 92(4), pages 464-478.
    5. 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.
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    1. Turati, Pietro & Pedroni, Nicola & Zio, Enrico, 2016. "Advanced RESTART method for the estimation of the probability of failure of highly reliable hybrid dynamic systems," Reliability Engineering and System Safety, Elsevier, vol. 154(C), pages 117-126.

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