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Reliability properties of consecutive k-out-of-n systems of arbitrarily dependent components

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  • Eryılmaz, Serkan

Abstract

In this paper, the reliability properties of consecutive k-out-of-n systems with arbitrarily dependent components are studied. For 2k⩾n we present efficient formulas to compute the reliability characteristics such as meantime to failure, failure rate, and mean residual lifetime. Approximations for the survival functions when 1⩽k⩽n are also provided. The results are illustrated for the multivariate survival distribution generated by a Weibull and Inverse-Gaussian mixture.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:reensy:v:94:y:2009:i:2:p:350-356
    DOI: 10.1016/j.ress.2008.03.027
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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. Navarro, Jorge & Ruiz, Jose M. & Sandoval, Carlos J., 2005. "A note on comparisons among coherent systems with dependent components using signatures," Statistics & Probability Letters, Elsevier, vol. 72(2), pages 179-185, April.
    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. Jorge Navarro & Pedro Hernandez, 2008. "Mean residual life functions of finite mixtures, order statistics and coherent systems," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 67(3), pages 277-298, April.
    5. 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.
    6. Sigeo Aki & Katuomi Hirano, 1996. "Lifetime distribution and estimation problems of consecutive-k-out-of-n:F systems," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 48(1), pages 185-199, March.
    7. 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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