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RESIDUAL LIFETIME OF A SYSTEM WITH A COLD STANDBY UNIT

Year 2017, Volume: 10 Issue: 1, 24 - 32, 31.01.2017

Abstract

In this paper, we de ne and study two di erent residual life random variables corresponding to a single unit system equipped with a cold standby unit. We obtain the conditional survival functions when the lifetimes of active and standby units are dependent. Some properties of the associated mean residual life functions are also investigated. Graphical illustrations are presented to observe time dependent behaviors of associated mean residual life functions.

References

  • Asadi, M. and Bayramoglu I. (2006). On the mean residual life function of the k-out-of-n systems at system level. IEEE Transactions on Reliability, 55, 314-318.
  • Asadi, M. and Goliforushani S. (2008). On the mean residual life function of coherent systems. IEEE Transactions on Reliability, 57, 574-580.
  • Bayramoglu (Bairamov), I. and Ozkut, M. (2016). Mean residual life and inactivity time of a coherent system subjected to Marshall-Olkin type shocks, Journal of Computational and Applied Mathematics, 298, 190-200.
  • Eryilmaz, S. (2011). The behavior of warm standby components with respect to a coherent system. Statistics & Probability Letters, 81, 1319-1325.
  • Eryilmaz, S. (2013). On residual lifetime of coherent systems after the rth failure. Statistical Papers, 54, 243-250.
  • Eryilmaz, S. and Xie, M. (2014). Dynamic modeling of general three-state k-out-of-n : G systems: Permanent-based computational results. Journal of Computational and Applied Mathematics, 272, 97-106.
  • Eryilmaz, S. (2012). On the mean residual life of a k-out-of-n:G system with a single cold standby component. European Journal of Operational Research, 222 , 273-277.
  • Eryilmaz, S. and Tank, F. (2012). On reliability analysis of a two-dependent-unit series system with a standby unit. Applied Mathematics and Computation, 218, 7792-7797.
  • Eryilmaz, S. (2013). Reliability of a k-out-of-n system equipped with a single warm standby component. IEEE Transactions on Reliability, 62, 499-503.
  • Gurler, S. and Capar, S. (2011). An algorithm for mean residual life computation of (n􀀀k+1)-out-of-n systems: An application of exponentiated Weibull distribution. Applied Mathematics and Computation, 217, 7806-7811.
  • Levitin, G., Xing, G L. and Dai, Y. (2014). Optimal component loading in 1-out-of-N cold standby systems. Reliability Engineering & System Safety, 127, 58-64.
  • Li, X. and Xu, M. (2006). Some results about MIT order and IMIT class of life distributions. Probability in the Engineering and Informational Sciences, 20, 481-496.
  • Navarro, J. and Hernandez, P.J. (2008). Mean residual life functions of nite mixtures, order statistics and coherent systems. Metrika, 67, 277-298.
  • Poursaeed, M.H. (2010). A note on the mean past and the mean residual life of a (n􀀀k +1)-out-of-n system under multi-monitoring. Statistical Papers, 51, 409-419.
  • Shaked, M. Shanthikumar, J.G. (2007). Stochastic orders and their applications. Springer, New York.
  • Tavangar, M. and Asadi, M. (2010). A study on the mean past lifetime of the components of to appear system at the system level. Metrika, 72, 59-73.
  • Wu, Q. andWu, S. (2011). Reliability analysis of two-unit cold standby repairable systems under Poisson shocks. Applied Mathematics and Computation, 218, 171-182.
  • Xing, L., Tannous, O. and Dugan, J.B. (2012). Reliability analysis of nonrepairable cold-standby systems using sequential binary decision diagrams. IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans, 42(3), 715-726.
Year 2017, Volume: 10 Issue: 1, 24 - 32, 31.01.2017

Abstract

References

  • Asadi, M. and Bayramoglu I. (2006). On the mean residual life function of the k-out-of-n systems at system level. IEEE Transactions on Reliability, 55, 314-318.
  • Asadi, M. and Goliforushani S. (2008). On the mean residual life function of coherent systems. IEEE Transactions on Reliability, 57, 574-580.
  • Bayramoglu (Bairamov), I. and Ozkut, M. (2016). Mean residual life and inactivity time of a coherent system subjected to Marshall-Olkin type shocks, Journal of Computational and Applied Mathematics, 298, 190-200.
  • Eryilmaz, S. (2011). The behavior of warm standby components with respect to a coherent system. Statistics & Probability Letters, 81, 1319-1325.
  • Eryilmaz, S. (2013). On residual lifetime of coherent systems after the rth failure. Statistical Papers, 54, 243-250.
  • Eryilmaz, S. and Xie, M. (2014). Dynamic modeling of general three-state k-out-of-n : G systems: Permanent-based computational results. Journal of Computational and Applied Mathematics, 272, 97-106.
  • Eryilmaz, S. (2012). On the mean residual life of a k-out-of-n:G system with a single cold standby component. European Journal of Operational Research, 222 , 273-277.
  • Eryilmaz, S. and Tank, F. (2012). On reliability analysis of a two-dependent-unit series system with a standby unit. Applied Mathematics and Computation, 218, 7792-7797.
  • Eryilmaz, S. (2013). Reliability of a k-out-of-n system equipped with a single warm standby component. IEEE Transactions on Reliability, 62, 499-503.
  • Gurler, S. and Capar, S. (2011). An algorithm for mean residual life computation of (n􀀀k+1)-out-of-n systems: An application of exponentiated Weibull distribution. Applied Mathematics and Computation, 217, 7806-7811.
  • Levitin, G., Xing, G L. and Dai, Y. (2014). Optimal component loading in 1-out-of-N cold standby systems. Reliability Engineering & System Safety, 127, 58-64.
  • Li, X. and Xu, M. (2006). Some results about MIT order and IMIT class of life distributions. Probability in the Engineering and Informational Sciences, 20, 481-496.
  • Navarro, J. and Hernandez, P.J. (2008). Mean residual life functions of nite mixtures, order statistics and coherent systems. Metrika, 67, 277-298.
  • Poursaeed, M.H. (2010). A note on the mean past and the mean residual life of a (n􀀀k +1)-out-of-n system under multi-monitoring. Statistical Papers, 51, 409-419.
  • Shaked, M. Shanthikumar, J.G. (2007). Stochastic orders and their applications. Springer, New York.
  • Tavangar, M. and Asadi, M. (2010). A study on the mean past lifetime of the components of to appear system at the system level. Metrika, 72, 59-73.
  • Wu, Q. andWu, S. (2011). Reliability analysis of two-unit cold standby repairable systems under Poisson shocks. Applied Mathematics and Computation, 218, 171-182.
  • Xing, L., Tannous, O. and Dugan, J.B. (2012). Reliability analysis of nonrepairable cold-standby systems using sequential binary decision diagrams. IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans, 42(3), 715-726.
There are 18 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Altan Tuncel

Publication Date January 31, 2017
Acceptance Date January 10, 2017
Published in Issue Year 2017 Volume: 10 Issue: 1

Cite

APA Tuncel, A. (2017). RESIDUAL LIFETIME OF A SYSTEM WITH A COLD STANDBY UNIT. Istatistik Journal of The Turkish Statistical Association, 10(1), 24-32.
AMA Tuncel A. RESIDUAL LIFETIME OF A SYSTEM WITH A COLD STANDBY UNIT. IJTSA. January 2017;10(1):24-32.
Chicago Tuncel, Altan. “RESIDUAL LIFETIME OF A SYSTEM WITH A COLD STANDBY UNIT”. Istatistik Journal of The Turkish Statistical Association 10, no. 1 (January 2017): 24-32.
EndNote Tuncel A (January 1, 2017) RESIDUAL LIFETIME OF A SYSTEM WITH A COLD STANDBY UNIT. Istatistik Journal of The Turkish Statistical Association 10 1 24–32.
IEEE A. Tuncel, “RESIDUAL LIFETIME OF A SYSTEM WITH A COLD STANDBY UNIT”, IJTSA, vol. 10, no. 1, pp. 24–32, 2017.
ISNAD Tuncel, Altan. “RESIDUAL LIFETIME OF A SYSTEM WITH A COLD STANDBY UNIT”. Istatistik Journal of The Turkish Statistical Association 10/1 (January 2017), 24-32.
JAMA Tuncel A. RESIDUAL LIFETIME OF A SYSTEM WITH A COLD STANDBY UNIT. IJTSA. 2017;10:24–32.
MLA Tuncel, Altan. “RESIDUAL LIFETIME OF A SYSTEM WITH A COLD STANDBY UNIT”. Istatistik Journal of The Turkish Statistical Association, vol. 10, no. 1, 2017, pp. 24-32.
Vancouver Tuncel A. RESIDUAL LIFETIME OF A SYSTEM WITH A COLD STANDBY UNIT. IJTSA. 2017;10(1):24-32.