Reliability and failure functions of some weighted systems

  • Authors

    • Imad Nashwan Al Quds Open University
    2017-01-02
    https://doi.org/10.14419/ijamr.v6i1.6917
  • Consecutive weighted k-out-of-n, F system, Weighted f-out-of-n, Weighted system, Modular arithmetic.
  • In modern systems, not only the number and the position of the functioning or the failed components are the main factors that keep the system into the functioning state or transform it into failure state, but the contribution or the working probability of the component is also a very important one. This contribution is usually called the component weight. In this paper, the reliability and the failure functions of the consecutive weighted k-out-of-n: F linear and circular system, the weighted f-out-of-n: F system, the weighted  (n,f,k) linear and circular system and the weighted  linear and circular system are obtained.

  • References

    1. [1] Chang C. J., Chen R. J. and Hwang F. K., “A fast reliability algorithm for the circular weighted-k-out-of-n: F systemâ€, IEEE Transactions on Reliability, Vol. 47, pp.472-474, 1998. https://doi.org/10.1109/24.756092.

      [2] Chang, G. J., Lirong C. and K. H., “Reliabilities for (n; f; k) systemsâ€, Statistics and Probability Letters, Vol. 43, pp. 237-242, 1999. https://doi.org/10.1016/S0167-7152(98)00263-6.

      [3] Chao M. T., Fu J. C. and Koutras M. V. “Survey of reliability studies of consecutive k-out-of-n: F and related systemâ€, IEEE Transactions on Reliability, Vol. 44, No. 1, pp. 120-127, 1995. https://doi.org/10.1109/24.376531.

      [4] Chiang, D. T., and Niu, S.-C., “Reliability of consecutive k-out-of-n: F system†â€, IEEE Transactions on Reliability, Vol. 30, No.1, pp. 87-89, 1981. https://doi.org/10.1109/TR.1981.5220981.

      [5] Chiang, D. T., and Niu, S.-C., “Reliability of consecutive k-out-of-n: F system†â€, IEEE Transactions on Reliability, Vol. 30, No.1, pp. 87-89, 1981. https://doi.org/10.1109/TR.1981.5220981.

      [6] Derman C, Lieberman G.J., and Ross S.M. “On the consecutive k-out-of-n: F systemâ€, IEEE Transactions on Reliability, Vol. 31, pp. 57-63, 1982. https://doi.org/10.1109/TR.1982.5221229.

      [7] Erylmaz, S. and Tutuncu G. Y., “Reliability evaluation of linear consecutive weighted-k-out-of-n: F system, Asia-Pacific Journal of Operational Research, in press, Vol. 26, pp. 805-816, 2009. https://doi.org/10.1142/S0217595909002481.

      [8] Eryilmaz S., Aksoy T., “Reliability of linear (n, f, k) systems with weighted componentsâ€, Journal of Systems Science and Systems Engineering, Vol. 19, pp. 277-284, 2010. https://doi.org/10.1007/s11518-010-5131-0.

      [9] Kamalja K. K. and Shinde R. L., “On the reliability of systemsâ€, Communication in Statistics-Theory and Methods, Vol. 43, pp. 1649-1665, 2014. https://doi.org/10.1080/03610926.2012.673674.

      [10] Nashwan I. I. H, “Reliability of some consecutive systemâ€, Ph. D thesis, Ain Shams University, pp. 65-70, 2012.

      [11] Nashwan, I. I. H, “New algorithms to find reliability and unreliability functions of the consecutive k-out-of-n: F linear & circular Systemâ€, The International Arab Conference on Information Technology, ACIT 2015.

      [12] Sfakianakis, M. E., and Papastavridis S. G.†Reliability of a general consecutive k-out-of-n: F Systemâ€, IEEE Transactions on Reliability, Vol. 42, pp. 491-496, 1993. https://doi.org/10.1109/24.257837.

      [13] Tung, S. S., “Combinatorial analysis in determining reliabilityâ€, Proceedings of annual Reliability & Maintainability Symposium, pp. 262-266, 1982.

      [14] Way, k. Zou M., “optimal reliability modeling principals and applicationsâ€, JOHN WILEY & SONS, pp. 231-232, 2003.

      [15] Wu, J. and Chen R., “An algorithm for computing the reliability of weighted-k-out-of-n systems, IEEE Transactions on Reliability, Vol. 43, 327-328, 1994. Wu J. and Chen R., “Efficient Algorithms for k-out-of-n & Consecutive-Weighted-k-out-of-n: F Systemâ€, IEEE Transaction on Reliability, Vol. 43, pp. 650-655, 1994.

      [16] Zuo, M.J., Lin, D. & Wu, Y., “Reliability evaluation of combined k-out-of-n: F, consecutive k-out-of-n: F, and linear connected (r,s)-out-of-(m,n): F system structuresâ€, IEEE Transactions on Reliability, Vol. 49, pp. 99–104, 2000. https://doi.org/10.1109/24.855542.

  • Downloads

  • How to Cite

    Nashwan, I. (2017). Reliability and failure functions of some weighted systems. International Journal of Applied Mathematical Research, 6(1), 7-13. https://doi.org/10.14419/ijamr.v6i1.6917