A Maintenance Design of Connected-(r,s)-out-of-(m,n):F System Using Genetic Algorithm

유전자 알고리듬을 이용한(m,n)중-연속(r,s):고장 격자 시스템의 정비 모형

  • Yun, Won-Young (Department of Industrial Engineering, Pusan National University) ;
  • Kim, Gui-Rae (Department of Industrial Engineering, Pusan National University) ;
  • Jeong, Cheol-Hun (Department of Industrial Engineering, Pusan National University)
  • Published : 2004.09.30

Abstract

This study considers a linear connected-(r,s)-out-of-(m,n):F lattice system whose components are ordered like the elements of a linear (m,n )-matrix. We assume that all components are in the state 1 (operating) or 0 (failed) and identical and s-independent. The system fails whenever at least one connected (r,s)-submatrix of failed components occurs. The purpose of this paper is to present an optimization scheme that aims at minimizing the expected cost per unit time. To find the optimal threshold of maintenance intervention, we use a genetic algorithm for the cost optimization procedure. The expected cost per unit time is obtained by Monte Carlo simulation. The sensitivity analysis to the different cost parameters has also been made.

Keywords

References

  1. Abraham, J. A.(1979), An improved method for network reliability, IEEE Trans. Reliability R-28(1), 58-61
  2. Blanks, H. S. and Tordan, M. J.(1986), Optimum replacement of deteriorating and inadequate equipment, Quality and Reliability Engineering 2, 183-197
  3. Boehme, T. K., Kossow, A. and Preuss, W.(1992), A generalization of consecutive-k-out-of-n:F systems, IEEE Trans. Reliability 41(3), 451-457
  4. Boutsikas, M. V. and Koutras, M. V.(2000), Generalized reliability bounds for coherent structures, Journal of Applied Probability 37, 778-794
  5. Fu, J. C. and Koutras, M. V.(1994), Poisson approximation for 2-dimensional patterns, Annals of the Institute of Statistical Mathematics 46(1), 179-192
  6. Jardine, A. K. S.(1973), Maintenance, replacement, and reliability, New York, John Wiley
  7. Kontoleon, J. M.(1980), Reliability determination of a r-successiveout- of-n:F system, IEEE Trans. Reliability R-29, 437
  8. Koutras, M. V., Papadopoulos, G. K. and Papastavridis, S. G.(1993), Reliability of 2-dimensional consecutive-k-out-of-n:F systems, IEEE Trans. Reliability 42(4), 658-661
  9. Koutras, M.V., Papadopoulos, G. K. and Papastavridis, S. G.(1997), A reliability bound for 2-dimensional consecutive-k-out-of-n:F systems, Nonlinear Analysis, Theory, Methods and Applications 30(6), 3345-3348
  10. Ksir, B.(1992), Comment on: 2-dimensional consecutive k-out-of-n:F models, IEEE Trans. Reliability 41(4), 575
  11. Locks, M. O.(1987), A minimizing algorithm for sum of disjoint products, IEEE Trans. Reliability R-36, 120-127 https://doi.org/10.1109/TR.1987.5222436
  12. Makri, F. S. and Psillakis, Z. M.(1996), Bounds for reliability of k-within two-dimensional consecutive-r-out-of-n failure systems, Microelectronics and Reliability 36(3), 341-345
  13. Malanie, M.(1996), An introduction to genetic algorithms, Massachusetts, Massachusetts Institute of Technology
  14. Malinowski, J. and Preuss, W.( 1996), Lower & upper bounds for the reliability of connected-(r,s)-out-of-(m,n):F lattice systems, IEEE Trans. Reliability 45(1), 156-160
  15. Noguchi, K., Sasaki, M., Yanagi, S. and Yuge, T.(1996), Reliability of connected-(r,s)-out-of-(m,n):F lattice system, IEICE Transac tions Fundamentals J79-A(4), 954-963
  16. Salvia, A. A. and Lasher, W. C.(1990), 2-Dimensional consecutive-zout- of-n:F models, IEEE Trans. Reliability 39(3), 333-336
  17. Wilson, J. M.(1990), An improved minimizing algorithm for sum of disjoint products, IEEE Trans. Reliability 39(1), 42-45
  18. Yamamoto, H. and Miyakawa, M.(1995), Reliability of a linear connected-(r,s)-out-of-(m,n):F lattice systems, IEEE Trans. Reliability 44(2), 333-336
  19. Yamamoto, H. and Miyakawa, M.,(1996), Reliability of circular connected-(r,s)-out-of-(m,n):F lattice systems, Journal of the Operations Research Society of Japan 39(3), 389-406
  20. Yun, W. Y. and Kim, G. R.(2000), Economic design of consecutive k-out-of-n.F system, Journal of the Korean Institute of Industrial Engineers 26(2), 128-135(InKorean)
  21. Zuo, M. G.(1993), Reliability & design of 2-dimensional consecutive-k-out-of-n:F systems, IEEE Trans. Reliability 42(4), 488-490