Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics and Stochastic Analysis
Volume 2008, Article ID 905721, 13 pages
http://dx.doi.org/10.1155/2008/905721
Research Article

On the Survival Time of a Duplex System: A Sokhotski-Plemelj Problem

Department of Decision Sciences, University of South Africa, P.O. Box 392, Pretoria 0003, South Africa

Received 9 June 2008; Accepted 1 September 2008

Academic Editor: Karl Sigman

Copyright © 2008 Edmond J. Vanderperre. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. A. Birolini, Reliability Engineering: Theory and Practice, Springer, Berlin, Germany, 2004.
  2. A. Birolini, Quality and Reliability of Technical Systems: Theory-Practice-Management, Springer, Berlin, Germany, 1994. View at Zentralblatt MATH
  3. I. B. Gertsbakh, Statistical Reliability Theory, vol. 4 of Probability: Pure and Applied, Marcel Dekker, New York, NY, USA, 1989. View at Zentralblatt MATH · View at MathSciNet
  4. B. Gnedenko and I. A. Ushakov, Probabilistic Reliability Engineering, John Wiley & Sons, New York, NY, USA, 1995.
  5. M. Shaked and I. G. Shanthikumar, “Reliability and maintainability,” in Handbook in Operations Research and Management Science 2, D. P. Heyman and M. J. Sobel, Eds., North-Holland, Amsterdam, The Netherlands, 1996. View at Google Scholar
  6. J. A. Buzacott, “Availability of priority redundant systems,” IEEE Transactions on Reliability, vol. 20, pp. 60–63, 1971. View at Google Scholar
  7. B. B. Fawzi and A. G. Hawkes, “Availability of a series system with replacement and repair,” Journal of Applied Probability, vol. 27, no. 4, pp. 873–887, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. R. Gupta, “Analysis of a two-unit cold standby system with degradation and linearly increasing failure rates,” International Journal of Systems Science, vol. 22, no. 11, pp. 2329–2338, 1991. View at Google Scholar · View at MathSciNet
  9. Y. Lam and Y. L. Zhang, “Repairable consecutive-k-out-of-n: F system with Markov dependence,” Naval Research Logistics, vol. 47, no. 1, pp. 18–39, 2000. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. S. S. Makhanov and E. J. Vanderperre, “A note on a Markov time related to a priority system,” WSEAS Transactions on Mathematics, vol. 6, no. 9, pp. 811–816, 2007. View at Google Scholar
  11. H. Mine, “Repair priority effect on the availability of a two-unit system,” IEEE Transactions on Reliability, vol. 28, pp. 325–326, 1979. View at Google Scholar
  12. D. Montoro-Cazorla and R. Pérez-Ocòn, “A deteriorating two-system with two repair modes and sojourn times phase-type distributed,” Reliability Engineering & System Safety, vol. 91, no. 1, pp. 1–9, 2006. View at Publisher · View at Google Scholar
  13. T. Nakagawa and S. Osaki, “Stochastic behaviour of a two-unit priority standby redundant system with repair,” Microelectronics and Reliability, vol. 14, no. 3, pp. 309–313, 1975. View at Google Scholar
  14. S. Osaki, “Reliability analysis of a two-unit standby redundant system with priority,” Canadian Journal of Operations Research, vol. 8, pp. 60–62, 1970. View at Google Scholar · View at Zentralblatt MATH
  15. D.-H. Shi and L. Liu, “Availability analysis of a two-unit series system with a priority shut-off rule,” Naval Research Logistics, vol. 43, no. 7, pp. 1009–1024, 1996. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. R. Subramanian and N. Ravichandran, “A two-unit priority redundant system with preemptive resume repair,” IEEE Transactions on Reliability, vol. 29, pp. 183–184, 1980. View at Google Scholar
  17. E. J. Vanderperre, “Long-run availability of a two-unit standby system subjected to a priority rule,” Bulletin of the Belgian Mathematical Society. Simon Stevin, vol. 7, no. 3, pp. 355–364, 2000. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. E. J. Vanderperre and S. S. Makhanov, “Long-run availability of a priority system: a numerical approach,” Mathematical Problems in Engineering, vol. 2005, no. 1, pp. 75–85, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  19. E. J. Vanderperre, “A Markov time related to a priority system,” Mathematical Problems in Engineering, vol. 2006, Article ID 92613, 9 pages, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  20. R. C. M. Yam, M. J. Zuo, and Y. L. Zhang, “A method for evaluation of reliability indices for repairable circular consecutive k-out-of-n: F systems,” Reliability Engineering & System Safety, vol. 79, pp. 1–9, 2003. View at Google Scholar
  21. F. D. Gakhov, Boundary Value Problems, Pergamon Press, Oxford, UK, 1996.
  22. E. J. Vanderperre, “A Sokhotski-Plemelj problem related to a robot-safety device system,” Operations Research Letters, vol. 27, no. 2, pp. 67–71, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  23. P. Brêmaud, Point Processes and Queues, Springer Series in Statistics, Springer, Berlin, Germany, 1981.
  24. T. M. Apostol, Mathematical Analysis, Addison-Wesley, Amsterdam, The Netherlands, 1998.
  25. E. J. Vanderperre, “Reliability analysis of a renewable multiple cold standby system,” Operations Research Letters, vol. 32, no. 3, pp. 288–292, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet