On Allocation of Active Redundancies to Systems: A Brief Review

Chapter
Part of the Lecture Notes in Statistics book series (LNS, volume 208)

Abstract

In reliability engineering and system security, it is of great practical interest to allocate active redundancies at either component or system level so as to enhance the system’s lifetime or improve some other performances of the system. This topic has been paid much attention ever since reliability theory took its form in the early 1970s. In this paper, we review these results in the reliability literature on allocating active redundancies to a coherent system. Using these theories, engineers are guided to design a better system or to optimize the performance of the original system in the sense of some stochastic orders. Recent theoretical results as well as some applications are also presented.

Notes

Acknowledgments

Xiaohu Li and Weiyong Ding are supported by National Natural Science Foundation of China (10771090)

Bibliography

  1. [39]
    Barlow, R. E. and Proschan, F.: Statistical Theory of Reliability and Life Testing. To Begin With, Silver Spring, Maryland (1981)Google Scholar
  2. [53]
    Belzunce, F., Martínez-Puertas, H. and Ruiz, J. M.: On optimal allocation of redundant components for series and parallel systems of two dependent components. Journal of Statistical Planning and Inference, 141, 3094–3104 (2011)MathSciNetMATHCrossRefGoogle Scholar
  3. [66]
    Boland, P. J. and El-Newehi, E.: Component redundancy vs. system redundancy in the hazard rate ordering. IEEE Transactions on Reliability, 44, 614–619 (1995)CrossRefGoogle Scholar
  4. [68]
    Boland, P. J., EI-Newehi, E. and Proschan, F.: Active redundancy allocation in coherent systems. Probability in the Engineering and Informational Science, 2, 343–353 (1988)Google Scholar
  5. [70]
    Boland, P. J., EI-Newehi, E. and Proschan, F.: Stochastic order for redundancy allocations in series and parallel systems. Advancesin Applied Probability, 24, 161–171 (1992)Google Scholar
  6. [82]
    Cha, J. H., Mi, J. and Yun, W. Y.: Modelling a general standby system and evaluation of its performance. Applied Stochastic Models in Business and Industry, 24, 159–169 (2008)MathSciNetMATHCrossRefGoogle Scholar
  7. [133]
    Ding, W. and Li, X.: Optimal allocation of active redundancies to k-out-of-n systems with respect to the hazard rate order. Journal of Statistical Planning and Inference, 142, 1878–1887 (2012)MathSciNetMATHCrossRefGoogle Scholar
  8. [146]
    EI-Newehi, E., Proschan, F. and Sethuraman, J.: Optimal allocation of components in parallel-series and series-parallel systems. Journal of Applied Probability, 23, 770–777 (1986)Google Scholar
  9. [147]
    EI-Newehi, E. and Sethuraman, J.: Optimal allocation under partial ordering of lifetimes of components. Advances in Applied Probability, 25, 914–925 (1993)Google Scholar
  10. [153]
    Esary, J. D., Marshall, A. W. and Proschan, F.: Some reliability applications of the hazard transform. SIAM Journal of Applied Mathematics, 18, 849–860 (1970)MathSciNetMATHCrossRefGoogle Scholar
  11. [201]
    Hu, T. and Wang, Y.: Optimal allocation of active redundancies in r-out-of-n system. Journal of Statistical Planning and Inference, 139, 3733–3737 (2009)MathSciNetMATHCrossRefGoogle Scholar
  12. [253]
    Kochar, S. C., Mukerjee, H. and Samaniego, F. J.: The “signature” of a coherent system and its application to comparison among systems. Naval Research Logistics, 46, 507–523 (1999)MathSciNetMATHCrossRefGoogle Scholar
  13. [287]
    Li, X. and Ding, W.: Optimal allocation of active redundancies to k-out-of-n systems with heterogenous components. Journal of Applied Probability, 47, 254–263 (2010)MathSciNetMATHCrossRefGoogle Scholar
  14. [288]
    Li, X. and Hu, X.: Some new stochastic comparisons for redundancy allocations in series and parallel systems. Statistics and Probability Letters, 78, 3388–3394 (2008)MathSciNetMATHCrossRefGoogle Scholar
  15. [293]
    Li, X., Wu, Y. and Zhang, Z.: On allocation of general standby redundancy to series and parallel systems. Communications in Statistics-Theory and Methods. (in press) (2012)Google Scholar
  16. [294]
    Li, X., Yan, R. and Hu, X.: On the allocation of redundancies in series and parallel systems. Communications in Statistics-Theory and Methods, 40, 959–968 (2011)MathSciNetMATHCrossRefGoogle Scholar
  17. [295]
    Li, X., Zhang, Z. and Wu, Y.: Some new results involving general standby systems. Applied Stochastic Models in Business and Industry, 25, 632–642 (2009)MathSciNetMATHCrossRefGoogle Scholar
  18. [312]
    Marshall, A. W., Olkin, I. and Arnold, B. C.: Inequalities: Theory of Majorization and Its Applications. Springer, New York (2011)MATHCrossRefGoogle Scholar
  19. [319]
    Mi, J.: Optimal active redundancy allocation in k-out-of-n system. Journal of Applied Probability, 36, 927–933 (1999)MathSciNetMATHCrossRefGoogle Scholar
  20. [322]
    Misra, N., Dhariyal, I. and Gupta, N.: Optimal allocation of active spares in series systems and comparison of component and system redundancies. Journal of Applied Probability, 46, 19–34 (2009)MathSciNetMATHCrossRefGoogle Scholar
  21. [324]
    Misra, N., Misra, A. K. and Dhariyal, I.: Active redundancy allocations in series systems. Probability in the Engineering and Informational Sciences, 25, 219–235 (2011)MathSciNetMATHCrossRefGoogle Scholar
  22. [325]
    Misra, N., Misra, A. K. and Dhariyal, I.: Standby redundancies allocation in series and parallel systems. Journal of Applied Probability, 48, 1–13 (2011)MathSciNetCrossRefGoogle Scholar
  23. [335]
    Müller, A. and Stoyan, D.: Comparison Methods for Stochastic Models and Risks. Wiley, Chichester (2002)MATHGoogle Scholar
  24. [408]
    Samaniego, F. J.: System Signatures and Their Applications in Engineering Reliability. New York: Springer (2007)MATHCrossRefGoogle Scholar
  25. [421]
    Shaked, M. and Shanthikumar, J. G.: Optimal allocation of resources to nodes of series and parallel systems. Advances in Applied Probability, 24, 894–914. (1992)MathSciNetMATHCrossRefGoogle Scholar
  26. [426]
    Shaked, M. and Shanthikumar, J. G.: Stochastic Orders. Springer, New York (2007)MATHCrossRefGoogle Scholar
  27. [434]
    Singh, H. and Misra, N.: On redundancy allocation in systems. Journal of Applied Probability 31, 1004–1014 (1994).MathSciNetMATHCrossRefGoogle Scholar
  28. [435]
    Singh, H. and Singh, R. S.: On allocation of spares at component level vs system level. Journal of Applied Probability, 34, 283–287 (1997)MathSciNetMATHCrossRefGoogle Scholar
  29. [436]
    Singh, H. and Singh, R. S.: Optimal allocation of resourses to nodes of series systems with respect to failure-rate ordering. Naval Research Logistics, 44, 147–152 (1997)MATHCrossRefGoogle Scholar
  30. [457]
    Valdès, J. E., Arango, G., Zequeira, R. I. and Brito, G.: Some stochastic comparisons in series system with active redundancies. Statistics and Probability Letters, 80, 945–949 (2010)MathSciNetMATHCrossRefGoogle Scholar
  31. [458]
    Valdès, J. E. and Zequeira, R. I.: On the optimal allocation of an active redundancy in a two-component series system. Statistics and Probability Letters, 63, 235–332 (2003)CrossRefGoogle Scholar
  32. [459]
    Valdès, J. E. and Zequeira, R. I.: On the optimal allocation of two active redundancies in a two-component series system. Operations Research Letters, 34, 49–52 (2006)MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.School of Mathematical SciencesXiamen UniversityXiamenChina
  2. 2.College of ScienceHebei United UniversityTangshanChina

Personalised recommendations