Hostname: page-component-7bb8b95d7b-nptnm Total loading time: 0 Render date: 2024-09-18T09:16:15.603Z Has data issue: false hasContentIssue false
  • English
  • Français

ON STOCHASTIC COMPARISONS FOR LOAD-SHARING SERIES AND PARALLEL SYSTEMS

Published online by Cambridge University Press:  08 November 2016

Maxim Finkelstein  and
Nil Kamal Hazra
Maxim Finkelstein
Affiliation:
Department of Mathematical Statistics and Actuarial Science, University of the Free State, PO Box 339, Bloemfontein 9300, South Africa ITMO University, 49 Kronverkskiy pr., St. Petersburg 197101, Russia E-mail: FinkelM@ufs.ac.za
Nil Kamal Hazra
Affiliation:
Department of Mathematical Statistics and Actuarial Science, University of the Free State, PO Box 339, Bloemfontein 9300, South Africa
Get access Rights & Permissions [Opens in a new window]

Abstract

We study the allocation strategies for redundant components in the load-sharing series/parallel systems. We show that under the specified assumptions, the allocation of a redundant component to the stochastically weakest (strongest) component of a series (parallel) system is the best strategy to achieve its maximal reliability. The results have been studied under cumulative exposure model and for a general scenario as well. They have a clear intuitive meaning; however, the corresponding additional assumptions are not obvious, which can be seen from the proofs of our theorems.

Keywords

accelerated lifetime modelcumulative exposure modelhazard rate functionreversed hazard rate functionstochastic ordersvirtual age
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 31 , Issue 3 , July 2017 , pp. 311 - 329
Copyright
Copyright © Cambridge University Press 2016 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Barlow, R.E. & Proschan, F. (1965). Mathematical theory of reliability and life testing. New York: Wiley.Google Scholar
2. Boland, P.J., El-Neweihi, E., & Proschan, F. (1992). Stochastic order for redundancy allocations in series and parallel systems. Advances in Applied Probability 24: 161–171.Google Scholar
3. Brito, G., Zequeira, R.I. & Valdés, J.E. (2011). On the hazard rate and reversed hazard rate orderings in two-component series systems with active redundancies. Statistics and Probability Letters 81: 201–206.Google Scholar
4. Cha, J.H., Mi, J., & Yun, W.Y. (2008). Modelling a general standby system and evaluation of its performance. Applied Stochastic Models in Business and Industry 24: 159–169.Google Scholar
5. Finkelstein, M. (2007). On statistical and information-based virtual age of degrading system. Reliability Engineering and System Safety 92: 676–681.CrossRefGoogle Scholar
6. Finkelstein, M. (2008). Failure rate modelling for reliability and risk. London: Springer-Verlag.Google Scholar
7. Hazra, N.K. & Nanda, A.K. (2014). Component redundancy versus system redundancy in different stochastic orders. IEEE Transactions on Reliability 63: 567–582.Google Scholar
8. Hazra, N.K. & Nanda, A.K. (2014). General standby component allocation in series and parallel systems. arXiv:1401.0132 [stat.AP].Google Scholar
9. Kapur, K.C. & Lamberson, L.R. (1977). Reliability in engineering design. New York: Wiley.Google Scholar
10. Keccecioglu, D. (1991). Reliability engineering handbook. New Jersey: Prentice-Hall.Google Scholar
11. Kijima, M. (1989). Some results for repairable systems with general repair. Journal of Applied Probability 26: 89–102.CrossRefGoogle Scholar
12. Li, X., Wu, Y., & Zhang, Z. (2013). On allocation of general standby redundancy to series and parallel systems. Communications in Statistics – Theory and Methods 42: 4056–4069.Google Scholar
13. Li, X., Zhang, Z., & Wu, Y. (2009). Some new results involving general standby systems. Applied Stochastic Models in Business and Industry 25: 632–642.Google Scholar
14. Lin, H.H., Chen, K.H., & Wang, R.T. (1993). A multivariate exponential shared-load model. IEEE Transactions on Reliability 42: 165–171.Google Scholar
15. Liu, H. (1998). Reliability of a load-sharing k-out-of-n:G system: Non iid components with arbitrary distributions. IEEE Transactions on Reliability 47: 279–284.Google Scholar
16. Misra, A.K. & Misra, N. (2011). A note on active redundancy allocations in k-out-of-n systems. Statistics and Probability Letters 81: 1518–1523.Google Scholar
17. Misra, N., Misra, A.K., & Dhariyal, I.D. (2011). Active redundancy allocations in series systems. Probability in the Engineering and Informational Sciences 25: 219–235.Google Scholar
18. Misra, N., Misra, A.K., & Dhariyal, I.D. (2011). Standby redundancy allocations in series and parallel systems. Journal of Applied Probability 48: 43–55.Google Scholar
19. Nelson, W. (1990). Accelerated testing: statistical methods, test plans, and data analysis. New York: Wiley.Google Scholar
20. Romera, R., Valdés, J.E., & Zequeira, R.I. (2004). Active redundancy allocation in systems. IEEE Transactions on Reliability 53: 313–318.Google Scholar
21. Scheuer, E.M. (1988). Reliability of a m-out-of-n system when component failure induces higher failure rates in survivors. IEEE Transactions on Reliability 37: 73–74.Google Scholar
22. Shaked, M. & Shanthikumar, J.G. (2007). Stochastic orders. New York: Springer.CrossRefGoogle Scholar
23. Shao, J. & Lamberson, L.R. (1991). Modeling a shared-load k-out-of-n:G system. IEEE Transactions on Reliability 40: 205–209.CrossRefGoogle Scholar
24. Shechner, Z. (1984). A load-sharing model: the linear break down rule. Naval Research Logistics 31: 137–144.Google Scholar
25. Valdés, J.E. & Zequeira, R.I. (2003). On the optimal allocation of an active redundancy in a two component series system. Statistics and Probability Letters 63: 325–332.Google Scholar
26. Valdés, J.E. & Zequeira, R.I. (2006). On the optimal allocation of two active redundancies in a two component series system. Operations Research Letters 34: 49–52.Google Scholar
27. Wang, K.S., Huang, J.J., Tsai, Y.T., & Hsu, F.S. (2000). Study of loading policies for unequal strength shared-load system. Reliability Engineering and System Safety 67: 119–128.Google Scholar
28. Yinghui, T. & Jing, Z. (2008). New model for load-sharing k-out-of-n:G system with different components. Journal of Systems Engineering and Electronics 19: 748–751.CrossRefGoogle Scholar
29. Yun, W.Y. & Cha, J.H. (2009). A stochastic model for a general load-sharing system under overload condition. Applied Stochastic Models in Business and Industry 26: 624–638.CrossRefGoogle Scholar
30. Yun, W.Y. & Cha, J.H. (2010). Optimal design of a general warm standby system. Reliability Engineering and System Safety 95: 880–886.CrossRefGoogle Scholar