Advances in Decision Sciences

Advances in Decision Sciences / 2007 / Article
Special Issue

Statistics and Applied Probability: A Tribute to Jeffrey J. Hunter

View this Special Issue

Research Article | Open Access

Volume 2007 |Article ID 043565 |

Mark Bebbington, Chin-Diew Lai, Ricardas Zitikis, "Reliability of Modules with Load-Sharing Components", Advances in Decision Sciences, vol. 2007, Article ID 043565, 18 pages, 2007.

Reliability of Modules with Load-Sharing Components

Academic Editor: Paul Cowpertwait
Received17 Apr 2007
Accepted08 Aug 2007
Published16 Sep 2007


To increase the reliability of modules, and thus of systems assembled from them, they are frequently constructed using parallel load-sharing components. Examples include jet engines, electrical power networks, and telecommunications networks. We consider the situation when the components operate independently, but when any one of them fails, the load of the failed component is instantaneously distributed among the working components. The entire module fails when the last working component fails. We analyze the survival probability and residual life expectancy of such modules. An obvious application is to the case of the 1998 Auckland power supply failure in New Zealand.


  1. J. Shao and L. R. Lamberson, “Modeling a shared-load k-out-of-n:G system,” IEEE Transactions on Reliability, vol. 40, no. 2, pp. 205–209, 1991. View at: Publisher Site | Google Scholar | Zentralblatt MATH
  2. Flight Saftey Australia, “Deadstick in an Airbus 330,” 2001, View at: Google Scholar
  3. Wikipedia, “Gimli Gilder,” 2007, View at: Google Scholar
  4. Wikipedia, “1998 Auckland Power Crisis,” 2006,\Auckland\power\crisis. View at: Google Scholar
  5. Ministry of Economic Development, “Auckland Power Supply Failure 1998: The Report of the Ministerial Inquiry into the Auckland Power Supply Failure,” 1998, Ministry of Economic Development, Wellington, New Zealand, View at: Google Scholar
  6. W. Q. Meeker and L. A. Escobar, Statistical Methods for Reliability Data, John Wiley & Sons, New York, NY, USA, 1998. View at: Zentralblatt MATH
  7. C.-D. Lai and M. Xie, Stochastic Ageing and Dependence for Reliability, Springer, New York, NY, USA, 2006. View at: Zentralblatt MATH | MathSciNet
  8. D. N. P. Murthy and D. G. Nguyen, “Study of two-component system with failure interaction,” Naval Research Logistics Quarterly, vol. 32, no. 2, pp. 239–247, 1985. View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet
  9. D. N. P. Murthy and R. J. Wilson, “Parameter estimation in multi-component systems with failure interaction,” Applied Stochastic Models and Data Analysis, vol. 10, no. 1, pp. 47–60, 1994. View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet
  10. H. Kim and P. H. Kvam, “Reliability estimation based on system data with an unknown load share rule,” Lifetime Data Analysis, vol. 10, no. 1, pp. 83–94, 2004. View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet
  11. P. H. Kvam and E. A. Peña, “Estimating load-sharing properties in a dynamic reliability system,” Journal of the American Statistical Association, vol. 100, no. 469, pp. 262–272, 2005. View at: Publisher Site | Google Scholar | MathSciNet
  12. H. Liu, “Reliability of a load-sharing k-out-of-n:G system: non-iid components with arbitrary distributions,” IEEE Transactions on Reliability, vol. 47, no. 3, part 1, pp. 279–284, 1998. View at: Publisher Site | Google Scholar
  13. R. I. Zequeira and C. Bérenguer, “On the inspection policy of a two-component parallel system with failure interaction,” Reliability Engineering & System Safety, vol. 88, no. 1, pp. 99–107, 2005. View at: Publisher Site | Google Scholar
  14. W. B. Nelson, Accelerated Testing: Statistical Models, Test Plans, and Data Analysis, John Wiley & Sons, New York, NY, USA, 2004.
  15. N. Mimoto and R. Zitikis, “The Atkinson index, the Moran statistic, and testing exponentiality,” submitted to Journal of the Japan Statistical Society. View at: Google Scholar
  16. R. E. Barlow and F. Proschan, Statistical Theory of Reliability and Life Testing, To Begin With, Silver Spring, Md, USA, 1981.

Copyright © 2007 Mark Bebbington et al. 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.

More related articles

124 Views | 386 Downloads | 6 Citations
 PDF Download Citation Citation
 Order printed copiesOrder

Related articles

We are committed to sharing findings related to COVID-19 as quickly as possible. We will be providing unlimited waivers of publication charges for accepted research articles as well as case reports and case series related to COVID-19. Review articles are excluded from this waiver policy. Sign up here as a reviewer to help fast-track new submissions.