Advances in Decision Sciences

Advances in Decision Sciences / 2006 / Article

Open Access

Volume 2006 |Article ID 34506 | 11 pages | https://doi.org/10.1155/JAMDS/2006/34506

New approximate solutions per unit of time for periodically checked systems with different lifetime distributions

Received26 Oct 2005
Revised19 Sep 2006
Accepted24 Sep 2006
Published08 Nov 2006

Abstract

Systems with different lifetime distributions, associated with increasing, decreasing, constant, and bathtub-shaped hazard rates, are examined in this paper. It is assumed that a failure is only detected if systems are inspected. New approximate solutions for the inspection period and for the expected duration of hidden faults are presented, on the basis of the assumption that only periodic and perfect inspections are carried out. By minimizing total expected cost per unit of time, on the basis of numerical results and a range of comparisons, the conclusion is drawn that these new approximate solutions are extremely useful and simple to put into practice.

References

  1. J. A. Amaral, M. B. Rosário, and M. T. Paixão, “Data and projections of HIV and AIDS in Portugal,” Journal of Applied Statistics, vol. 27, no. 3, pp. 269–279, 2000. View at: Publisher Site | Google Scholar | Zentralblatt MATH
  2. F. G. Badía, M. D. Berrade, and C. A. Campos, “Optimization of inspection intervals based on cost,” Journal of Applied Probability, vol. 38, no. 4, pp. 872–881, 2001. View at: Google Scholar | Zentralblatt MATH | MathSciNet
  3. R. E. Barlow, L. C. Hunter, and F. Proschan, “Optimum checking procedures,” Journal of Society for Industrial and Applied Mathematics, vol. 11, no. 4, pp. 1078–1095, 1963. View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet
  4. L. Dieulle, “Reliability of a system with Poisson inspection times,” Journal of Applied Probability, vol. 36, no. 4, pp. 1140–1154, 1999. View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet
  5. U. Hjorth, “A reliability distribution with increasing, decreasing, constant and bathtub-shaped failure rates,” Technometrics, vol. 22, no. 1, pp. 99–107, 1980. View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet
  6. T. Nakagawa and K. Yasui, “Approximate calculation of inspection policy with Weibull failure times,” IEEE Transactions on Reliability, vol. 28, no. 5, pp. 403–404, 1979. View at: Google Scholar | Zentralblatt MATH
  7. J. Rodrigues Dias, “Influence de la période d'inspection sur les Couts dans l'inspection périodique des systêmes,” Revue de Statistique Appliquée, vol. 31, no. 4, pp. 5–15, 1983. View at: Google Scholar
  8. J. Rodrigues Dias, “A new approximation for the inspection period of systems with different failure rates,” European Journal of Operational Research, vol. 45, no. 2-3, pp. 219–223, 1990. View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet
  9. J. Rodrigues Dias, “Some approximate inspection policies for a system with imperfect inspections,” RAIRO Recherche Opérationnelle, vol. 24, no. 2, pp. 191–199, 1990. View at: Google Scholar | MathSciNet
  10. J. Rodrigues Dias, “Analysis of a new method for obtaining different sampling intervals in statistical quality control,” in Actas do IV Congreso Galego de Estatística e Investigación de Operacións, pp. 155–158, University of Santiago da Compostela, Spain, 1999. View at: Google Scholar
  11. J. Rodrigues Dias, “Sampling in quality control with different predetermined intervals: a new approach,” in Jornadas de Classificação e Análise de Dados (JOCLAD '02), Lisbon, 2002. View at: Google Scholar
  12. J. Rodrigues Dias and P. Infante, “Parallel systems with different hazard rates: analysis of inspection periods and costs,” Pesquisa Operacional, vol. 24, no. 3, pp. 343–354, 2004. View at: Google Scholar
  13. S. M. Ross, Stochastic Processes, Wiley Series in Probability and Statistics: Probability and Statistics, John Wiley & Sons, New York, 2nd edition, 1996. View at: Google Scholar | Zentralblatt MATH | MathSciNet
  14. E. M. Saniga and L. E. Shirland, “Quality control in practice—a survey,” Quality Progress, vol. 10, no. 5, pp. 30–33, 1977. View at: Google Scholar
  15. W. G. Schneeweiss, “On the mean duration of hidden faults in periodically checked systems,” IEEE Transactions on Reliability, vol. 25, no. 5, pp. 346–348, 1976. View at: Google Scholar | Zentralblatt MATH
  16. S. H. Sheu, Y. C. Chen, W. Y. Wang, and N. H. Shin, “Economic optimization of off-line inspection with inspection errors,” Journal of the Operational Research Society, vol. 54, no. 8, pp. 888–895, 2003. View at: Publisher Site | Google Scholar
  17. J. K. Vaurio, “Optimization of test and maintenance intervals based on risk and cost,” Reliability Engineering & System Safety, vol. 49, no. 1, pp. 23–36, 1995. View at: Publisher Site | Google Scholar

Copyright © 2006 J. Rodrigues Dias. 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.

0 Views | 0 Downloads | 0 Citations
 PDF  Download Citation  Citation
 Order printed copiesOrder