Skip to main content
Have a personal or library account? Click to login
A Simple Discrete Approximation for the Renewal Function Cover

A Simple Discrete Approximation for the Renewal Function

Open Access
|May 2013

References

  1. 1. Ayhan H., Limon-Robles, J., Wortman M. A. (1999), „An approach for computing tight numerical bounds on renewal functions”, IEEE Transactions on Reliability, Vol. 48 No. 2, pp. 182-188.
  2. 2. Barlow, R. E., Proschan, F., Hunter, L. C. (1996). Mathematical Theory of Reliability, Philadelphia, SIAM.
  3. 3. Barouch, E., Kaufman, G. M. (1976), „On Sums of Lognormal Random Variables”. Working paper, Alfred P. Sloan School of Management, Cambridge, Massachusetts, available at http://dspace.mit.edu/bitstream/handle/1721.1/48703/onsumsoflognorma00baro.pdf / (10 June 2011).
  4. 4. Bebbington, M., Davydov, Y., Zitikis, R. (2007), „Estimating the renewal function when the second moment is infinite”, Stochastic Models, Vol. 23 No.1, pp. 27 - 48.
  5. 5. Beichelt, F. (2006). Stochastic Processes in Science, Engineering And Finance, Boca Raton, Chapman & Hall/CRC.
  6. 6. Brezavšček, A. (2011), „Simple Stochastic Model for Planning the Inventory of Spare Components Subject to Wear-out”, Organizacija, Vol. 44 No. 4, pp. 120 - 127.
  7. 7. Chaudhry, M. L. (1995), „On computations of the mean and variance of the number of renewals: a unified approach”, The Journal of the Operational Research Society, Vol. 46 No. 11, pp. 1352-1364.
  8. 8. Cox, D. R. (1970). Renewal Theory, London & Colchester: Methuen.
  9. 9. Cui, L., Xie, M. (2003), „Some normal approximations for renewal function of large Weibull shape parameter”, Communications in Statistics - Simulation and Computation, Vol. 32 No. 1, pp. 1-16.
  10. 10. Garg, A., Kalagnanam, J. R. (1998), „Approximations for the renewal function”, IEEE Transactions on Reliability, Vol. 47 No. 1, pp. 66-72.
  11. 11. Gertsbakh, I. (2000). Reliability Theory, With Applications to Preventive Maintenance, Berlin: Springer Verglag.
  12. 12. Hu, X. (2006), „Approximation of partial distribution in renewal function calculation”, Computational Statistics & Data Analysis, Vol. 50 No. 6, pp. 1615-1624.
  13. 13. Jardine, A. K. S. (1973). Maintenance, Replacement, and Reliability, London, Pitman.
  14. 14. Jardine, A. K. S., Tsang, A. H. C. (2006). Maintenance, Replacement, and Reliability: Theory and Applications, Boca Raton, CRC/Taylor & Francis.
  15. 15. Jiang, R. (2008), „A Gamma-normal series truncation approximation for computing the Weibull renewal function”, Reliability Engineering & System Safety, Vol. 93 No. 4, pp. 616- 626.
  16. 16. Jiang, R. (2010), „A simple approximation for the renewal function with an increasing failure rate”, Reliability Engineering & System Safety, Vol. 95 No. 9, pp. 963-969.
  17. 17. Johnson, N. L, Kotz, S., Balakrishnan, N. (1994), Continuous Univariate Distributions, Volumes I and II, 2nd. Ed., New York: John Wiley and Sons.
  18. 18. Kottegoda, N. T., Rosso, R. (1997). Statistics, Probability, and Reliability for Civil and Environmental Engineers, New York: McGraw-Hill.
  19. 19. Lam, C. L. J., Le-Ngoc, T. (2006), „Estimation of typical sum of lognormal random variables using log shifted gamma approximation”, IEEE Communications Letters, Vol. 10 No. 4, pp. 234- 235.
  20. 20. Nakagawa, T. (2011). Stochastic Processes: with Applications to Reliability Theory, London: Springer-Verlag.
  21. 21. O'Connor, A. N. (2011). Probability Distributions Used in Reliability Engineering, Maryland: RIAC.
  22. 22. Politis, K., Koutras, M. V. (2006), „Some new bounds for the renewal function”, Probability in the Engineering and Informational Sciences, Vol. 20 No. 2, pp. 231 - 250.
  23. 23. Rinne, H. (2009). The Weibull Distribution: A Handbook, New York: CRC Press, Taylor & Francis Group.
  24. 24. Robinson, N. I. (1997), „Renewal functions as series”, Stochastic Models, Vol. 13 No. 3, pp. 577- 604.
  25. 25. Romeo, M., Da Costa, V., Bardou, F. (2003), „Broad distribution effects in sums of lognormal random variables”, The European Physical Journal B - Condensed Matter and Complex Systems, Vol. 32 No. 4, pp. 513-525.
  26. 26. Sheikh, A. K., Younas, M. (1985), “Renewal Models in Reliability Engineering”, in Deopker, P. E. (Ed.), Failure and Prevention and Reliability, ASME, pp. 93-103.
  27. 27. Smeitink, E., Dekker, R. (1990), „A simple approximation to the renewal function”, IEEE Transactions on Reliability, Vol. 39 No. 1, pp. 71-75.
  28. 28. Tijms, H. C. (2003). A First Course in Stochastic Models, Chichester: John Wiley & Sons.
  29. 29. van Noortwijk, J. M., van der Weide, J. A. M. (2008), „Applications to continuous-time processes of computational techniques for discrete-time renewal processes”, Reliability Engineering & System Safety, Vol. 93 No. 12, pp. 1853-1860.
DOI: https://doi.org/10.2478/bsrj-2013-0006 | Journal eISSN: 1847-9375 | Journal ISSN: 1847-8344
Language: English
Page range: 65 - 75
Published on: May 14, 2013
Published by: IRENET - Society for Advancing Innovation and Research in Economy
In partnership with: Paradigm Publishing Services

© 2013 Alenka Brezavšček, published by IRENET - Society for Advancing Innovation and Research in Economy
This work is licensed under the Creative Commons License.