Bayesian Inference for Credible Intervals of Optimal Software Release Time

  • Hiroyuki Okamura
  • Tadashi Dohi
  • Shunji Osaki
Part of the Communications in Computer and Information Science book series (CCIS, volume 257)


This paper deals with the estimation of a credible interval of the optimal software release time in the context of Bayesian inference. In the past literature, the optimal software release time was often discussed under the situation where model parameters are exactly known. However, in practice, we should evaluate effects of the optimal software release time on uncertainty of the model parameters. In this paper, we apply Bayesian inference to evaluating the uncertainty of the optimal software release time. More specifically, a Markov chain Monte Carlo (MCMC) method is proposed to compute a credible interval of the optimal software release time.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Achcar, J.A., Dey, D.K., Niverthi, M.: A Bayesian approach using nonhomogeneous Poisson processes for software reliability models. In: Basu, A.P., Basu, K.S., Mukhopadhyay, S. (eds.) Frontiers in Reliability, pp. 1–18. World Scientific, Singapore (1998)CrossRefGoogle Scholar
  2. 2.
    Dohi, T., Nishio, Y., Osaki, S.: Optimal software release scheduling based on artifical neural networks. Annals of Software Engineering 8, 167–185 (1999)CrossRefGoogle Scholar
  3. 3.
    Goel, A.L.: Software reliability models: Assumptions, limitations and applicability. IEEE Transactions on Software Engineering SE-11, 1411–1423 (1985)CrossRefGoogle Scholar
  4. 4.
    Goel, A.L., Okumoto, K.: Time-dependent error-detection rate model for software reliability and other performance measures. IEEE Transactions on Reliability R-28, 206–211 (1979)CrossRefzbMATHGoogle Scholar
  5. 5.
    Gokhale, S.S., Trivedi, K.S.: Log-logistic software reliability growth model. In: Proc. 3rd IEEE Int’l. High-Assurance Systems Eng. Symp. (HASE 1998), pp. 34–41 (1998)Google Scholar
  6. 6.
    Hirata, T., Okamura, H., Dohi, T.: A Bayesian Inference Tool for NHPP-Based Software Reliability Assessment. In: Lee, Y.-h., Kim, T.-h., Fang, W.-c., Ślęzak, D. (eds.) FGIT 2009. LNCS, vol. 5899, pp. 225–236. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  7. 7.
    Littlewood, B.: Rationale for a modified duane model. IEEE Transactions on Reliability R-33(2), 157–159 (1984)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Ohba, M.: Inflection S-shaped software reliability growth model. In: Osaki, S., Hatoyama, Y. (eds.) Stochastic Models in Reliability Theory, pp. 144–165. Springer, Berlin (1984)CrossRefGoogle Scholar
  9. 9.
    Ohba, M.: Software reliability analysis. IBM J. Research & Development 28, 428–443 (1984)CrossRefGoogle Scholar
  10. 10.
    Ohishi, K., Okamura, H., Dohi, T.: Gompertz software reliability model: estimation algorithm and empirical validation. Journal of Systems and Software 82(3), 535–543 (2009)CrossRefGoogle Scholar
  11. 11.
    Okamura, H., Dohi, T.: Building phase-type software reliability model. In: Proc. of the 17th Int’l Symp. on Software Reliab. Eng. (ISSRE 2006), pp. 289–298 (2006)Google Scholar
  12. 12.
    Okamura, H., Dohi, T.: Hyper-Erlang software reliability model. In: Proceedings of 14th Pacific Rim International Symposium on Dependable Computing (PRDC 2008), pp. 232–239. IEEE Computer Society Press, Los Alamitos (2008)CrossRefGoogle Scholar
  13. 13.
    Okamura, H., Dohi, T., Osaki, S.: Software reliability growth model with normal distribution and its parameter estimation. In: Proceedings of the International Conference on Quality, Reliability, Maintenance and Safety Engieering (ICQR2MSE), pp. 424–429 (2011)Google Scholar
  14. 14.
    Okumoto, K., Goel, L.: Optimum release time for software systems based on reliability and cost criteria. Journal of Systems and Software 1, 315–318 (1980)CrossRefGoogle Scholar
  15. 15.
    Xie, M., Hong, G.Y.: A study of the sensitivity of software release time. The Journal of Systems and Software 44, 163–168 (1998)CrossRefGoogle Scholar
  16. 16.
    Yamada, S., Ohba, M., Osaki, S.: S-shaped reliability growth modeling for software error detection. IEEE Transactions on Reliability R-32, 475–478 (1983)CrossRefGoogle Scholar
  17. 17.
    Yamada, S., Osaki, S.: Cost-reliability optimal release policies for software systems. IEEE Transactions on Reliability R-34, 422–424 (1985)CrossRefGoogle Scholar
  18. 18.
    Zhao, M., Xie, M.: On maximum likelihood estimation for a general non-homogeneous Poisson process. Scand. J. Statist. 23, 597–607 (1996)MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Hiroyuki Okamura
    • 1
  • Tadashi Dohi
    • 1
  • Shunji Osaki
    • 2
  1. 1.Department of Information Engineering, Graduate School of EngineeringHiroshima UniversityHigashi-HiroshimaJapan
  2. 2.Faculty of Information Sciences and EngineeringNanzan UniversitySetoJapan

Personalised recommendations