Bayesian Inferences for Software Reliability Models Based on Beta-Mixture Mean Value Functions

Nam, Seung-Min;Kim, Ki-Woong;Cho, Sin-Sup;Yeo, In-Kwon

  • Published : 2008.10.31


In this paper, we investigate a Bayesian inference for software reliability models based on mean value functions which take the form of the mixture of beta distribution functions. The posterior simulation via the Markov chain Monte Carlo approach is used to produce estimates of posterior properties. Its applicability is illustrated with two real data sets. We compute the predictive distribution and the marginal likelihood of various models to compare the performance of them. The model comparison results show that the model based on the beta-mixture performs better than other models.


Beta-mixture;MCMC;mean value function;nonhomogeneous Poisson processes


  1. Achcar, J. A., Dey, D. K. and Niverthi, M. (1997). A Bayesian approach using nonhomogeneous Poisson process for software reliability models, In Frontiers in Reliability, A.P. Basu, S. K. Basu and S. Mukhopadhyay,(Eds.), 1-18, World Scientific Publishing: Singapore
  2. Goel, A. L. and Okumoto, K. (1979). Time-dependent error detection rate model for software reliability and other performance measures, IEEE Transactions on Reliability, 28, 206-211
  3. Jelinski, Z. and Moranda, P. B. (1972). Software reliability research, In Statistical Computer Performance Evaluation, Freiburger, W. (Eds.), Academic Press, New York, 465-497
  4. Kim, D. K., Yeo, I. K. and Park, D. H. (2006). Nonhomogeneous Poisson processes based on Beta-mixtures in software reliability models, Advanced Reliability Modeling II - Reliability Testing and Improvement, 403-410
  5. Gelman, A. and Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences, Statistical Science, 7, 457-472
  6. Goel, A. L. (1983). A Guide Book for Software reliability Assessment, Technical Report, Rome air Development Center, Rome, New York
  7. Cox, D. R. and Lewis, P. A. (1966). Statistical Analysis of Series of Events, Chapman & Hall/CRC, London
  8. Diaconis, P. and Ylvisaker, D. (1985). Quantifying prior opinion, In Bayesian Statistics 2, J. M. Bernado, M. H. DeGroot, D. V. Lindley and A. F. M. Smith,(Eds.), 133-156, Amsterdam: North Holland
  9. Duane, J. T. (1964). Learning curve approach to reliability monitoring, IEEE Transactions on Aerospace, AS-2, 563-566
  10. Kuo, L. and Yang, T. Y. (1995). Bayesian computation of software reliability, Journal of Computational and Graphical Statistics, 4, 65-82
  11. Kuo, L. and Yang, T. Y. (1996). Bayesian computation for nonhomogeneous Poisson processes in software reliability, Journal of the American Statistical Association, 91, 763-772
  12. Musa, J. D. and Okumoto, K. (1984). A logarithmic Poisson execution time model for software reliability measurement, In Proceedings of the Seventh nternational conference on software engineering, 230-238
  13. Ohba, M., Yamada, S., Takeda, K. and Osaki, S. (1982). S-shaped software reliability growth curve: How good is it?, COMPSAC '82, 38-44
  14. Singpurwalla, N. D. and Soyer, R. (1985). Assessing (software) reliability growth using a random coefficient autoregressive process and its ramifications, IEEE Transactions on Software Engineering, 11, 1456- 1464
  15. Tohma, Y., Yamano, H., Obha, M. and Jacoby, R. (1991). The estimation of parameters of the hypergeometric distribution and its application to the software reliability growth model, IEEE Transactions on Software Engineering, 17, 483-489
  16. Basu, S. and Ebrahimi, N. (2003). Bayesian software reliability models based on Martingale processes, Technometrics, 45, 150-158
  17. Gelfand, A. E. and Mallick, B. K. (1995). Bayesian analysis of proportional hazards models built from monotone functions, Biometrics, 51, 843-852
  18. Littlewood, B. and Verall, J. L. (1973). A Bayesian reliability growth model for computer science, Applied Statistics, 22, 332-346
  19. Mallick, B. K. and Gelfand, A. E. (1994). Generalized linear models with unknown link functions, Biometrika, 81, 237-245
  20. Mazzuchi, T. A. and Soyer, R. (1988). A Bayes empirical-Bayes model for software reliability, IEEE Transactions on Reliability, 37, 248-254