Bayesian Analysis of Software Reliability Growth Model with Negative Binomial Information

음이항분포 정보를 가진 베이지안 소프트웨어 신뢰도 성장모형에 관한 연구

  • 김희철 (송호대학 정보산업계열) ;
  • 박종구 (원광대학교 컴퓨터공학과) ;
  • 이병수 (시립인천대학교 컴퓨터정보통신학부)
  • Published : 2000.03.01

Abstract

Software reliability growth models are used in testing stages of software development to model the error content and time intervals betwewn software failures. In this paper, using priors for the number of fault with the negative binomial distribution nd the error rate with gamma distribution, Bayesian inference and model selection method for Jelinski-Moranda and Goel-Okumoto and Schick-Wolverton models in software reliability. For model selection, we explored the sum of the relative error, Braun statistic and median variation. In Bayesian computation process, we could avoid the multiple integration by the use of Gibbs sampling, which is a kind of Markov Chain Monte Carolo method to compute the posterior distribution. Using simulated data, Bayesian inference and model selection is studied.

Keywords

References

  1. Abdel-Ghaly, A, A and Chan, P, Y and Littlewood, B., (1986), 'Evaluation of Competing Software Reliability Predictions,' IEEE Transactions on Software Engineering, 9, pp.950-967
  2. Berger, J. O. and Sun, D., 'Bayesian Analysis For The Poly-Weibull Distribution,' Jourral of the American Statistical Association, 88, pp.1412-1418, 1993 https://doi.org/10.2307/2291285
  3. Box, G., 'Sampling and Bayes' Inference in Scientific Modeling and Robustness (with discussion),' Jourral of the Royal Statistical Society, Ser. A, 143, pp.382-430, 1980 https://doi.org/10.2307/2982063
  4. Casella, G. and George, E. I., 'Explaining the Gibbs Sampler,' The Ameriwn Statistician, 46, pp.167-174, 1992 https://doi.org/10.2307/2685208
  5. Cinlar, E., 'Introduction To Stodastic Process,' New Jersey: Prentice-Hall, 1975
  6. Cox, D. R. and Lewis, P. A, 'Statistical Analysis of Series of Events,' Londen: Methuen, 1966
  7. Dawid, A P., 'Statistical Theory: The Prequential Approach,' Journal of the Royal Statistical Society, Ser. A, 147, pp.278-292, 1984
  8. Geisser, S., and Eddy, W., 'A Predictive Approach to Model Selection,' Journal of the American Statistical Association, 74, pp.153-160, 1979 https://doi.org/10.2307/2286745
  9. Gelfand, A. E. and Smith, A F. M., 'SamplingBased Approaches to Calculating Marginal Densities,' Journal of the American Statistical Association, 85, pp.398-409, 1990 https://doi.org/10.2307/2289776
  10. Gelman, A E., and Rubin D., 'Inference from Iterative Simulation Using Multiple Sequences,' Statistical Science, 7, pp.457-472. 1992
  11. Goel, A. L. and Okumoto, K, 'An analysis of recurrent software failures on a real-time control systems,' Proceedings of the ACM Annual Technical Conference, ACM: Washing D. C. pp.496-500, 1978
  12. Greenberg, E. and Chib, S, 'Understanding the Metropolis-Hastings Agorithm,' The American Statistician' 49, pp.327-335, 1995 https://doi.org/10.2307/2684568
  13. Jelinski, Z., and Moranda, P. B., 'Software Reliability Research, in Statistical Computer Performance Evaluation,' ed. W. Freiberger, New York: Academic Press, pp.465-497, 1972
  14. Joe, H, 'Statistical Inference for General Order Statistics and Nonhogeneous Poisson process Software Reliability Models,' IEEE Transactions on Software Engineering, 15, pp.1485-1490, 1989 https://doi.org/10.1109/32.41340
  15. Kuo, L., and Yang, T. Y., 'Bayesian Computation of Software Reliability,' Journal of Computational and Graphical Statistics, pp.65-82, 1995 https://doi.org/10.2307/1390628
  16. Kuo, L., and Yang, T. Y., 'Bayesian Computation for Nonhomogeneous Poisson process in Software Reliability,' Journal of the American Statistical Association, 91, pp,763-773, 1996 https://doi.org/10.2307/2291671
  17. Langberg, N., and Singpurwalla, N. D., A Unification of Some Software Reliability Models, SIAM Journal on Scientific and Statistical Computing, 6, pp,781-790, 1985 https://doi.org/10.1137/0906053
  18. Lawless, J. F., 'Statistical Models and Methods for lifetime Data,' New York: John Wiley & Sons, 1982
  19. Musa, J. D. and. Iannino, A., and Okumoto, K, 'Software Reliability: Measurement, Prediction, Application,' New York: McGraw Hill, 1987
  20. Musa, J. D., and Okumoto, K, A, 'Logarithmic Poisson Execution Time Model for Software Reliability Measurement,' in Proceedings Seventh International Conference on Software Engineering Orlando, pp.230-238, 1984
  21. Parzen, E., 'Stochastic Process,' San Francisco:Holden-Day, 1962
  22. Raftery, A. E., 'Inference and Prediction for a General Order Statistic Model with Unknown Population Size,' Journal of the American Statistical Association, 92, pp.1195-1212, 1997 https://doi.org/10.2307/2289395
  23. Pesnick, S. I., 'Extreme Values, Regular Variation, and Point Process,' Berlin: Springer-Verlag, 1987
  24. Schick, G. J and Wolverton, R. W., 'An Analysis of Competing Software Reliability Models,' IEEE Transactions on Software Engineering, SE-4, 2, pp.104-120, 1978
  25. Shiha, D. and Day, D. K, 'Semiparametric Bayesian Analysis of Survival Data,' Journal of the American Statistical Association, 81, pp.82-86, 1987 https://doi.org/10.2307/2965586
  26. Tanner, M. and Wong, W., 'The Calculation of Posterior Distributions by Data Augmentation (with discussion),' Journal of the American Statistical Association, 81, pp.82-86, 1987 https://doi.org/10.2307/2289457
  27. USER'S MANUAL STAT/LIBRARY FORTRAN Subroutines for statistical analysis,' IMSL, Vol.3, pp.1050-1054, 1987