Browse > Article
http://dx.doi.org/10.3745/KIPSTD.2003.10D.5.805

The Bayesian Analysis for Software Reliability Models Based on NHPP  

Lee, Sang-Sik (송호대학 정보산업계열)
Kim, Hee-Cheul (송호대학 정보산업계열)
Kim, Yong-Jae (경희대학교 컴퓨터공학과)
Abstract
This paper presents a stochastic model for the software failure phenomenon based on a nonhomogeneous Poisson process (NHPP) and performs Bayesian inference using prior information. The failure process is analyzed to develop a suitable mean value function for the NHPP; expressions are given for several performance measure. The parametric inferences of the model using Logarithmic Poisson model, Crow model and Rayleigh model is discussed. Bayesian computation and model selection using the sum of squared errors. The numerical results of this models are applied to real software failure data. Tools of parameter inference was used method of Gibbs sampling and Metropolis algorithm. The numerical example by T1 data (Musa) was illustrated.
Keywords
Software Reliability Model; Gibbs Sampling; Nonhomogeneous Poisson Process; Logarithmic Poisson Model; Software Reliability; Sum of the Squared Errors;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
연도 인용수 순위
1 cinlar, E., 'Introduction To Stochastic Process,' New Jersey, Prentice-Hall, 1975
2 김희철, 이승주, 'RAYLEIGH와 ERLANG 추세를 가진 혼합 고장모형에 대한 베이지안 추론에 관한 연구', 응용통계연구, 제13권 제2호, pp.505-514, 2000   과학기술학회마을
3 이상식, 김희철, 송영재, 'NHPP에 기초한 소프트웨어 신뢰도 모형에 대한 베이지안 추론에 관한 연구', 정보처리학회논문지D, 제9-D권 제3호, pp.389-398, 2002   과학기술학회마을   DOI
4 Casella, G. and George, E. I., 'Explaining the Gibbs Sam-pler,' The American Statistician, 46, pp.167-174, 1992   DOI
5 Geman, S. and Geman, D., 'Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images,' IEEE Transactions on Pattern Analysis and Machine In-telligence, 6, pp.721-741, 1984   DOI   ScienceOn
6 Hossain, S. A. and Dahiya, R. C., 'Estimating the Param-eters of a Non-homogeneous Poission-Process Model for Software Reliability,' IEEE Trans. Rel., Vol.R-42, No.4, pp.604-612, 1993
7 Chib, S ang Greenberg, E., 'Understanding the Metropo-lis-Hastings Algorithm,' The American Statistican, Vol. 49, pp.327-335, 1995   DOI
8 cinlar, E., 'Introduction To Stochastic Process,' New Jer-sey, Prentice-Hall, 1975
9 Gelfand, A. E. and Smith, A. F. M., 'Sampling-Based Ap-proaches to Calculating Marginal Densities,' Journal of the American Statistical Association, 85, pp.398-409, 1990   DOI
10 Musa, J. D., Iannino, A. and Okumoto, K., 'Software Reli-ability : Measurement, Prediction, Application,' New York, McGraw Hill, 1987
11 Okumoto, K., 'A Statistical Method for Software Quality Control,' IEEE Transactions on Software Engineering, Vol.se-11, No.12, pp.1424-1430, 1985   DOI   ScienceOn
12 Gelman, A. E. and Rubin D., 'Inference from Iterative Simulation Using Multiple Sequences,' Statistical Science, 7, pp.457-472, 1992   DOI   ScienceOn
13 Goel, A. L. and Okumoto, K, 'Time Dependent Error Detection Rate Model for Software Reliability and Other Performance Measures,' IEEE Transactions on Reliability, 28, pp.206-211, 1979   DOI   ScienceOn
14 Kuo, L. and Yang, T. Y., 'Bayesian Computation of Soft-ware Reliability,' Journal of Computational and Graphical Statistics, 1995   DOI   ScienceOn
15 Kuo, L. and Yang, T. Y., 'Bayesian Computation for Non-homogeneous Poisson process in Software Reliability,' Journal of the American Statistical Association, 91, pp, 763-773, 1996   DOI
16 'USER'S MANUAL, STAT/LIBRARY FORTRAN Sub-routines for statistical analysis,' IMSL, Vol.3, pp.1050-1054, 1987
17 Lawless, J. F., 'Statistical Models and Methods for Life-time Data,' pp.494-500, 1981
18 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   DOI