정보처리학회논문지D (The KIPS Transactions:PartD)

한국정보처리학회 (Korea Information Processing Society)
권호 표지
DOI QR코드

DOI QR Code

NHPP 소프트웨어 신뢰도 모형에 대한 모수 추정 비교

The Comparison of Parameter Estimation for Nonhomogeneous Poisson Process Software Reliability Model

  • 김희철 (한라대학교 정보통신학부) ;
  • 이상식 (송호대학 정보산업계열) ;
  • 송영재 (경희대학교 컴퓨터공학과)
  • 발행 : 2004.10.01
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

본 논문에서는 기존의 소프트웨어 신뢰성 모형인 Goel-Okumoto 모형과 Yamada-Ohba-Osaki 모형을 재조명하고 또, 랄리 분포를 이용한 랄리 모형을 적용하여 모수 추정방법을 연구하였다. 본 연구에서는 기존의 최우추정법과 잠재변수를 도입하여 깁스 샘플링(Gibbs sampling)을 이용한 베이지안 모수추정 방법을 비교하고 그 특징을 분석하고자 한다. 또, 효율적 모형을 위한 모형선택으로서 잔차제곱합(Sum of the squared errors ; SSE)과 Braun 통계량을 적용하여 모형들에 대한 효율성 입증방법을 설명하였다. 그리고 수치적인 예로서 실제 자료를 이용한 수치 견과를 나열하였다. 이 접근방법을 기초로 하여 수명분포가 중첩(Superposition) 및 혼합(Mixture)인 경우에 대한 접근방법이 연구되었으면 한다.

The Parameter Estimation for software existing reliability models, Goel-Okumoto, Yamada-Ohba-Osaki model was reviewed and Rayleigh model based on Rayleigh distribution was studied. In this paper, we discusses comparison of parameter estimation using maximum likelihood estimator and Bayesian estimation based on Gibbs sampling to analysis of the estimator' pattern. Model selection based on sum of the squared errors and Braun statistic, for the sake of efficient model, was employed. A numerical example was illustrated using real data. The current areas and models of Superposition, mixture for future development are also employed.

키워드

참고문헌

  1. Casella, G. and George, E. I., 'Explaining the Gibbs Sampler,' The American Statistician, 46, pp.167-174, 1992 https://doi.org/10.2307/2685208
  2. Chib, S ang Greenberg, E., 'Understanding the Metropolis-Hastings Algorithm,' The American Statistican, Vol.49, pp.327-335, 1995 https://doi.org/10.2307/2684568
  3. Gelfand, A. E. and Smith, A. F. M., 'Sampling-Based Approaches to Calculating Marginal Densities,' Journal of the American Statistical Association, 85, pp.398-409, 1990 https://doi.org/10.2307/2289776
  4. Geman, S. and Geman, D., 'Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images,' IEEE Transactions on Pattern Analysis and Machine Intelligence, 6, pp.721-741, 1984
  5. Gelman, A. E. and Rubin D., 'Inference from Iterative Simulation Using Multiple Sequences,' Statistical Science, 7, pp.457-472, 1992 https://doi.org/10.1214/ss/1177011136
  6. Goel, A. L., Software Reliability Model: Assumption, Limitations, and Applicability, IEEE Trans. Software Eng., Vol.SE-11, No.12, pp.1411-1423, 1985 https://doi.org/10.1109/TSE.1985.232177
  7. 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 https://doi.org/10.1109/TR.1979.5220566
  8. Kuo, L. and Yang, T. Y., 'Bayesian Computation of Software Reliability,' Journal of Computational and Graphical Statistics, 1995 https://doi.org/10.2307/1390628
  9. 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 https://doi.org/10.2307/2291671
  10. Lawless, J. F., Statistical Models and Methods for Lifetime Data, New York: John Wiley & Sons, 1981
  11. Lyu, M. R., Handbook of Software Reliability Engineeringa, New York, NY : McGraw Hill, pp.128-131, 1996
  12. Musa, J. D., Iannino, A. and Okumoto, K, Software Reliability: Measurement, Prediction, Application, New York : McGraw Hill, 1987.
  13. Okumoto, K., 'A Statistical Method for Software Quality Control,' IEEE Transactions on Software Engineering, Vol.se-11, No.12, pp.1424-1430, 1985 https://doi.org/10.1109/TSE.1985.232178
  14. User Manual STAT/LIBRARY Fortran Subroutines for statiatical analysis, IMSL, Vol.3, 1987
  15. Yamada, S., Ohba, M. and Osaki, S., 'S-shaped Reliability Growth Modeling for Software Error Detection,' IEEE Trans. Rel., Vol.R-32, No.5, pp.475-47, 1983 https://doi.org/10.1109/TR.1983.5221735
  16. Yamada, S., Ohtera, H. and Narihisa, H., 'Software Reliability Growth Models with Testing-Effort,' IEEE Trans. Rel., Vol.R-35, No.1, pp.19-23, 1986