Journal of the Korea Academia-Industrial cooperation Society (한국산학기술학회논문지)

The Korea Academia-Industrial cooperation Society (한국산학기술학회)
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The Study of Software Reliability Model from the Perspective of Learning Effects for Burr Distribution

Burr분포 학습 효과 특성을 적용한 소프트웨어 신뢰도 모형에 관한 연구

  • Kim, Dae-Soung (Division of e-Business, Gyeonggi College of Science and Technology) ;
  • Kim, Hee-Cheul (Division of Industrial and Management Engineering, Namseoul University)
  • 김대성 (경기과학기술대학교 e-비즈니스과) ;
  • 김희철 (남서울대학교 산업경영공학과)
  • Received : 2011.08.30
  • Accepted : 2011.10.06
  • Published : 2011.10.31
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Abstract

In this study, software products developed in the course of testing, software managers in the process of testing software test and test tools for effective learning effects perspective has been studied using the NHPP software. The Burr distribution applied to distribution was based on finite failure NHPP. Software error detection techniques known in advance, but influencing factors for considering the errors found automatically and learning factors, by prior experience, to find precisely the error factor setting up the testing manager are presented comparing the problem. As a result, the learning factor is greater than automatic error that is generally efficient model could be confirmed. This paper, a numerical example of applying using time between failures and parameter estimation using maximum likelihood estimation method, after the efficiency of the data through trend analysis model selection were efficient using the mean square error and $R^2$.

본 연구에서는 소프트웨어 제품을 개발하여 테스팅을 하는 과정에서 소프트웨어 관리자들이 소프트웨어 및 검사 도구에 효율적인 학습기법을 이용한 NHPP 소프트웨어 모형에 대하여 연구 하였다. 적용분포는 버르 분포를 적용한 유한고장 NHPP에 기초하였다. 소프트웨어 오류 탐색 기법은 사전에 알지 못하지만 자동적으로 발견되는 에러를 고려한 영향요인과 사전 경험에 의하여 세밀하게 에러를 발견하기 위하여 테스팅 관리자가 설정해놓은 요인인 학습효과의 특성에 대한 문제를 비교 제시 하였다. 그 결과 학습요인이 자동 에러 탐색요인보다 큰 경우가 대체적으로 효율적인 모형임을 확인 할 수 있었다. 본 논문의 수치적인 예에서는 고장 간격 시간 자료를 적용하고 모수추정 방법은 최우추정법을 이용하여 추세분석을 통하여 자료의 효율성을 입증한 후 평균자승오차와 $R^2$(결정계수)를 이용하여 효율적인 모형을 선택 비교하였다.

Keywords

References

  1. Gokhale, S. S. and Trivedi, K. S. "A time/structure based software reliability model", Annals of Software Engineering. 8, pp. 85-121. 1999. https://doi.org/10.1023/A:1018923329647
  2. Goel AL, Okumoto K, "Time-dependent fault detection rate model for software and other performance measures", IEEE Trans Reliab 28, pp.206-11, 1978.
  3. Yamada S, Ohba H. "S-shaped software reliability modeling for software error detection", IEEE Trans Reliab, 32, pp.475-484, 1983. https://doi.org/10.1109/TR.1983.5221735
  4. Zhao M. "Change-point problems in software and hardware reliability", Commun. Stat Theory Methods, 22(3), pp.757-768, 1993. https://doi.org/10.1080/03610929308831053
  5. Shyur H-J. "A stochastic software reliability model with imperfect debugging and change-point", J Syst. Software 66, pp.135-141, 2003. https://doi.org/10.1016/S0164-1212(02)00071-7
  6. Pham H, Zhang X. "NHPP software reliability and cost models with testing coverage", Eur J Oper Res, 145, pp.445-454, 2003.
  7. Huang C-Y. "Performance analysis of software reliability growth models with testing-effort and change-point". J Syst Software 76, pp. 181-194, 2005. https://doi.org/10.1016/j.jss.2004.04.024
  8. Kuei-Chen, C., Yeu-Shiang, H., and Tzai-Zang, L. "A study of software reliability growth from the perspective of learning effects". Reliability Engineering and System Safety 93, pp. 1410-1421, 2008. https://doi.org/10.1016/j.ress.2007.11.004
  9. Hee-Cheul Kim and Jong-Goo Park "The study for NHPP Software Growth Model based on Burr Distribution", THE KOREAN INSTITUDE OF MARITIME INFORMATION & COMMUNICATION SCIENCES, Vol 11(3), pp. 514-522, 2007.
  10. I. W. Burr,"Cumulative frequency function", Ann. Math. Statistic. Vol 13, pp. 215-232, 1942. https://doi.org/10.1214/aoms/1177731607
  11. J, A. Austin, "Control chart constants for largest and smallest in sampling from a normal distribution using the generalized Burr estimation," Technometrics, Vol. 15, 1971, pp. 931-933.
  12. S. D. Dubey,"Statistical treatment of certain life testing and reliability problems", ARL TR, pp. 73-0155, AD 774537,1973.
  13. P. K. Tadikamamlla, "A look at the Burr and related distributions," Inter. Statist. Rev. 48, 1980, pp.337-344. https://doi.org/10.2307/1402945
  14. S. K. Upadhyay and I. A. Javed and M. Peshwani, "Bayesian analysis of generalized four-parameter Burr distribution via Gibbs sampler," METRON-International Journal of statistics, Vol. LXII, n.1, 2004, pp.115-135.
  15. J. F. Lawless. Statistical Models and Methods for Lifetime Data. John Wiley & Sons, New York, 1981.
  16. L. Kuo and T. Y. Yang."Bayesian Computation of Software Reliability".Journal of the American Statistical Association, Vol.91, pp. 763-773, 1996. https://doi.org/10.2307/2291671
  17. K. Kanoun and J. C. Laprie, "Handbook of Software Reliability Engineering", M.R.Lyu, Editor, chapter Trend Analysis. McGraw-Hill New York, NY: 1996; p.401-437.