Journal of the Korea Institute of Information and Communication Engineering (한국정보통신학회논문지)

The Korea Institute of Information and Commucation Engineering (한국정보통신학회)
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An Approach for the NHPP Software Reliability Model Using Erlang Distribution

어랑 분포를 이용한 NHPP 소프트웨어 신뢰성장 모형에 관한 연구

  • 김희철 (남서울대학교 산업정보시스템공학부) ;
  • 최유순 (원광대학교 컴퓨터공학과) ;
  • 박종구 (원광대학교 컴퓨터공학과)
  • Published : 2006.01.01
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Abstract

The finite failure NHPP models proposed in the literature exhibit either constant, monotonic increasing or monotonic decreasing failure occurrence rates per fault. In this paper, we propose the Erlang reliability model, which can capture the increasing nature of the failure occurrence rate per fault. Equations to estimate the parameters of the Erlang finite failure NHPP model based on failure data collected in the form of inter-failure times are developed. For the sake of proposing shape parameter of the Erlang distribution, we used to the goodness-of-fit test of distribution. Data set, where the underlying failure process could not be adequately described by the existing models, which motivated the development of the Erlang model. Analysis of the failure data set which led us to the Erlang model, using arithmetic and Laplace trend tests, goodness-of-fit test, bias tests is presented.

비동질적인 포아송 과정에 기초한 모형들에서 잔존 결함 1개 당 고장 발생률은 일반적으로 상수, 혹은 단조증가 및 단조 감소 추세를 가지고 있다. 본 논문에서는 잔존 결함 1개당 고장 발생률이 증가추세를 가진 어랑 분포를 이용한 어랑 모형을 제안하였다. 고장 간격시간으로 구성된 실측자료를 이용하여 기존의 모형과 어랑 모형의 모수 추정을 실시하였다. 어랑 모형의 형상모수를 선택하기 위하여 (누적)분포적합도 검정을 사용하였고 이 자료들에서 어랑 모형의 제안과 비교를 위하여 산술적 및 라플라스 검정, 적합도 검정, 편의 검정 등을 이용하였다.

Keywords

References

  1. A.A.Abdel-Ghally, P.Y.Chan, and B.Littlewood. 'Evaluation of competing Software Reliability Predections', IEEE Trans. on Software Engineering, SE-12(9):538-546, Sept. 1989
  2. A. L. Goel and K. Okumoto. 'Time-Dependent Error-Detection Rate Models for Software Reliability and Other Performance Measures'. IEEE Trans. on Reliability, R-28(3):206-211, Aug. 1979 https://doi.org/10.1109/TR.1979.5220566
  3. A. L .Goel. 'Software Reliability Models: Assumptions, Limitations and Applicability'. IEEE Trans. on Software Engineering, SE-11(12) :1411-1423, Dec. 1985 https://doi.org/10.1109/TSE.1985.232177
  4. A. P. Nikora and M. R. Lyu. Handbook of Software Reliability Engineering, M.R.Lyu, Editor, chapter Software Reliability Measurement Experience, pp.255-301. MacGraw-Hill, New York, 1996
  5. J. D. Musa. 'A Theory of Software Reliability and its Application'. IEEE Trans. on Software Engineering, SE-1(1):312-327, Sept. 1975 https://doi.org/10.1109/TSE.1975.6312856
  6. J. D. Musa, A. Iannino and K. Okumoto. Software Reliability: Measurement, Prediction, Application. McGraw Hill, New York, 1987
  7. J. F. Lawless. Statistical Models and Methods for Lifetime Data. John Wiley & Sons, New York, 1981
  8. K. Kanoun and J. C. Laprie. Handbook of Software Reliability Engineering, M.R.Lyu, Editor, chapter Trend Analysis, pp.401-437. MacGraw-Hill, New York, 1996
  9. 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
  10. M. R. Lyu. Handbook of Software Reliability Engineering, M.R.Lyu, Editor, chapter Introduction, pp.3-25. MacGraw-Hill, New York, 1996
  11. O. Gauodin. 'Optimal Properties of the Laplace Trend Test for Software-Reliability Models'. IEEE Trans. on Reliability, 41(4):525-532, Dec. 1992 https://doi.org/10.1109/24.249579
  12. H. Pham and L. Nordmann and X. Zhang 'A General Imperfect-Software -Debugging Model with S-Shaped Fault-Detection Rate'. IEEE Trans. on reliability, VOL, 48, NO 2, 1999
  13. S. Selvin. Moden Applied Biostatistical Methods Using S-Plus, pages 141-184. Oxford University Press, New York, 1998
  14. S. S. Gokhale and K. S. Trivedi. 'A time/structure based software reliability model'. Annals of Software Engineering. 8,85-121. 1999 https://doi.org/10.1023/A:1018923329647
  15. S. Yamada, M. Ohba and S. Osaki. 'S-Shaped Reliability Growth Modeling for Software Error Detection'. IEEE Trans. On Reliability. R-32(5):475-485, Dec. 1983 https://doi.org/10.1109/TR.1983.5221735
  16. V. K, Rohatgi. Statistical inference, pages 398-416. JOHN WILEY & SONS, INCl, New York, 1984
  17. W. Farr. Handbook of Software Reliability Engineering, M.R.Lyu, Editor, chapter Software Reliability Modeling Survery, pages 71-117. McGraw-Hill, New York, NY, 1996
  18. W. Q. Meeker and L. A, Escobar. Statistical Methods for Reliability Data, pages 98-101. JOHN WILEY & SONS, INCl, New York, 1998
  19. http://www.answers.com/gamma%20distribution (site visited 2005-5-15)