Failure Time Prediction Capability Comparative Analysis of Software NHPP Reliability Model

소프트웨어 NHPP 신뢰성모형에 대한 고장시간 예측능력 비교분석 연구

  • Kim, Hee-Cheul (Dept. of Industrial & Management Engineering, Namseoul University) ;
  • Kim, Kyung-Soo (Dept. of Internet information, BaekSeok Culture University)
  • 김희철 (남서울대학교 산업경영공학과) ;
  • 김경수 (백석문화대학교 인터넷정보학부)
  • Received : 2015.08.30
  • Accepted : 2015.12.20
  • Published : 2015.12.28


This study aims to analyze the predict capability of some of the popular software NHPP reliability models(Goel-Okumo model, delayed S-shaped reliability model and Rayleigh distribution model). The predict capability analysis will be on two key factors, one pertaining to the degree of fitment on available failure data and the other for its prediction capability. Estimation of parameters for each model was used maximum likelihood estimation using first 80% of the failure data. Comparison of predict capability of models selected by validating against the last 20% of the available failure data. Through this study, findings can be used as priori information for the administrator to analyze the failure of software.


NHPP;Rayleigh Distribution;Delayed S-shaped Reliability Model;Prediction of Failure Time;Maximum Likelihood Estimation


  1. L. Kuo and T. Y. Yang., Bayesian Computation of Software Reliability, Journal of the American Statistical Association, Vol.91, pp. 763-773, 1996.
  2. Gokhale, S. S. and Trivedi, K. S. A time/structure based software reliability model, Annals of Software Engineering. 8, pp. 85-121. 1999.
  3. Goel A L, Okumoto K, Time-dependent fault detection rate model for software and other performance measures, IEEE Trans. Reliab. 28, pp.206-11, 1978.
  4. Yamada S, Ohba H. and Osaki S., S-shaped software reliability modeling for software error detection", IEEE Trans. Reliab, 32, pp.475-484, 1983.
  5. Zhao M., Change-point problems in software and hardware reliability", Commun. Stat. Theory Methods, 22(3), pp.757-768, 1993.
  6. Shyur H-J., A stochastic software reliability model with imperfect debugging and change-point, J. Syst. Software 66, pp.135-141, 2003.
  7. Pham H, Zhang X., NHPP software reliability and cost models with testing coverage", Eur. J. Oper. Res, 145, pp.445-454, 2003.
  8. Huang C-Y., Performance analysis of software reliability growth models with testing-effort and change-point, J. Syst. Software 76, pp. 181-194, 2005.
  9. 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.
  10. Hee-Cheul KIM, "The Comparative Study of NHPP Half-Logistic Distribution Software Reliability Model using the Perspective of Learning Effects", Journal of Next Generation Information Technology, Vol. 4, No. 8, pp. 132-139, 2013.
  11. Hee-Cheul KIM, "The Comparative Study of NHPP Delayed S-Shaped and Extreme Value Distribution Software Reliability Model using the Perspective of Learning Effects", International Journal of Advancements in Computing Technology, Vol. 5, No.9, pp. 1210 -1218, 2013.
  12. Kim, Hee-cheul, " The Assessing Comparative Study for Statistical Process Control of Software Reliability Model Based on Rayleigh and Burr Type", Journal of the Korea Society of Digital Industry and Information Management, pp. 1-11, 2014.
  13. Y. HAYAKAWA and G. TELFAR, "Mixed Poisson Type Processes with Application in Software Reliability", Mathematical and Computer Modelling, 31, pp. 151-156, 2000.
  14. K. Kanoun and J. C. Laprie, "Handbook of Software Reliability Engineering", M.R.Lyu, Editor, chapter Trend Analysis. McGraw-Hill New York, NY, pp. 401-437, 1996.
  15. D. R. Prince Williams, Prediction Capability Analysis of Two and Three Parameters Software Reliability Growth Models, Infoprmation Technology Journal, 5(6), pp.1048-1052, 2006.