An Application of the Chains-of-Rare-Events Model to Software Development Failure Prediction

  • Néstor R. Barraza
  • Jonas D. Pfefferman
  • Bruno Cernuschi-Frías
  • Félix Cernuschi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1845)


Some of the best known models for software reliability are based on non homogeneous Poisson processes. Here, we analyze the application of the Chains-of-Rare-Events model to model grouped failures production. As it has been previously shown, this model can be analyzed as a compound Poisson with a Poisson Truncated at Zero as the compounding distribution. We introduce the mode estimator for the parameter of the Poisson Truncated at Zero. This estimator has the important characteristic of quickly reaching stability around the true value. We apply this model to several data and compare it with a non homogenous Poisson process model, and the Poisson distribution compounded by a geometric model.


Interval Time Software Reliability Mode Estimator Failure Production Software Failure 
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  1. 1.
    Goel, A.L., Okumoto, K.: Time-Dependent Error-Detection Rate Model for Software Reliability and Other Performance Measures. IEEE Trans. Reliability 28, 206–211 (1979)zbMATHCrossRefGoogle Scholar
  2. 2.
    Miller, A.M.B.: A Study of the Musa Reliability Mode. M.Sc. Thesis, University of Maryland (1980)Google Scholar
  3. 3.
    Sukert, A.N.: A Software Reliability Modeling Study. Technical report RADCTR- 76-247. Rome Air Development Center, USA (1976)Google Scholar
  4. 4.
    Sukert, A.N.: Empirical Validation of Three Error Prediction Models. IEEE Trans. Reliability 28, 199–205 (1979)CrossRefGoogle Scholar
  5. 5.
    Musa, J.D., Iannino, A., Okumoto, K.: Software Reliability: Measurement, Prediction, Application. McGraw-Hill, New York (1987)Google Scholar
  6. 6.
    Pfefferman, J.D., Cernuschi-Frías, B.: A Non-Stationary Model for Time-Dependent Software Reliability Analysis. In: Proceedings of the 1999 IASTED International Conference on Modeling and Simulation, MS 1999, Philadelphia, Pennsylvania, pp. 427–431 (1999)Google Scholar
  7. 7.
    Derriennic, H., Le Gall, G.: Use of Failure-Intensity Models in the Software- Validation Phase for Telecommunications. IEEE Trans. Reliability 44, 658–665 (1995)CrossRefGoogle Scholar
  8. 8.
    Lyu, M.R. (ed.): Handbook of Software Reliability Engineering. McGraw Hill, New York (1996)Google Scholar
  9. 9.
    Wood, A.: Software Reliability Growth Models. Tandem Tech. Report 96.1 (1996) Google Scholar
  10. 10.
    Sahinoglu, M.: Compound-Poisson Software Reliability Model. IEEE Trans. On Software Engineering 18, 624–630 (1992)CrossRefGoogle Scholar
  11. 11.
    Cernuschi, F., Castagnetto, L.: Chains of Rare Events. Annals of Mathematical Statistics XVII, 53–61 (1946)CrossRefMathSciNetGoogle Scholar
  12. 12.
    Barraza, N.R., Cernuschi-Frías, B., Cernuschi, F.: A Probabilistic Model for Grouped Events Analysis. In: Proceedings of the 1995 IEEE Int. Conf. on Systems, Man and Cybernetics, Vancouver, Canada, vol. 4, pp. 3386–3390 (1995)Google Scholar
  13. 13.
    Barraza, N.R., Cernuschi-Frías, B., Cernuschi, F.: Applications & Extensions of the Chains-of-Rare-Events Model. IEEE Trans. Reliability 45, 417–421 (1996)CrossRefGoogle Scholar
  14. 14.
    Plackett, R.L.: The Truncated Poisson Distribution. Biometrics 9, 485–488 (1953)CrossRefMathSciNetGoogle Scholar
  15. 15.
    Tate, R.F., Goen, R.L.: Minimum Variance Unbiased Estimation for the Truncated Poisson Distribution. Annals of Mathematical Statistics 29, 755–765 (1958)zbMATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Feller, W.: An Introduction to Probability Theory and its Applications, vol. 1, 2. Wiley, New York (1967)Google Scholar
  17. 17.
    Wood, A.: Predicting Software Reliability. IEEE Computer 29, 69–77 (1996)Google Scholar
  18. 18.
    Haight, F.A.: Handbook of the Poisson Distribution. Wiley, New York (1966)Google Scholar
  19. 19.
    Knuth, D.E.: The Art of Computer Programming, vol. 1. AddisonWesley, Reading (1969)zbMATHGoogle Scholar
  20. 20.
    Musa, J. D.: Software Reliability Data. Bell Telephone Laboratories, Whippany NJ (1980) Google Scholar
  21. 21.
    Hossain, S.A., Dahiya, R.C.: Estimating the Parameters of a Nonhomogeneous Poisson-Process Model for Software Reliability. IEEE Transactions on Reliability 42, 604–612 (1993)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Néstor R. Barraza
    • 1
  • Jonas D. Pfefferman
    • 1
  • Bruno Cernuschi-Frías
    • 1
  • Félix Cernuschi
    • 1
  1. 1.Facultad de IngenieríaUniversidad de Buenos Aires, and CONICETBuenos AiresArgentina

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