Skip to main content
Log in

Parameter estimation of discrete logistic curve models for software reliability assessment

  • Published:
Japan Journal of Industrial and Applied Mathematics Aims and scope Submit manuscript

Abstract

We describe software reliability growth models that yield accurate parameter estimates in spite of a small amount of input data in an actual software testing. These models are based on discrete analogs of a logistic curve model. The models are described with two difference equations, one each proposed by Morishita and Hirota. The difference equations have exact solutions. The equations tend to a differential equation on which the logistic curve model is defined when the time interval tends to zero. The exact solutions also tend to the exact solution of the differential equation when the time interval tends to zero. The discrete models conserve the characteristics of the logistic model because the difference equations have exact solutions. Therefore, the proposed models provide accurate parameter estimates, making it possible to predict in the early development phase when software can be released.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. W.D. Brooks and R.W. Montley, Analysis of discrete software reliability models. Technical Report RADC-TR-80–84, Rome Air Development Center, New York, 1980.

    Google Scholar 

  2. R. Hirota, Nonlinear partial difference equations. V. Nonlinear equations reducible to linear equations. J. Phys. Soc. Japan,46 (1979), 312–319.

    Article  MathSciNet  Google Scholar 

  3. A. Kanno, Software Engineering (in Japanese). JUSE Press, Tokyo, 1979.

    Google Scholar 

  4. J.-C. Laprie, K. Kanoun, C. Béounes and M. Kaâniche, The KAT (Knowledge-Action-Transformation) approach to the modeling and evaluation of reliability and availability growth. IEEE Trans. Software Engineering,17 (1991), 370–382.

    Article  Google Scholar 

  5. M.R. Lyu, ed., Handbook of Software Reliability Engineering. McGraw-Hill, New York, 1995.

    Google Scholar 

  6. T. Mitsuhashi, A Method of Software Quality Evaluation (in Japanese). JUSE Press, Tokyo, 1981.

    Google Scholar 

  7. F. Morishita, The fitting of the logistic equation to the rate of increase of population density. Res. Popul. Ecol.,VII (1965), 52–55.

    Article  Google Scholar 

  8. M. Ohba, S. Yamada, K. Takeda and S. Osaki, S-shaped software reliability growth curve: how good is it? Proceedings IEEE COMPSAC 82, Chicago, 1982, 38–44.

  9. K. Ohmori and E. Shinohara, Predictive precision analysis of undiscovered errors. IEICE Tech. Rep. Switching System Engineering,98–190 (1999), 25–30.

    Google Scholar 

  10. C.V. Ramamoorthy and F.B. Bastani, Software reliability— Status and perspectives. IEEE Trans. Software Engineering,8 (1982), 354–371.

    Article  Google Scholar 

  11. T. Sakamaki, Software reliability — Software reliability forecast for quality management. IEICE Tech. Rep. Reliability,81–8 (1981), 17–24.

    Google Scholar 

  12. K. Sakata, Formulation for predictive methods in software production control: Static prediction and failure rate transition model. IEICE Trans. Inf. & Syst.,J57 (1974), 277–283.

    Google Scholar 

  13. D. Satoh, A discrete Gompertz equation and a software reliability growth model. IEICE Trans. Inf. & Syst.,E83 (2000), 1508–1513.

    Google Scholar 

  14. D. Satoh, A discrete Bass model and its parameter estimation. J. Oper. Res. Soc. Japan,44, No. 1 (2001), 1–18.

    MATH  MathSciNet  Google Scholar 

  15. S. Ushiki, Central difference scheme and chaos. Physica D,4 (1982), 407–424.

    Article  MathSciNet  Google Scholar 

  16. S. Yamada, Software Reliability Model — Fundamentals and Applications (in Japanese). JUSE Press, Tokyo, 1994.

    Google Scholar 

  17. S. Yamada, Software quality/reliability measurement and assessment: Software reliability growth models and data analysis. J. Inform. Process.,14 (1991), 254–266.

    Google Scholar 

  18. A. Iannino, J.D. Musa, K. Okumoto and B. Littlewood, Criteria for software reliability model comparisons. IEEE Trans. Software Engineering,10 (1984), 687–691.

    Article  Google Scholar 

  19. J.D. Musa, A. Iannino and K. Okumoto, Software Reliability: Measurement, Prediction. Application. McGraw-Hill, New York, 1987.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Daisuke Satoh.

About this article

Cite this article

Satoh, D., Yamada, S. Parameter estimation of discrete logistic curve models for software reliability assessment. Japan J. Indust. Appl. Math. 19, 39–53 (2002). https://doi.org/10.1007/BF03167447

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03167447

Key words

Navigation