Skip to main content

A Discrete Lognormal Model for Software Defects Affecting Quality of Protection

  • Conference paper
Quality of Protection

Part of the book series: Advances in Information Security ((ADIS,volume 23))

Abstract

Many computer and network security crises arise because of the exploitation of software defects and are remedied only by repair. The effect of security related software defects and their occurrence rates is an important aspect of Quality of Protection (QoP). Existing arguments and evidence suggests that the distribution of occurrence rates of software defects is lognormal and that the first occurrence times of defects follows the Laplace transform of the lognormal. We extend this research to hypothesize that the distribution of occurrence counts of security related defects follows the Discrete Lognormal. We find that the observed occurrence counts for three sets of defect data relating specifically to network security are consistent with our hypothesis. This paper demonstrates how existing concepts and techniques in software reliability engineering can be applied to study the occurrence phenomenon of security related defects that impact QoP.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. E. N. Adams. “Optimizing preventive service of software products”. IBM Journal of Research and Development, 28(1):2–14, January 1984.

    Article  Google Scholar 

  2. J. Aitchison and J.A.C. Brown. The Lognormal Distribution. Cambridge University Press, NY, 1969.

    Google Scholar 

  3. P. Bishop and R. Bloomfield. “A conservative theory for long-term reliability growth prediction”. In Proc. of Intl. Symposium on Software Reliability Engineering (ISSRE 96), White Plains, NY, 1996.

    Google Scholar 

  4. P. Bishop and R. Bloomfield. “Using a log-normal failure rate distribution for worst case bound reliability prediction”. In Proc. 14th International Symposium on Software Reliability Engineering (ISSRE 03), pages 237–245, 2003.

    Google Scholar 

  5. M. Butcher, H. Munro, and T. Kratschmer. “Improving software testing via ODC: Three case studies”. IBM Systems Journal, 41(1), 2002.

    Google Scholar 

  6. J. Charzinski. “HTTP/TCP connection flow characteristics”. Performance Evaluation, 42:149–162,2000.

    Article  MATH  Google Scholar 

  7. R. Chillarege. Handbook of Software Reliability Engineering, M.R. Lyu (Eds.), chapter Orthogonal Defect Classification. McGraw Hill, 1996.

    Google Scholar 

  8. M. Crovella and M. Taqqu. Methodology and Computing in Applied Probability, chapter Estimating the Heavy Tail Index from Scaling Properties, pages 3–26. Chapman and Hall, 1999.

    Google Scholar 

  9. E. L. Crow and K. Shimizu. Lognormal Distributions: Theory and Applications. Marcel Dekker, New York, 1988.

    MATH  Google Scholar 

  10. A. Downey. “Lognormal and Pareto distributions in the Internet”. Computer Communications, 2003.

    Google Scholar 

  11. M. Faloutsos, P. Faloutsos, and C. Faloutsos. “On the Power-law relationships of the Internet topology”. In Proc. of ACM SIGCOMM, 1999.

    Google Scholar 

  12. A. Feldmann, A. Gilbert, W. Willinger, and T. Kurtz. “The changing nature of network traffic: Scaling phenomenon”. ACM Computer Communication Review, pages 5–28, 1998.

    Google Scholar 

  13. S. Gokhale and R. Mullen. “From test count to code coverage using the lognormal”. In Proc. of 15th International Symposium on Software Reliability Engineering (ISSRE 04), 2004.

    Google Scholar 

  14. K. Goseva-Postojanova, S. Mazimdar, and A. Singh. “Empirical study of session-based workload and reliability of web-servers”. In Proc. of 15th International Symposium on Software Reliability Engineering (ISSRE 04), 2004.

    Google Scholar 

  15. N. L. Johnson, S. Kotz, and N. Balakrishnan. Continuous Univariate Distributions. Wiley, New York, 1994.

    MATH  Google Scholar 

  16. N. L. Johnson, S. Kotz, and A. Kemp. Univariate Discrete Distributions. Wiley, New York,1993.

    Google Scholar 

  17. G. Q. Kenney. “Estimating defects in commercial software during operational use”. IEEE Trans. on Reliability, 42(l):107–115, January 1993.

    Article  MATH  Google Scholar 

  18. Y. Levende. “Reliability analysis of large software systems: Defect data modeling”. IEEE Trans. on Software Engineering, 16(2): 141–152, February 1990.

    Article  Google Scholar 

  19. R.E. Megill. Introduction to Risk Analysis. Pennwell Books, Tulsa, OK, 1984.

    Google Scholar 

  20. D. R. Miller. “Exponential order statistic models of software reliability growth”. Technical Report NASA Contractor Report 3909, NTIS, 1985.

    Google Scholar 

  21. R.E. Mullen. “The lognormal distribution of software failure rates: Application to software reliability growth modeling”. In Proc. of 9th International Symposium on Software Reliability Engineering (ISSRE 98), 1998.

    Google Scholar 

  22. R.E. Mullen. “The lognormal distribution of software failure rates: Origin and evidence”. In Proc. of 9th International Symposium on Software Reliability Engineering (ISSRE 98), 1998.

    Google Scholar 

  23. J. D. Musa. “A theory of software reliability and its application”. IEEE Trans. on Software Engineering, SE-l(l), September 1975.

    Google Scholar 

  24. J. D. Musa. “The operational profile in software reliability engineering: An overview”. In Proc. of the 3rd International Symposium on Software Reliability Engineering (ISSRE 92), pages 140–154, 1992.

    Google Scholar 

  25. P.M. Nagel, F.W. Scholtz, and J.A. Skirvan. “Software reliability: Additional investigations into modeling with replicated experiments”. Technical Report NASA CR-172378, NTIS, 1984.

    Google Scholar 

  26. V. Paxson and S. Floyd. “Wide area traffic: The failure of poisson modeling”. IEEE/ACM Trans. on Networking, (3):244–266, 1995.

    Google Scholar 

  27. R. Perline. “Strong, weak and inverse power laws”. Statistical Science, 20(l):68–88, 2005.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer Science+Business Media, LLC.

About this paper

Cite this paper

Mullen, R.E., Gokhale, S.S. (2006). A Discrete Lognormal Model for Software Defects Affecting Quality of Protection. In: Gollmann, D., Massacci, F., Yautsiukhin, A. (eds) Quality of Protection. Advances in Information Security, vol 23. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-36584-8_4

Download citation

  • DOI: https://doi.org/10.1007/978-0-387-36584-8_4

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-0-387-29016-4

  • Online ISBN: 978-0-387-36584-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics