Recent Developments in Software Reliability Modeling

Part of the SpringerBriefs in Statistics book series (BRIEFSSTATIST)


Management technologies for improving software reliability are very important for software TQM (Total Quality Management). The quality characteristics of software reliability is that computer systems can continue to operate regularly without the occurrence of failures on software systems. In this chapter, we describe several recent developments in software reliability modeling and its applications as quantitative techniques for software quality/reliability measurement and assessment. That is, a quality engineering analysis of human factors affecting software reliability during the design-review phase, which is the upper stream of software development, and software reliability growth models based on stochastic differential equations and discrete calculus during the testing phase, which is the lower one, are discussed. And, we discuss quality-oriented software management analysis by applying the multivariate analysis method and the existing software reliability growth models to actual process monitoring data. Finally, we investigate an operational performability evaluation model for the software-based system, introducing the concept of systemability which is defined as the reliability characteristic subject to the uncertainty of the field environment.


Human factor analysis Design-review experiment OSS reliability Stochastic differential equation Discrete modeling Difference equation Software management Software project assessment Software performability modeling Systemability assessment 


  1. 1.
    Basili, V. R., & Reiter, R. W, Jr. (1979). An investigation of human factors in software development. IEEE Computer Magazine, 12, 21–38.CrossRefGoogle Scholar
  2. 2.
    Curtis, B. (Ed.). (1985). Tutorial: Human factors in software development. Los Alamitos: IEEE Computer Society Press.Google Scholar
  3. 3.
    Nakajo, T., & Kume, H. (1991). A case history analysis of software error cause-effect relationships. IEEE Transactions on Software Engineering, 17, 830–838.CrossRefGoogle Scholar
  4. 4.
    Taguchi, G. (Ed.). (1998). Signal-to-noise raito for quality evaluation (in Japanese). Tokyo: Japanese Standards Association.Google Scholar
  5. 5.
    Taguchi, G. (1976). A method of design of experiment (2nd ed., Vol. 1). Tokyo: Maruzen.Google Scholar
  6. 6.
    Yamada, S. (2011). Elements of software reliability -modeling approach (in Japanese). Tokyo: Kyoritsu-Shuppan.Google Scholar
  7. 7.
    Esaki, K., Yamada, S., & Takahashi, M. (2001). A quality engineering analysis of human factors affecting software reliability in software design review process (in Japanese). Transactions of IEICE Japan, J84-A, 218–228.Google Scholar
  8. 8.
    Yamada, S. (2008). Early-stage software product quality prediction based on process measurement data. In K. B. Misra (Ed.), Springer handbook of performability engineering (pp. 1227–1237). London: Springer.Google Scholar
  9. 9.
    Yamada, S. (2006). A human factor analysis for software reliability in design-review process. International Journal of Performability Engineering, 2, 223–232.Google Scholar
  10. 10.
    Miyamoto, I. (1982). Software engineering -current status and perspectives (in Japanese). Tokyo: TBS Publishing.Google Scholar
  11. 11.
    Esaki, K., & Takahashi, M. (1997). A software design review on the relationship between human factors and software errors classified by seriousness (in Japanese). Journal of Quality Engineering Forum, 5, 30–37.Google Scholar
  12. 12.
    E-Soft Inc., Internet Research Reports. Available:
  13. 13.
    Yamada, S. (2002). Software reliability models. In S. Osaki (Ed.), Stochastic models in reliability and maintenance (pp. 253–280). Berlin: Springer.Google Scholar
  14. 14.
    MacCormack, A., Rusnak, J., & Baldwin, C. Y. (2006). Exploring the structure of complex software designs: An empirical study of open source and proprietary code. Informs Journal of Management Science, 52, 1015–1030.Google Scholar
  15. 15.
    Kuk, G. (2006). Strategic interaction and knowledge sharing in the KDE developer mailing list. Informs Journal of Management Science, 52, 1031–1042.Google Scholar
  16. 16.
    Zhou, Y., & Davis, J. (2005). Open source software reliability model: An empirical approach. In Proceedings of the Fifth Workshop on Open Source Software Engineering (WOSSE) (pp. 67–72).Google Scholar
  17. 17.
    Li, P., Shaw, M., Herbsleb, J., Ray, B., & Santhanam, P. (2004). Empirical evaluation of defect projection models for widely-deployed production software systems. Proceedings of the 12th International Symposium on Foundations of, Software Engineering (FSE-12) (pp. 263–272).Google Scholar
  18. 18.
    Arnold, L. (1974). Stochastic differential equations-theory and applications. New York: John Wiley & Sons.Google Scholar
  19. 19.
    Wong, E. (1971). Stochastic Processes in Information and Systems. New York: McGraw-Hill.MATHGoogle Scholar
  20. 20.
    Yamada, S., Kimura, M., Tanaka, H., & Osaki, S. (1994). Software reliability measurement and assessment with stochastic differential equations. IEICE Transactions on Fundamentals of Electronics, Communications, and Computer Sciences, E77-A, 109–116.Google Scholar
  21. 21.
    The Apache HTTP Server Project, The Apache Software Foundation. Available:
  22. 22.
    Apache Tomcat, The Apache Software Foundation. Available:
  23. 23.
    PostgreSQL, PostgreSQL Global Development Group. Available:
  24. 24.
    Tamura, Y., & Yamada, S. (2007). Software reliability growth model based on stochastic differential equations for open source software. Proceedings of the 4th IEEE International Conference on Mechatronics, CD-ROM (ThM1-C-1).Google Scholar
  25. 25.
    Tamura, Y., & Yamada, S. (2006). A flexible stochastic differential equation model in distributed development environment. European Journal of Operational Research, 168, 143–152.MathSciNetCrossRefMATHGoogle Scholar
  26. 26.
    Tamura, Y., & Yamada, S. (2009). Optimisation analysis for reliability assessment based on stochastic differential equation modeling for open source software. International Journal of Systems Science, 40, 429–438.MathSciNetCrossRefMATHGoogle Scholar
  27. 27.
    Tamura, Y., & Yamada, S. (2013). Reliability assessment based on hazard rate model for an embedded OSS porting phase. Software Testing, Verification and Reliability, 23, 77–88.CrossRefGoogle Scholar
  28. 28.
    Satoh, D. (2000) A discrete Gompertz equation and a software reliability growth model. IEICE Transactions on Information and Systems, E83-D, 1508–1513.Google Scholar
  29. 29.
    Satoh, D., & Yamada, S. (2001). Discrete equations and software reliability growth models. Proceedings of the 12th International Symposium on Software Reliability Engineering (ISSRE’01) (pp. 176–184).Google Scholar
  30. 30.
    Inoue, S., & Yamada, S. (2007). Generalized discrete software reliability modeling with effect of program size. IEEE Transactions on System, Man, and Cybernetics (Part A), 37, 170–179.Google Scholar
  31. 31.
    Hirota, R. (1979). Nonlinear partial difference equations. V. Nonlinear equations reducible to linear equations. Journal of Physical Society of Japan, 46, 312–319.Google Scholar
  32. 32.
    Bass, F. M. (1969). A new product growth model for consumer durables. Management Science, 15, 215–227.CrossRefMATHGoogle Scholar
  33. 33.
    Satoh, D. (2001). A discrete Bass model and its parameter estimation. Journal of Operations Research Society of Japan, 44, 1–18.MathSciNetMATHGoogle Scholar
  34. 34.
    Kasuga, K., Fukushima, T., & Yamada, S. (2006). A practical approach software process monitoring activities (in Japanese). Proceedings of the 25th JUSE Software Quality Symposium (pp. 319–326).Google Scholar
  35. 35.
    Yamada, S., & Fukushima, T. (2007). Quality-oriented software management (in Japanese). Tokyo: Morikita-Shuppan.Google Scholar
  36. 36.
    Yamada, S., & Takahashi, M. (1993). Introduction to software management model (in Japanese). Tokyo: Kyoritsu-Shuppan.Google Scholar
  37. 37.
    Yamada, S., & Kawahara, A. (2009). Statistical analysis of process monitoring data for software process improvement. International Journal of Reliability, Quality and Safety Engineering, 16, 435–451.CrossRefGoogle Scholar
  38. 38.
    Yamada, S., Yamashita, T., & Fukuta, A. (2010). Product quality prediction based on software process data with development-period estimation. International Journal of Systems Assurance Engineering and Management, 1, 69–73.CrossRefGoogle Scholar
  39. 39.
    Pfening, A., Garg, S., Puliafito, A., Telek, M., & Trivedi, K. S. (1996). Optimal software rejuvenation for tolerating soft failures. Performance Evaluation, 27–28, 491–506.Google Scholar
  40. 40.
    Garg, S., Puliafito, A., Telek, M., & Trivedi, K. S. (1998). Analysis of preventive maintenance in transactions based software systems. IEEE Transactions on Computers, 47, 96–107.CrossRefGoogle Scholar
  41. 41.
    Tokuno, K., & Yamada, S. (2008). Dynamic performance analysis for software system considering real-time property in case of NHPP task arrival. Proceedings of 2nd International Conference on Secure System Integration and Reliability Improvement (SSIRI 2008) (pp. 73–80).Google Scholar
  42. 42.
    Nagata, T., Tokuno, K., & Yamada, S. (2011). Stochastic performability evaluation based on NHPP reliability growth model. International Journal of Reliability, Quality, and Safety Engineering, 18, 431–444.CrossRefGoogle Scholar
  43. 43.
    Jeske, D. R., Zhang, X., & Pham, L. (2005). Adjusting software failure rates that are estimated from test data. IEEE Transactions on Reliability, 54, 107–114.CrossRefGoogle Scholar
  44. 44.
    Pham, H. (2006). System software reliability. London: Springer.Google Scholar
  45. 45.
    Okamura, H., Dohi, T., & Osaki, S. (2001). A reliability assessment method for software products in operational phase: Proposal of an accelerated life testing model. Electronics and Communications in Japan, 84, 25–33.Google Scholar
  46. 46.
    Morita, H., Tokuno, K., & Yamada, S. (2005). Markovian operational software reliability measurement based on accelerated life testing model. Proceedings of the 11th ISSAT International Conference on Reliability and Quality in Design (pp. 204–208).Google Scholar
  47. 47.
    Tokuno, K., & Yamada, S. (2007). User-oriented and -perceived software availability measurement and assessment with environmental factors. Journal of Operations Research Society of Japan, 50, 444–462.MathSciNetMATHGoogle Scholar
  48. 48.
    Pham, H. (2005). A new generalized systemability model. International Journal of Performability Engineering, 1, 145–155.Google Scholar
  49. 49.
    Pham, H. (2010). Mathematical systemability function approximations. Proceedings of the 16th ISSAT International Conference on Reliability and Quality in Design (pp. 6–10).Google Scholar
  50. 50.
    Teng, X., & Pham, H. (2006). A new methodology for predicting software reliability in the random field environments. IEEE Transactions on Reliability, 55, 458–468.CrossRefGoogle Scholar
  51. 51.
    Lyu, M. R. (Ed.). (1996). Handbook of software reliability engineering. Los Alamitos: McGraw-Hill, IEEE Computer Society Press.Google Scholar
  52. 52.
    Tokuno, K., & Yamada, S. (2000). An imperfect debugging model with two types of hazard rates for software reliability measurement and assessment. Mathematical and Computer Modeling, 31, 343–352.MathSciNetCrossRefMATHGoogle Scholar
  53. 53.
    Tokuno, K., Kodera, T., & Yamada, S. (2009). Generalized markovian software reliability modeling and its alternative calculation. International Journal of Reliability, Quality and Safety Engineering, 16, 385–402.CrossRefGoogle Scholar
  54. 54.
    Ross, S. M. (2007). Introduction to probability models (9th ed.). San Diego: Academic Press.Google Scholar
  55. 55.
    Osaki, S. (1992). Applied stochastic system modeling. Heidelberg: Springer.CrossRefMATHGoogle Scholar
  56. 56.
    Oldham, K. B., Myland, J. C., & Spanier, J. (2008). An atlas of functions, with equator, the atlas function calculator (2nd ed.). New York: Springer.Google Scholar
  57. 57.
    Tokuno, K., Fukuda, T., & Yamada, S. (2012). Operational software performability evaluation based on markovian reliability growth model with systemability. International Journal of Reliability, Quality and Safety, Engineering, 19, 1240001.Google Scholar
  58. 58.
    Moranda, P. B. (1979). Event-altered rate models for general reliability analysis. IEEE Transactions on Reliability, R-28, 376–381.Google Scholar

Copyright information

© The Author(s) 2014

Authors and Affiliations

  1. 1.Graduate School of EngineeringTottori UniversityTottoriJapan

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