Software Reliability Growth Models

Part of the Springer Series in Reliability Engineering book series (RELIABILITY)


Studies in software reliability modeling started as early as early 1960s. The issues related software quality quantification and reliability measurement arose even during the time when the development of computing systems started. Since in the 1960s the cost of the computing systems were very high, use was limited to few organizations, hardware design, test and maintainability was immature, the concepts of software reliability were in infancy stage as much of the studies were concerned with the productivity and quality of the hardware systems.


Software Reliability Reliability Growth Failure Intensity Simple Fault Fault Removal 



  1. 1.
    Haugk G et al (1964) System testing of the no. 1 electronic switching system. Bell Syst Tech J 9:2575–2592Google Scholar
  2. 2.
    Jelinski Z, Moranda P (1972) Software reliability research. In: Freiberger W (ed) Statistical computer performance evaluation. Academic Press, New York, pp 465–484Google Scholar
  3. 3.
    Moranda P (1975) Predictions of software reliability during debugging. In: Proceedings annual reliability and maintainability symposium, Washington, DC, pp 327–332Google Scholar
  4. 4.
    Goel AL, Okumoto K (1979) Time dependent error detection rate model for software reliability and other performance measures. IEEE Trans Reliab R-28(3):206–211CrossRefGoogle Scholar
  5. 5.
    Littlewood B, Verrall JL (1973) A Bayesian reliability growth model for computer software. Appl Stat 22:332–346MathSciNetCrossRefGoogle Scholar
  6. 6.
    Musa JD (1975) A theory of software reliability and its application. IEEE Trans Softw Eng SE-1:312–327CrossRefGoogle Scholar
  7. 7.
    Schneidewind NF (1972) An approach to software in reliability prediction and quality control. In: Fall joint computer conference, AFIPS conference proceedings. AFIPS Press, Montvale, pp 837–847Google Scholar
  8. 8.
    Schneidewind NF (1975) Analysis of error processes in computer software. Sigplan Not 10:337–346CrossRefGoogle Scholar
  9. 9.
    Shooman M (1972) Probabilistic models for software reliability prediction. In: Freidberger W (ed) Statistical computer performance evaluation. Academic Press, New York, pp 485–502Google Scholar
  10. 10.
    Schick GL, Wolverton RW (1973) Assessment of software reliability. Proceedings operations research. Physica-Verlag, Wurzburg Wein, pp 395–422Google Scholar
  11. 11.
    Musa JD, Okumoto K (1984) A logarithmic Poisson execution time model for software reliability measurement. In: Proceedings 7th international conference on software engineering, Orlando, pp 230–237Google Scholar
  12. 12.
    Trachtenberg M (1990) A general theory of software reliability modeling. IEEE Trans Reliab 39(1):92–96MATHCrossRefGoogle Scholar
  13. 13.
    Yamada S, Ohba M, Osaki S (1983) S-shaped software reliability growth modeling for software error detection. IEEE Trans Reliab R-32(5):475–484CrossRefGoogle Scholar
  14. 14.
    Ohba M (1984) Software reliability analysis models. IBM J Res Dev 28:428–443CrossRefGoogle Scholar
  15. 15.
    Yamada S, Osaki S (1985) Software reliability growth modeling: models and applications. IEEE Trans Softw Eng 11:1431–1437CrossRefGoogle Scholar
  16. 16.
    Bittanti S, Bolzern P, Pedrotti E, Pozzi N, Scattolini R (1988) A flexible modeling approach for software reliability growth. In: Goos G, Harmanis J (eds) Software reliability modelling and identification. Springer, Berlin, pp 101–140CrossRefGoogle Scholar
  17. 17.
    Kapur PK, Garg RB (1992) A software reliability growth model for an error removal phenomenon. Softw Eng J 7:291–294CrossRefGoogle Scholar
  18. 18.
    Putnam LH (1978) A general empirical solution to the macro software sizing and estimating problem. IEEE Trans Softw Eng 4:345–367MATHCrossRefGoogle Scholar
  19. 19.
    Yamada S, Ohtera H, Narihisa H (1986) Software reliability growth models with testing-effort. IEEE Trans Reliab R-35:19–23CrossRefGoogle Scholar
  20. 20.
    Yamada S, Hishitani J, Osaki S (1991) Test-effort dependent software reliability measurement. Int J Syst Sci 22(1):73–83MathSciNetMATHCrossRefGoogle Scholar
  21. 21.
    Yamada S, Hishitani J, Osaki S (1993) Software reliability growth model with Weibull testing effort: a model and application. IEEE Trans Reliab 42:100–105MATHCrossRefGoogle Scholar
  22. 22.
    Bokhari MU, Ahmad N (2006) Analysis of software reliability growth models: the case of log-logistic test-effort function. In: Proceedings 7th IASTED international conference on modeling and simulation, Montreal, QC, Canada, pp 540–545Google Scholar
  23. 23.
    Kapur PK, Goswami DN, Gupta A (2004) A software reliability growth model with testing effort dependent learning function for distributed systems. Int J Reliab Qual Safety Eng 11(4):365–377CrossRefGoogle Scholar
  24. 24.
    Kuo SY, Huang CY, Lyu MR (2001) Framework for modeling software reliability, using various testing-efforts and fault-detection rates. IEEE Trans Reliab 50(3):310–320CrossRefGoogle Scholar
  25. 25.
    Huang CY (2005) Performance analysis of software reliability growth models with testing-effort and change-point. J Syst Softw 76:181–194CrossRefGoogle Scholar
  26. 26.
    Huang CY, Lo JH, Kuo SY, Lyu MR (2002) Optimal allocation of testing resources for modular software systems. In: Proceedings 13th IEEE international symposium on software reliability engineering (ISSRE 2002), November 2002, Annapolis, MD, pp 129–138Google Scholar
  27. 27.
    Huang CY, Kuo SY, Lyu MR (2007) An assessment of testing-effort dependent software reliability growth models. IEEE Trans Reliab 56(2):198–211CrossRefGoogle Scholar
  28. 28.
    Downs T (1985) An approach to the modeling of software testing with some applications. IEEE Trans Softw Eng 11(4):375–386CrossRefGoogle Scholar
  29. 29.
    Trachtenberg M (1985) The linear software reliability model and uniform testing. IEEE Trans Reliab R34(1):8–16CrossRefGoogle Scholar
  30. 30.
    Dale CJ (1982) Software reliability evaluation methods. Technical Report ST-26750, British Aerospace Dynamics GroupGoogle Scholar
  31. 31.
    Ramamoorthy CV, Bastani FB (1982) Software reliability status and perspectives. IEEE Trans Reliab 37(1):88–91Google Scholar
  32. 32.
    Musa JD, Iannino A, Okumoto K (1987) Software reliability: measurement, prediction, application. McGraw-Hill, New York ISBN 0–07-044093-XGoogle Scholar
  33. 33.
    Ohba M (1984) Inflection S-shaped software reliability growth models. In: Osaki S, Hatoyama Y (eds) Stochastic models in reliability theory. Springer, Berlin, pp 44–162Google Scholar
  34. 34.
    Kareer N, Kapur PK, Grover PS (1990) An S-shaped software reliability growth model with two types of errors. Microelectron Reliab 30(6):1085–1090CrossRefGoogle Scholar
  35. 35.
    Kapur PK, Younes S, Agarwala S (1995) Generalized Erlang software reliability growth model. ASOR Bull 35(2):273–278Google Scholar
  36. 36.
    Kapur PK, Bardhan AK, Kumar S (2000) On categorization of errors in a software. Int J Manag Syst 16(1):37–48Google Scholar
  37. 37.
    Kapur PK, Bardhan AK, Shatnawi O (2002) Why software reliability growth modeling should define errors of different severity. J Indian Stat Assoc 40(2):119–142MathSciNetGoogle Scholar
  38. 38.
    Shatnawi O, Kapur PK (2008) A generalized software fault classification. WSEAS Trans Comput 7(9):1375–1384Google Scholar
  39. 39.
    Kapur PK, Kumar A, Yadav K, Kumar J (2007) Software reliability growth modeling for errors of different severity using change point. Int J Reliab Qual Safety Eng 14(4):311–326CrossRefGoogle Scholar
  40. 40.
    Kapur PK, Singh VB, Yang BO (2007) Software reliability growth model for determining fault types. In: Misra RB, Naikan VNA, Chaturvedi SK, Goyal NK (eds) Proceedings 3rd international conference on reliability and safety engineering, INCREASE 2007, Udaipur, pp 334–349Google Scholar
  41. 41.
    Kapur PK, Singh VB, BasirZadeh M (2008) Considering errors of different severity in software reliability growth modeling using fault dependency and debugging time lag functions. In: Verma AK, Kapur PK, Ghadge SG (eds) Advances in performance and safety of complex systems. MacMillan India Ltd, Bangalore, pp 839–849Google Scholar
  42. 42.
    Kapur PK, Gupta A, Jha PC (2007) Reliability analysis of project and product type software in operational phase incorporating the effect of fault removal efficiency. Int J Reliab Qual Safety Eng 14(3):219–240CrossRefGoogle Scholar
  43. 43.
    Kenny GQ (1993) Estimating defects in a commercial software during operational use. IEEE Trans Reliab 42(1):107–115CrossRefGoogle Scholar
  44. 44.
    Kapur PK, Bardhan AK, Jha PC (2003) Optimal reliability allocation problem for a modular software system. OPSEARCH J Oper Res Soc India 40(2):133–148MathSciNetGoogle Scholar
  45. 45.
    Bass FM (1969) A new product growth model for consumer durables. Manag Sci 15:215–227MATHCrossRefGoogle Scholar
  46. 46.
    Xie M, Zao M (1992) The Schneidewind software reliability model revisited. In: Proceedings 3rd international symposium on software reliability engineering, pp 184–192Google Scholar
  47. 47.
    Kapur PK, Younes S (1995) Software reliability growth model with error dependency. Microelectron Reliab 35(2):273–278CrossRefGoogle Scholar
  48. 48.
    Huang CY, Lin CT (2006) Software reliability analysis by considering fault dependency and debugging time lag. IEEE Trans Reliab 35(3):436–449CrossRefGoogle Scholar
  49. 49.
    Lo HJ, Huang CY (2004) Incorporating imperfect debugging into software fault processes. In: TENCON 2004. 2004 IEEE region 10 conference, vol 2, 21–24 November 2004, pp 326–329Google Scholar
  50. 50.
    Singh VB, Yadav K, Kapur R, Yadavalli VSS (2007) Considering fault dependency concept with debugging time lag in software reliability growth modeling using a power function of testing time. Int J Autom Comput 4(4):359–368CrossRefGoogle Scholar
  51. 51.
    Huang CY (2005) Cost reliability optimal release policy for software reliability models incorporating improvements in testing efficiency. J Syst Softw 77:139–155CrossRefGoogle Scholar
  52. 52.
    Kapur PK, Kumar A, Yadavalli VSS (2006) A general software reliability growth models for a distributed environment. S Afr Stat J 40:151–185MathSciNetMATHGoogle Scholar
  53. 53.
    Chu-Ti Lin, Chin-Yu Huang, Jun-Ru Chang (2005) Integrating generalized weibull-type testing-effort function and multiple change-points into software reliability growth models. APSEC, pp 431–438Google Scholar
  54. 54.
    Gupta A, Kapur R, Jha PC (2008) Considering testing efficiency in estimating software reliability based on testing variation dependent SRGM. Int J Reliab Qual Safety Eng 15(2):77–81CrossRefGoogle Scholar
  55. 55.
    Norden PV (1977) Project life cycle modeling: background and application of the life cycle curves. Presented at the software life cycle management workshop, Airlie, VA sponsored by US Army Computer Systems CommandGoogle Scholar
  56. 56.
    Kapur PK, Gupta A, Shatnawi O, Yadavalli VSS (2006) Testing effort control using flexible software reliability growth model with change point. Int J Performability Eng—Special issue on Dependability of Software/Computing Systems 2:245–262Google Scholar
  57. 57.
    Parr FN (1980) An alternative to the Rayleigh curve for software development effort. IEEE Trans Softw Eng SE-6:291–296CrossRefGoogle Scholar
  58. 58.
    Huang CY, Kuo SY, Chen IY (1997) Analysis of a software reliability growth model with logistic testing effort function. In: Proceedings 8th international symposium software reliability engineering (ISSRE’97), pp 378–388Google Scholar
  59. 59.
    Huang CY, Lo JH, Kuo SY, Lyu MR (1999) Software reliability modeling and cost estimation incorporating testing-effort and efficiency. In: Proceedings 10th international symposium software reliability engineering (ISSRE’1999), pp 62–72Google Scholar
  60. 60.
    Mudholkar GS, Srivastava DK (1993) Exponentiated Weibull family analyzing bathtub failure-rate data. IEEE Trans Reliab 42:299–302MATHCrossRefGoogle Scholar
  61. 61.
    Yamada S, Tamura Y, Kimura M (2000) A software reliability growth model for a distributed development environment. Electron Commun Japan 83(3):1446–1453Google Scholar
  62. 62.
    Kapur PK, Gupta A, Kumar A, Yamada S (2005) Flexible software reliability growth models for distributed systems. OPSEARCH J Oper Res Soc India 42(4):378–398MATHGoogle Scholar
  63. 63.
    Kapur PK, Gupta A, Gupta A, Kumar A (2005) Discrete software reliability growth modeling. In: Kapur PK, Verma AK (eds) Quality, reliability and IT (trends and future directions). Narora Publications Pvt Ltd, New Delhi, pp 158–166Google Scholar
  64. 64.
    Yadav K, Goswami DN, Kapur PK (2007) Testing-domain based software reliability growth models for distributed environment. In: Proceedings 3rd international conference on reliability and safety engineering (INCRESE-2007), Udaipur, pp 614–628Google Scholar
  65. 65.
    Kapur PK, Garg RB, Kumar S (1999) Contributions to hardware and software reliability. World Scientific, SingaporeMATHCrossRefGoogle Scholar
  66. 66.
    Pham H (2006) System software reliability. Reliability engineering series. Springer, LondonGoogle Scholar
  67. 67.
    Misra PN (1983) Software reliability analysis. IBM Syst J 22:262–270CrossRefGoogle Scholar

Copyright information

©  Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.Department of Operational ResearchUniversity of DelhiDelhiIndia
  2. 2.Department of Industrial and Systems EngineeringRutgers UniversityPiscatawayUSA

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