Development of software reliability models using a hybrid approach and validation of the proposed models using big data

  • P. Govindasamy
  • R. Dillibabu


This article proposes three software reliability models based on a hybrid approach combining NHPP models, Weibull model, and exponential model. The software failure is first categorised into three categories, namely pure software failures, hardware-induced software failures, and user-induced software failures. Based on the failure behaviour, NHPP models were adapted for pure software failures, Weibull model for hardware-induced failures, and exponential model for user-induced software failures. The failure intensity function, mean value function, and reliability function were determined. The proposed models are validated using big data analysis. From the data collected during the testing phase, the optimal values of parameters were estimated using maximum likelihood estimation and genetic algorithm. The expected number of failures and the cumulative number of failures were calculated, and comparison was made between the observed values to show the performance of the proposed models. A comparison criterion was also proposed to confirm the estimation accuracy. Finally, a t test was conducted to test the significance of the difference between the observed and estimated values. Experimental results confirm the better estimation accuracy of the proposed models.


Software failures Estimation accuracy Parameters Reliability models Hardware Big data analysis 


  1. 1.
    Smith DJ (2011) Reliability, maintainability and risk. Reliab Maintainab Risk. Google Scholar
  2. 2.
    Sommerville I (2010) Software engineering. Softw Eng. zbMATHGoogle Scholar
  3. 3.
    Yamada S, Ohtera H, Ohba M (1992) Testing-domain dependent software reliability models. Comput Math Appl 24(1–2):79–86. MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Goel AL (1985) Software reliability models: assumptions, limitations, and applicability. IEEE Trans Softw Eng SE-11(12):1411–1423. CrossRefGoogle Scholar
  5. 5.
    Schick GJ, Wolverton RW (1978) An analysis of competing software reliability models. IEEE Trans Softw Eng SE-4(2):104–120. CrossRefzbMATHGoogle Scholar
  6. 6.
    Iqbal R, Doctor F, More B, Mahmud S, Yousuf U (2016) Big data analytics: computational intelligence techniques and application areas. Int J Inf Manag. Google Scholar
  7. 7.
    Goel AL, Okumoto K (1979) Time-dependent error-detection rate model for software reliability and other performance measures. IEEE Trans Reliab R-28(3):206–211. CrossRefzbMATHGoogle Scholar
  8. 8.
    Yamada S, Hishitani J, Osaki S (1993) Software-reliability growth with a Weibull test-effort: a model and application. IEEE Trans Reliab 42(1):100–106. CrossRefzbMATHGoogle Scholar
  9. 9.
    Miller DR (1986) Exponential Order Statistic Models of Software Reliability Growth. IEEE Trans Softw Eng SE-12(1):12–24. MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Yamada S, Ohba M, Osaki S (1984) S-shaped software reliability growth models and their applications. IEEE Trans Reliab R-33(4):289–292. CrossRefGoogle Scholar
  11. 11.
    Kapur PK, Garg RB (1991) Optimum release policy for an inflection s-shaped software reliability growth model. Microelectron Reliab 31(1):39–41. CrossRefGoogle Scholar
  12. 12.
    Hossain SA, Dahiya RC (1993) Estimating the parameters of a non-homogeneous poisson-process model for software reliability. IEEE Trans Reliab 42(4):604–612. CrossRefGoogle Scholar
  13. 13.
    Yadav HB, Yadav DK (2017) Early software reliability analysis using reliability relevant software metrics. Int J Syst Assur Eng Manag 8(S4):2097–2108. CrossRefGoogle Scholar
  14. 14.
    Lakshmanan I, Ramasamy S (2015) An artificial neural-network approach to software reliability growth modeling. Procedia Comput Sci 57:695–702. CrossRefGoogle Scholar
  15. 15.
    Minohara T, Tohma Y (1995) Parameter estimation of hyper-geometric distribution software reliability growth model by genetic algorithms. In: Proceedings of the Sixth International Symposium on Software Reliability Engineering.
  16. 16.
    Choudhary A, Baghel AS, Sangwan OP (2018) Parameter estimation of software reliability model using firefly optimization. Adv Intell Syst Comput 542:407–415. Google Scholar
  17. 17.
    Majumdar R, Kapur PK, Khatri SK, Shrivastava AK (2018) Evolutionary algorithm based faults optimization of multi-modular software. Smart Innov Syst Technol 78:281–291. CrossRefGoogle Scholar
  18. 18.
    Otero CE, Peter A (2015) Research directions for engineering big data analytics software. IEEE Intell Syst 30(1):13–19. CrossRefGoogle Scholar
  19. 19.
    Meeker WQ, Hong Y (2014) Reliability meets big data: opportunities and challenges. Qual Eng 26:102–116. CrossRefGoogle Scholar
  20. 20.
    Sanborn AN (2017) Types of approximation for probabilistic cognition: sampling and variational. Brain Cogn 112:98–101. CrossRefGoogle Scholar
  21. 21.
    Sanborn AN (2017) Types of approximation for probabilistic cognition: sampling and variational. Brain Cogn 112:98–101. CrossRefGoogle Scholar
  22. 22.
    Sharma K, Garg R, Nagpal CK, Garg RK (2010) Selection of optimal software reliability growth models using a distance based approach. IEEE Trans Reliab 59(2):266–276. CrossRefGoogle Scholar
  23. 23.
    Lo J-H, Huang C-Y, Chen I-Y, Kuo S-Y, Lyu MR (2005) Reliability assessment and sensitivity analysis of software reliability growth modeling based on software module structure. J Syst Softw 76(1):3–13. CrossRefGoogle Scholar
  24. 24.
    Wang J, Zhang C (2018) Software reliability prediction using a deep learning model based on the RNN encoder–decoder. Reliab Eng Syst Saf 170:73–82. CrossRefGoogle Scholar
  25. 25.
    Montgomery DC (2012) Design and analysis of experiments. Wiley, New York. Google Scholar
  26. 26.
    Park J, Kim HJ, Shin JH, Baik J (2012) An embedded software reliability model with consideration of hardware related software failures. In Proceedings of the 2012 IEEE 6th International Conference on Software Security and Reliability, SERE 2012, pp 207–214.

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Industrial Engineering, CEG CampusAnna UniversityChennaiIndia
  2. 2.Department of Industrial EngineeringCEG Campus, Anna UniversityChennaiIndia

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