A three-parameter fault-detection software reliability model with the uncertainty of operating environments

Article

Abstract

As requirements for system quality have increased, the need for high system reliability is also increasing. Software systems are extremely important, in terms of enhanced reliability and stability, for providing high quality services to customers. However, because of the complexity of software systems, software development can be time-consuming and expensive. Many statistical models have been developed in the past years to estimate software reliability. In this paper, we propose a new three-parameter fault-detection software reliability model with the uncertainty of operating environments. The explicit mean value function solution for the proposed model is presented. Examples are presented to illustrate the goodness-of-fit of the proposed model and several existing non-homogeneous Poisson process (NHPP) models based on three sets of failure data collected from software applications. The results show that the proposed model fits significantly better than other existing NHPP models based on three criteria such as mean squared error (MSE), predictive ratio risk (PRR), and predictive power (PP).

Keywords

Nonhomogeneous Poisson process software reliability mean squared error predictive ratio risk predictive power fault detection 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

Acknowledgments

The authors would like to thank the reviewers for their comments and suggestions. This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2013R1A1A2009277).

References

  1. [1]
    Chang, I.H., Pham, H., Lee, S.W. & Song, K.Y. (2014). A testing-coverage software reliability model with the uncertainty of operation environments. International Journal of Systems Science: Operations & Logistics, 1 (4): 220–227.Google Scholar
  2. [2]
    Ehrlich, W., Prasanna, B., Stampfel, J. & Wu, J. (1993). Determining the cost of a stop testing decision. IEEE Software, 10 (2): 33–42.CrossRefGoogle Scholar
  3. [3]
    Goel, A.L. & Okumoto, K. (1979). Time dependent error detection rate model for software reliability and other performance measures. IEEE Transactions on Reliability, R-28 (3): 206–211.CrossRefMATHGoogle Scholar
  4. [4]
    Grag, R.P., Sharma, K., Kumar, R. & Grag, R.K. (2010). Performance analysis of software reliability models using matrix method. World Academy of Science, Engineering and Technology, 4 (11): 31–38.Google Scholar
  5. [5]
    Huang, C.Y., Kuo, S.Y., Lyu, M.R. & Lo, J.H. (2000). Quantitative software reliability modeling from testing from testing to operation. Proceedings of the International Symposium on Software Reliability Engineering IEEE, Los Alamitos, CA, USA: 72–82.Google Scholar
  6. [6]
    Jeske, D.R. & Zhang, X. (2005). Some successful approaches to software reliability modeling in industry. The Journal of Systems and Software, 74 (1): 85–99.CrossRefGoogle Scholar
  7. [7]
    Ohba, M. (1984). Inflexion s-shaped software reliability growth models. In: Osaki, S. & Hatoyama Y. (eds.), Stochastic Models in Reliability Theory, pp. 144–162. Berlin: Springer-Verlag.CrossRefGoogle Scholar
  8. [8]
    Pham, H. (1996). A software cost model with imperfect debugging, random life cycle and penalty cost. International Journal of Systems Science, 27 (5): 455–463.CrossRefMATHGoogle Scholar
  9. [9]
    Pham, H. (2000). Software Reliability. Singapore: Springer.MATHGoogle Scholar
  10. [10]
    Pham, H. (2006). System Software Reliability. London: Springer.CrossRefGoogle Scholar
  11. [11]
    Pham, H. (2007). An imperfect-debugging fault-detection dependent-parameter software. International Journal of Automation and Computing, 04 (4): 325–328.CrossRefGoogle Scholar
  12. [12]
    Pham, H. (2013). A software reliability model with Vtub-shaped fault-detection rate subject to operating environments. Proceedings of the 19th ISSAT International Conference on Reliability and Quality in Design, August 5-7, Hawaii, USA, 33–37.Google Scholar
  13. [13]
    Pham, H. (2014). A new software reliability model with Vtub-shaped fault detection rate and the uncertainty of operating environments. Optimization, 63 (10): 1481–1490.MathSciNetCrossRefMATHGoogle Scholar
  14. [14]
    Pham, H. & Deng, C. (2003). Predictive-ratio risk criterion for selecting software reliability models. In: Proceedings of the 9th ISSAT International Conference on Reliability and Quality in Design.Google Scholar
  15. [15]
    Pham, H., Nordmann, L. & Zhang, X. (1999). A general imperfect software debugging model with s-shaped fault detection rate. IEEE Transactions on Reliability, 48 (2): 169–175.CrossRefGoogle Scholar
  16. [16]
    Pham, H. & Zhang, X. (1997). An NHPP software reliability models and its comparison. International Journal of Reliability, Quality and Safety Engineering, 4 (3): 269–282.CrossRefGoogle Scholar
  17. [17]
    Pham, L. & Pham, H. (2000). Software reliability models with time dependent hazard function based on Bayesian approach. IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans, 30 (1): 25–35.MathSciNetCrossRefGoogle Scholar
  18. [18]
    Sgarbossa, F., Persona, A. & Pham, H. (2015). Using systemability function for periodic replacement policy in real environments. Quality and Reliability Engineering International, 31 (4): 617–633.CrossRefGoogle Scholar
  19. [19]
    Teng, X. & Pham, H. (2004). Software cost model for quantifying the gain with considerations of random field environments. IEEE Transactions on Computers, 53 (3): 380–384.CrossRefGoogle Scholar
  20. [20]
    Teng, X. & Pham, H. (2006). A new methodology for predicting software reliability in the random field environments. IEEE Transactions on Reliability, 55 (3): 458–468.CrossRefGoogle Scholar
  21. [21]
    Yamada, S. & Osaki, S. (1985). Software reliability growth modeling: models and applications. IEEE Transactions on Software Engineering, 11 (12): 1431–1437.CrossRefGoogle Scholar
  22. [22]
    Yamada, S., Tokuno, K. & Osaki, S. (1992). Imperfect debugging models with fault introduction rate for software reliability assessment. International Journal of Systems Science, 23 (12): 2241–2252.CrossRefMATHGoogle Scholar
  23. [23]
    Yamada, S., Ohba, M. & Osaki, S. (1983). S-shaped reliability growth modeling for software fault detection. IEEE Transactions on Reliability, 32 (5): 475–484.CrossRefGoogle Scholar
  24. [24]
    Yang, B. & Xie, M. (2000). A study of operational and testing reliability in software reliability analysis. Reliability Engineering and System Safety, 70 (3): 323–329.CrossRefGoogle Scholar
  25. [25]
    Zhang, X., Jeske, D. & Pham, H. (2002). Calibrating software reliability models when the test environment does not match the user environment. Applied Stochastic Models in Business and Industry, 18 (1): 87–99.MathSciNetCrossRefMATHGoogle Scholar
  26. [26]
    Zhang, X. & Pham, H. (2000). An analysis of factors affecting software reliability. Journal of Systems and Software, 50 (1): 43–56.CrossRefGoogle Scholar
  27. [27]
    Zhang, X. & Pham, H. (2006). Software field failure rate prediction before software deployment. Journal of Systems and Software, 79 (3): 291–300.CrossRefGoogle Scholar
  28. [28]
    Zhang, X., Teng, X. & Pham. H. (2003). Considering fault removal efficiency in software reliability assessment. IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans, 33 (1): 114–120.CrossRefGoogle Scholar
  29. [29]
    Zhu, M., Zhang, X. & Pham, H. (2015). A comparison analysis of environmental factors affecting software reliability. Journal of Systems and Software, 109: 150–160.CrossRefGoogle Scholar

Copyright information

© Systems Engineering Society of China and Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Department of Computer Science and StatisticsChosun UniversityGwangjuKorea
  2. 2.Department of Industrial and Systems EngineeringRutgers UniversityNew JerseyUSA

Personalised recommendations