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A Distribution-Level Combinational Model to Improve Reliability Prediction Accuracy

Volume 13, Number 6, October 2017 - Paper 5  - pp. 832-843
DOI: 10.23940/ijpe.17.06.p5.832843

Wenjun Xiea, Haiyan Suna, Lu Zhanga, Ji Wub,*

aThe LIMB of the Ministry of Education, School of Mathematics and Systems Science, Beihang University, Beijing, 100191, China
bSchool of Computer Science and Engineering, Beihang University, Beijing, 100191, China

(Submitted on July 25, 2017; Revised on August 30, 2017; Accepted on September 15, 2017)

(This paper was presented at the Third International Symposium on System and Software Reliability.)


Single reliability growth model usually only captures partial knowledge of a failure process. A combinational model tries to capture more knowledge by integrating two or more reliability growth models. Unlike the existing linear combinational models that simply adds up the weighted results by G-O, M-O and L-V model, this paper proposes the combinational model from G-O and S-Shaped model, at the level of failure distribution to reduce fitting errors and to maintain the mathematical properties of non-homogenous Poisson process. To evaluate the effectiveness of the proposed model, we use the failure data sets (21 projects) available in public sources. Ten out of the twenty-one projects, which pass the distribution test and have feasible solutions in parameter estimation, are selected to conduct experiments. We use mean squared error (MSE) to evaluate the historical predictive validity. The results show that our model is consistently stable and has lower MSE. It reduces 51.3% MSE of G-O, 67.2% MSE of S-Shaped, and over 56% MSE of the three linear combinational models in average. The proposed model tends to have a larger estimation of the expected number of failures, which can overcome the under estimation by G-O and S-Shaped model in some degree.


References: 28

    1. A. A. Abdel-Ghaly, P. Y. Chan, and B. Littlewood, "Evaluation of Competing Software Reliability Predictions," IEEE Transactions on Software Engineering, vol. 12, no. 1, pp. 950-967, December 1986

    2. S. Brocklehurst, P. Y. Chan, and B. Littlewood, "Recalibrating Software Reliability Model," IEEE Transactions on Software Engineering, vol. 16, no. 4, pp. 458-470, April 1990

    3. L. S. Dharmasena, P. Zeephongsekul, and C. L. Jayasinghe, "Software Reliability Growth Models based on Local Polynomial Modeling with Kernel Smoothing," International Symposium on Software Reliability Engineering (ISSRE). IEEE, 2011

    4. W. H. Farr, "A Survey of Software Reliability Modeling and Estimation," Technical Report NSWC TR 82-171, Naval Surface Weapons Center, pp. 4-88, 1983

    5. A. L. Goel, and K. Okumoto, "Time-dependent Error-detection Rate Model for Software Reliability and other Performance Measures," IEEE Transactions on Reliability, vol. 28, no. 3, pp. 206-211, 1979

    6. J. F. Hair, W. C. Black, B. J. Babin, R. E. Anderson, R. L. Tatham, Multivariate data analysis, Pearson Prentice Hall, Upper Saddle River, vol. 6, 2006

    7. IEEE Std 1633-2008, IEEE Recommended Practice on Software Reliability. New York: IEEE Reliabiliy Society, 2008

    8. T. Kim, K. Lee, and J. Baik, "An Effective Approach to Estimating the Parameters of Software Reliability Growth Models Using a Real-valued Genetic Algorithm," Journal of Systems & Software, 102.C:134-144, 2015

    9. B. Kitchenham, L. Madeyski, D. Budgen, K. Jacky, B. Pearl, C. Stuart, G. Shirley, and A. Pohthong, "Robust Statistical Methods for Empirical Software Engineering." Empirical Software Engineering, pp. 1-52, 2016

    10. B. Littlewood, J. L. Verrall, "A Bayesian Reliability Growth Model for Computer Software," Journal of the Royal Statistical Society, vol. 1, no. 22, pp.322-346, 1973

    11. M. R. Lyu, "Measuring Reliability of Embedded Software: An Empirical Study with JPL Project Data," pp.493-500, Feb 1991

    12. M. R. Lyu, Handbook of Software Reliability Engineering, McGraw-Hill Companies, 1996

    13. M. R. Lyu, and A. Nikora, "A Heuristic Approach for Software Reliability Prediction: The Equally-Weighted Linear Combination Model," International Symposium on Software Reliability, pp. 172-181, June 1991

    14. M. R. Lyu, and A. Nikora, "Software Reliability Measurements through Combination Models: Approaches, Results, and A CASE Tool," International Computer Software & Applications Conference, pp. 577-584, 1991

    15. R. E. Mullen, "The Lognormal Distribution of Software Failure Rates: Application to Software Reliability Growth Modeling," vol. 117, pp. 134-142, 1998

    16. J. D. Musa, DACS Software Reliability Dataset, Data & Analysis Center for Software, January 1980:

    17. J. D. Musa, A. Iannino, and K. Okumoto, Software Reliability-Measurement, Prediction, Application, 1987

    18. J. D. Musa, and K. Okumoto, "A Logarithmic Poisson Execution Time Model for Software Reliability Measurement," International Conference on Software Engineering, pp. 230-238, Mar.1984

    19. J. D. Musa, and K. Okumoto, "Software Reliability Models: Concepts, Classification, Comparisons, and Practics," Springer Berlin Heidelberg, 1983

    20. H. Okamura, Y. Etani, and T. Dohi, "A Multi-factor Software Reliability Model based on Logistic Regression," Software Reliability Engineering (ISSRE), 2010 IEEE 21st International Symposium on. IEEE, 2010

    21. J. Park, and J. Baik, "Improving Software Reliability Prediction through Multi-criteria based Dynamic Model Selection and Combination," Journal of Systems and Software, vol. 101, pp. 236-244, 2015

    22. S. Ramasamy, and G. Govindasamy, "A Software Reliability Growth Model Addressing Learning," Journal of Applied Statistics, vol. 35, no. 10, pp. 1151-1168, 2008

    23. N. F. Schneidewind, "Analysis of Error Processes in Computer Software," Acm Sigplan Notices, vol. 10, no. 6, pp. 337-346, 1975

    24. K. Sharma, C. K. Nagpal, R. K. Garg, "Selection of Optimal Software Reliability Growth Models Using a Distance Based Approach," IEEE Transaction on Reliability, vol. 59, no. 2, pp.266-276, 2010

    25. Y.S. Su, C.Y. Huang, "Neural-network-based Approaches for Software Reliability Estimation Using Dynamic Weighted Combinational Models," Journal of Systems & Software, vol. 80, no. 4, pp.606-615, 2007

    26. J. Wu, Shaukat Ali, T. Yue, J. Tian, and C. Liu, "Assessing the Quality of Industrial Avionics Software: an Extensive Empirical Evaluation," Empirical Software Engineering, pp. 1-50, 2016

    27. S. Yamada, M. Ohba, and S. Osaki, "S-Shaped Reliability Growth Modeling for Software Error Detection," IEEE Transactions on Reliability, vol. 32, no. 5, pp. 475-484, 1983

    28. J. Zhao, H. W. Liu, and C. Gang. "Software Reliability Growth Model Considering Testing Profile and Operation Profile," Computer Software and Applications Conference. COMPSAC 2005. 29th Annual International. Vol. 1. IEEE, 2005


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