Using Artificial Neural-Networks in Stochastic Differential Equations Based Software Reliability Growth Modeling

Sunil Kumar Khatri, Prakriti Trivedi, Shiv Kant, Nisha Dembla
DOI: 10.4236/jsea.2011.410070                

Abstract

Due to high cost of fixing failures, safety concerns, and legal liabilities, organizations need to produce software that is highly reliable. Software reliability growth models have been developed by software developers in tracking and measuring the growth of reliability. Most of the Software Reliability Growth Models, which have been proposed, treat the event of software fault detection in the testing and operational phase as a counting process. Moreover, if the size of software system is large, the number of software faults detected during the testing phase becomes large, and the change of the number of faults which are detected and removed through debugging activities becomes sufficiently small compared with the initial fault content at the beginning of the testing phase. Therefore in such a situation, we can model the software fault detection process as a stochastic process with a continuous state space. Recently, Artificial Neural Networks (ANN) have been applied in software reliability growth prediction. In this paper, we propose an ANN based software reliability growth model based on Ito type of stochastic differential equation. The model has been validated, evaluated and compared with other existing NHPP model by applying it on actual failure/fault removal data sets cited from real software development projects. The proposed model integrated with the concept of stochastic differential equation performs comparatively better than the existing NHPP based model.

Keywords

Software Reliability Growth Model, Artificial Neural Network, Stochastic Differential Equation (SDE), Stochastic Process

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	A. L. Goel and K. Okumoto, “Time Dependent Error Detection Rate Model for Software Reliability and Other Performance Measure,” IEEE Transactions on Reliability, Vol. 3, 1992, pp. 206-211. doi:10.1109/TR.1979.5220566
[2]	P. K. Kapur, R. B. Garg and S. Kumar, “Contributions to Hardware and Software Reliability,” World Scientific, Singapore, 1999.
[3]	B. Oksendal, “Stochastic Differential Equations—An Introduction with Applications,” Springer, Berlin, 2003.
[4]	S. Yamada and Y. Tamura, “A Flexible Stochastic Differential Equation Model in Distributed Development Environment,” European Journal of Operational Research, Vol. 168, No. 1, 2006, pp. 143-152. doi:10.1016/j.ejor.2004.04.034
[5]	C. H. Lee, Y. T. Kim and D. H. Park, “S-Shaped Software Reliability Growth Models Derived from Stochastic Differential Equations,” IIE Transactions, Vol. 36, No. 12, 2004, pp. 1193-1199. doi:10.1080/07408170490507792
[6]	N. Karunanithi and Y. K. Malaiya, “The Scaling Problem in Neural Networks for Software Reliability Prediction,” Proceedings of the 3rd International IEEE Symposium of Software Reliability Engineering, Los Alamitos, 7-10 October 1992, pp. 76-82. doi:10.1109/ISSRE.1992.285856
[7]	N. Karunanithi, Y. K. Malaiya and D. Whitley, “Prediction of Software Reliability Using Neural Networks,” Proceedings of the 2nd IEEE International Symposium on Software Reliability Engineering, Los Alamitos, 17-18 May 1991, pp. 124-130.
[8]	N. Karunanithi, D. Whitley and Y. K. Malaiya, “Using Neural Networks in Reliability Prediction,” IEEE Software, Vol. 9, No. 4, 1992, pp. 53-59. doi:10.1109/52.143107
[9]	K. Y. Cai, L. Cai, W. D. Wang, Z. Y. Yu and D. Zhang, “On the Neural Network Approach in Software Reliability Modeling,” The Journal of Systems and Software, Vol. 58, No. 1, 2001, pp. 47-62. doi:10.1016/S0164-1212(01)00027-9
[10]	S. A. Sherer, “Software Fault Prediction,” Journal of Systems and Software, Vol. 29, No. 2, 1995, pp. 97-105. doi:10.1016/0164-1212(94)00051-N
[11]	T. M. Khoshgoftar and R. M. Szabo, “Using Neural Networks to Predict Software Faults during Testing,” IEEE Transactions on Reliability, Vol. 45, No. 3, 1996, pp. 456-462. doi:10.1109/24.537016
[12]	Y. S. Su, C. Y. Huang and Y. S. Chen, “An Artificial Neural-Network Based Approach to Software Reliability Assessment,” Proceedings of IEEE Region 10 Conference, Melbourne, 21-24 November 2005, pp. 1-6.
[13]	P. K. Kapur, S. K. Khatri, M. Basirzadeh and N. Dembla, “Modeling Software Reliability Growth in Distributed Environment Using Artificial Neural-Networks,” In: S. K. Khatri and B. Kumar, Eds., Proceedings of International Conference on Reliability, Infocom Technology and Optimization, Faridabad, 1-3 November 2010, pp. 372-382.
[14]	P. K. Kapur, S. K. Khatri and D. N. Goswami, “A Generalized Dynamic Integrated Software Reliability Growth Model Based on Neural-Network Approach,” Proceedings of International Conference on Reliability, Safety and Quality Engineering, 5-7 January 2008, pp. 831-838.
[15]	S. K. Khatri, R. Kapur, P. Johri and P. Sharma, “Artificial Neural-Networks Based Software Reliability Growth Modeling with Two types of Imperfect Debugging,” In: S. K. Khatri and B. Kumar, Eds., Proceedings of International Conference on Reliability, Infocom Technology and Optimization, Faridabad, 1-3 November 2010, pp. 122-133.
[16]	S. Yamada, A. Nishigaki and M. Kimura, “A Stochastic Differential Equation Model for Software Reliability Assessment and Its Goodness of Fit,” International Journal of Reliability and Applications, Vol. 4, No. 1, 2003, pp. 1-11.
[17]	P. N. Misra, “Software Reliability Analysis,” IBM System Journal, Vol. 22, No. 3, 1983, pp. 262-270. doi:10.1147/sj.223.0262
[18]	H. Pham, “Software Reliability,” Springer-Verlag, Singapore City, 2000.
[19]	K. Pillai and V. S. S. Nair, “A Model for Software Development effort and Cost Estimation,” IEEE Transactions on Software Engineering, Vol. 23, No. 8, 1997, pp. 485-497. doi:10.1109/32.624305