A Bivariate Software Reliability Model with Change-Point and Its Applications

ABSTRACT

Testing-time when a change of a stochastic characteristic of the software failure-occurrence time or software failure-occurrence time-interval is observed is called change-point. It is said that effect of the change-point on the software reliability growth process influences on accuracy for software reliability assessment based on a software reliability growth model (SRGM). We propose an SRGM with the effect of the change-point based on a bivariate SRGM, in which the software reliability growth process is assumed to depend on the testing-time and testing-effort factors simultaneously, for accurate software reliability assessment. And we discuss an optimal software release problem for deriving optimal testing-effort expenditures based on our model. Further, we show numerical examples of software reliability assessment based on our bivariate SRGM and estimation of optimal testing-effort expenditures by using actual data.

Testing-time when a change of a stochastic characteristic of the software failure-occurrence time or software failure-occurrence time-interval is observed is called change-point. It is said that effect of the change-point on the software reliability growth process influences on accuracy for software reliability assessment based on a software reliability growth model (SRGM). We propose an SRGM with the effect of the change-point based on a bivariate SRGM, in which the software reliability growth process is assumed to depend on the testing-time and testing-effort factors simultaneously, for accurate software reliability assessment. And we discuss an optimal software release problem for deriving optimal testing-effort expenditures based on our model. Further, we show numerical examples of software reliability assessment based on our bivariate SRGM and estimation of optimal testing-effort expenditures by using actual data.

KEYWORDS

Software Reliability, Software Reliability Growth Factor, Change-Point, Bivariate Software Reliability Growth Model, Optimal Testing-Effort Expending Problem

Software Reliability, Software Reliability Growth Factor, Change-Point, Bivariate Software Reliability Growth Model, Optimal Testing-Effort Expending Problem

Cite this paper

nullS. Inoue and S. Yamada, "A Bivariate Software Reliability Model with Change-Point and Its Applications,"*American Journal of Operations Research*, Vol. 1 No. 1, 2011, pp. 1-7. doi: 10.4236/ajor.2011.11001.

nullS. Inoue and S. Yamada, "A Bivariate Software Reliability Model with Change-Point and Its Applications,"

References

[1] J.D. Musa, “A theory of software reliability and its application,” IEEE Transactions on Software Engineering, Vol. SE-1, No. 3, 1975, pp. 312-327.

[2] S. Yamada and S. Osaki, “Software reliability growth modeling: Models and applications,” IEEE Transactions on Software Engineering, Vol. SE-11, No. 12, 1985, pp. 1431-1437. doi:10.1109/TSE.1985.232179

[3] J.D. Musa, D. Iannio, and K. Okumoto, “Software Reliability: Measurement, Prediction, Application,” McGraw -Hill, 1987.

[4] H. Pham, “Software Reliability,” Springer-Verlag, 2000.

[5] T. Ishii and T. Dohi, “Two-dimensional software reliability models and their application,” Proceedings of the 12th Pacific Rim International Symposium on Dependable Computing, 2006, pp. 3-10.

[6] S. Inoue and S. Yamada, “A bivariate Weibull-type software reliability growth model and its goodness-of-fit evaluation,” (in Japanese) J. Information Processing Society of Japan, Vol. 49, no. 8, August 2008, pp. 2851 -2861.

[7] S. Inoue and S. Yamada, “A framework for two-dimensional software reliability modeling with program size,” Proceedings of the 14th ISSAT International Conference on Reliability and Quality in Design, 2008, pp. 198-202.

[8] M. Zhao, “Change-point problems in software and hardware reliability,” Communications in Statistics -- Theory and Methods, Vol. 22, No. 3, 1993, pp. 757-768. doi:10.1080/03610929308831053

[9] C.Y. Huang, “Performance analysis of software reliability growth models with testing-effort and change-point,” Journal of Systems and Software, Vol. 76, No. 2, 2005, pp. 181-194. doi:10.1016/j.jss.2004.04.024

[10] C.Y. Huang, “Cost-reliability-optimal release policy for software reliability models incorporating improvements in testing efficiency,” Journal of Systems and Software, Vol. 77, No. 2, 2005, pp. 139-155. doi:10.1016/j.jss.2004.10.014

[11] F.Z. Zou, “A change-point perspective on the software failure process,” Software Testing, Verification and Reliability, vol. 13, no. 2, 2003, pp. 85-93. doi:10.1002/stvr.268

[12] J. Zhao, H.W. Liu, G. Cui, and X.Z. Yang, “Software reliability growth model with change-point and environmental function,” Journal of Systems and Software, Vol. 79, No. 11, 2006, pp. 1578-1587. doi:10.1016/j.jss.2006.02.030

[13] S. Inoue and S. Yamada, “Software reliability measurement with change-point,” Proceedings of the International Conference on Quality and Reliability, 2007, pp. 170 -175.

[14] S. Inoue and S. Yamada, “Optimal software release policy with change-point,” Proceedings of the IEEE International Conference on Industrial Engineering and Engineering Management, 2008, pp. 531-535. doi:10.1109/IEEM.2008.4737925

[15] N. Langberg and N.D. Singpurwalla, “A unification of some software reliability models,” SIAM Journal on Scientific Computing, Vol. 6, No. 3, 1985, pp. 781-790. doi:10.1137/0906053

[16] D.S. Miller, “Exponential order statistic models of software reliability growth,” IEEE Transactions on Software Engineering, Vol. SE-12, No. 1, 1986, pp. 12-24.

[17] D.N.P. Murthy, J. Baik, R.J. Wilson, and M.R. Bulmer, “Two-dimensional failure modeling,” In: H. Pham, Ed., Springer Handbook of Engineering Statistics, Springer -Verlag, Berlin, 2006, pp. 97-111. doi:10.1007/978-1-84628-288-1_5

[18] H. Okamura, T. Dohi, and S. Osaki, “A reliability assessment method for software products in operational phase? Proposal of an accelerated life testing model,” (in Japanese), Transactions of IEICE, Vol. J83-A, No. 3, 2000, pp. 294-301.

[19] S. Yamada and S. Osaki, “Cost-reliability optimal release policies for software systems,” IEEE Transactions on Reliability, Vol. R-34, No. 5, 1985, pp. 422-424. doi:10.1109/TR.1985.5222222

[20] M. Ohba, “Software reliability analysis models,” IBM Journal of Research and Development, Vol. 28, No. 4, 1984, pp. 428-443. doi:10.1147/rd.284.0428

[21] E.J. Gumbel, “Bivariate exponential distributions,” Journal of the American Statistical Association, No. 55, 1960, pp. 698-707. doi:10.2307/2281591

[1] J.D. Musa, “A theory of software reliability and its application,” IEEE Transactions on Software Engineering, Vol. SE-1, No. 3, 1975, pp. 312-327.

[2] S. Yamada and S. Osaki, “Software reliability growth modeling: Models and applications,” IEEE Transactions on Software Engineering, Vol. SE-11, No. 12, 1985, pp. 1431-1437. doi:10.1109/TSE.1985.232179

[3] J.D. Musa, D. Iannio, and K. Okumoto, “Software Reliability: Measurement, Prediction, Application,” McGraw -Hill, 1987.

[4] H. Pham, “Software Reliability,” Springer-Verlag, 2000.

[5] T. Ishii and T. Dohi, “Two-dimensional software reliability models and their application,” Proceedings of the 12th Pacific Rim International Symposium on Dependable Computing, 2006, pp. 3-10.

[6] S. Inoue and S. Yamada, “A bivariate Weibull-type software reliability growth model and its goodness-of-fit evaluation,” (in Japanese) J. Information Processing Society of Japan, Vol. 49, no. 8, August 2008, pp. 2851 -2861.

[7] S. Inoue and S. Yamada, “A framework for two-dimensional software reliability modeling with program size,” Proceedings of the 14th ISSAT International Conference on Reliability and Quality in Design, 2008, pp. 198-202.

[8] M. Zhao, “Change-point problems in software and hardware reliability,” Communications in Statistics -- Theory and Methods, Vol. 22, No. 3, 1993, pp. 757-768. doi:10.1080/03610929308831053

[9] C.Y. Huang, “Performance analysis of software reliability growth models with testing-effort and change-point,” Journal of Systems and Software, Vol. 76, No. 2, 2005, pp. 181-194. doi:10.1016/j.jss.2004.04.024

[10] C.Y. Huang, “Cost-reliability-optimal release policy for software reliability models incorporating improvements in testing efficiency,” Journal of Systems and Software, Vol. 77, No. 2, 2005, pp. 139-155. doi:10.1016/j.jss.2004.10.014

[11] F.Z. Zou, “A change-point perspective on the software failure process,” Software Testing, Verification and Reliability, vol. 13, no. 2, 2003, pp. 85-93. doi:10.1002/stvr.268

[12] J. Zhao, H.W. Liu, G. Cui, and X.Z. Yang, “Software reliability growth model with change-point and environmental function,” Journal of Systems and Software, Vol. 79, No. 11, 2006, pp. 1578-1587. doi:10.1016/j.jss.2006.02.030

[13] S. Inoue and S. Yamada, “Software reliability measurement with change-point,” Proceedings of the International Conference on Quality and Reliability, 2007, pp. 170 -175.

[14] S. Inoue and S. Yamada, “Optimal software release policy with change-point,” Proceedings of the IEEE International Conference on Industrial Engineering and Engineering Management, 2008, pp. 531-535. doi:10.1109/IEEM.2008.4737925

[15] N. Langberg and N.D. Singpurwalla, “A unification of some software reliability models,” SIAM Journal on Scientific Computing, Vol. 6, No. 3, 1985, pp. 781-790. doi:10.1137/0906053

[16] D.S. Miller, “Exponential order statistic models of software reliability growth,” IEEE Transactions on Software Engineering, Vol. SE-12, No. 1, 1986, pp. 12-24.

[17] D.N.P. Murthy, J. Baik, R.J. Wilson, and M.R. Bulmer, “Two-dimensional failure modeling,” In: H. Pham, Ed., Springer Handbook of Engineering Statistics, Springer -Verlag, Berlin, 2006, pp. 97-111. doi:10.1007/978-1-84628-288-1_5

[18] H. Okamura, T. Dohi, and S. Osaki, “A reliability assessment method for software products in operational phase? Proposal of an accelerated life testing model,” (in Japanese), Transactions of IEICE, Vol. J83-A, No. 3, 2000, pp. 294-301.

[19] S. Yamada and S. Osaki, “Cost-reliability optimal release policies for software systems,” IEEE Transactions on Reliability, Vol. R-34, No. 5, 1985, pp. 422-424. doi:10.1109/TR.1985.5222222

[20] M. Ohba, “Software reliability analysis models,” IBM Journal of Research and Development, Vol. 28, No. 4, 1984, pp. 428-443. doi:10.1147/rd.284.0428

[21] E.J. Gumbel, “Bivariate exponential distributions,” Journal of the American Statistical Association, No. 55, 1960, pp. 698-707. doi:10.2307/2281591