Lognormal Process Software Reliability Modeling with Testing-Effort

Shinji Inoue, Shigeru Yamada

Department of Social Management Engineering, Graduate School of Engineering, Tottori University, Tottori, Japan.

DOI: 10.4236/jsea.2013.64A002                

Abstract

We propose a software reliability growth model with testing-effort based on a continuous-state space stochastic process, such as a lognormal process, and conduct its goodness-of-fit evaluation. We also discuss a parameter estimation method of our model. Then, we derive several software reliability assessment measures by the probability distribution of its solution process, and compare our model with existing continuous-state space software reliability growth models in terms of the mean square error and the Akaike’s information criterion by using actual fault count data.

Keywords

Software Reliability Growth Model; Lognormal Process; Testing-Effort Function; Software Reliability Assessment Measures; Goodness-of-Fit

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	J. D. Musa, D. Iannio and K. Okumoto, “Software Reliability: Measurement, Prediction, Application,” McGrawHill, New York, 1987.
[2]	H. Pham, “Software Reliability,” Springer-Verlag, Singapore City, 2000.
[3]	S. Osaki, “Applied Stochastic System Modeling,” SpringerVerlag, Berlin-Heidelberg, 1992. doi:10.1007/978-3- 642-84681-6
[4]	K. S. Trivedi, “Probability and Statistics with Reliability, Queueing and Computer Science Applications,” John Wiley & Sons, New York, 2002.
[5]	S. Yamada, “Software Reliability Models,” In: S. Osaki, Ed., Stochastic Models in Reliability and Maintenance, Springer-Verlag, Berlin-Heidelberg, 2002, pp. 253-280. doi:10.1007/978-3-540-24808-8_10
[6]	S. Yamada, M. Kimura, H. Tanaka and S. Osaki, “Software Reliability Measurement and Assessment with Stochastic Differential Equations,” IEICE Transactions on Fundamentals of Electronics, and Computer Sciences, Vol. E77-A, No. 1, 1994, pp. 109-116.
[7]	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.
[8]	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
[9]	S. Yamada, H. Ohtera and H. Narihisa, “Software Reliability Growth Models with Testing-Effort,” IEEE Transactions on Reliability, Vol. R-35, No. 1, 1986, pp. 19-23. doi:10.1109/TR.1986.4335332
[10]	H. Akaike, “A New Look at the Statistical Model Identification,” IEEE Transactions on Automatic Control, Vol. AC-19, No. 6, 1974, pp. 716-723. doi:10.1109/TAC.1974.1100705
[11]	B. oksendal, “Stochastic Differential Equations: An Introduction with Applications,” Springer-Verlag, BerlinHeidelberg, 1985.
[12]	S. Yamada, M. Ohba and S. Osaki, “S-Shaped Software Reliability Growth Models and Their Applications,” IEEE Transactions on Reliability, Vol. R-33, No. 4, 1984, pp. 289-292. doi:10.1109/TR. 1984.5221826
[13]	M. Ohba, “Inflection S-Shaped Software Reliability Growth Model,” In: S. Osaki and Y. Hatoyama, Eds., Stochastic Models in Reliability Theory, Springer-Verlag, Berlin, 1984, pp. 144-165. doi:10.1007/978- 3-642-45587-2_10
[14]	W. D. Brooks and R. W. Motley, “Analysis of Discrete Software Reliability Models,” Technical Report RADCTR-80-84, Rome Air Development Center, New York, 1974.