A Discussion of Software Reliability Growth Models with Time-Varying Learning Effects
American Journal of Software Engineering and Applications
Volume 2, Issue 3, June 2013, Pages: 92-104
Received: Jun. 24, 2013; Published: Jul. 20, 2013
Views 3587      Downloads 160
Author
Chiu, Kuei-Chen, Institute of Allied Health Sciences, College of Medicine, National Cheng Kung University, Tainan, Taiwan
Article Tools
PDF
Follow on us
Abstract
Over the last few decades, software reliability growth models (SRGM) has been developed to predict software reliability in the testing/debugging phase. Most of the models are based on the Non-Homogeneous Poisson Process (NHPP), and an S or exponential-shaped type of testing behavior is usually assumed. Chiu et al. (2008) provided an SRGM that considers learning effects, which is able to reasonably describe the S and exponential-shaped behaviors simultaneously. This paper considers both linear and exponential-learning effects in an SRGM to enhance the model in Chiu et al. (2008), assumes the learning effects depend on the testing-time, and discusses when and what learning effects would occur in the software development process. This research also verifies the effectiveness of the proposed models with R square (Rsq), and compares the results with these of other models by using four real datasets. The proposed models consider constant, linear, and exponential-learning effects simultaneously. The results reveal the proposed models fit the data better than other models, and that the learning effects occur in the software testing process. The results are helpful for the software testing/debugging managers to master the schedule of the projects, the performance of the programmers, and the reliability of the software system.
Keywords
Software Reliability, Non-Homogeneous Poisson Process (NHPP), Learning Effects, Time-Varying Learning Effects
To cite this article
Chiu, Kuei-Chen, A Discussion of Software Reliability Growth Models with Time-Varying Learning Effects, American Journal of Software Engineering and Applications. Vol. 2, No. 3, 2013, pp. 92-104. doi: 10.11648/j.ajsea.20130203.12
References
[1]
Achcar, J.A., Dey, D.K., and Niverthi, M. (1997) "A Bayesian approach using nonhomogeneous Poisson Process for software reliability models", In Frontiers in Reliability, Basu et al. (Eds).
[2]
Adam Smiarowski , Jr. , Hoda S. Abdel-Aty-Zohdy , Mostafa Hashem Sherif , Hemal Shah (2006) "Wavelet Based RDNN for Software Reliability Estimation", 11th IEEE Symposium on Computers and Communications (ISCC'06), iscc,pp.312-317.
[3]
Bai, C.G. (2005) "Bayesian network based software reliability prediction with an operational profile", The Journal of Systems and Software, 77: 103-112.
[4]
Bai, C.G., Hu, Q.P., Xie, M., and Ng, S.H. (2005) "Software failure prediction based on a Markov Bayesian network model", The Journal of Systems and Software, 74: 275-282.
[5]
Bunea, C., Charitosb, T., Cooke, R. M., and Beckerd, G. (2005) "Two-stage Bayesian models—application to ZEDB project", Reliability Engineering and System Safety, 90: 123-130.
[6]
Chin-Yu Huang, Sy-Yen Kuo, Michael R. Lyu, (2000) "Effort-Index-Based Software Reliability Growth Models and Performance Assessment," Computer Software and Applications Conference, Annual International, The Twenty-Fourth Annual International Computer Software and Applications Conference, 0:454.
[7]
Chiu, K.-C., Huang, Y.-S., and Lee, T.-Z. (2008) "A Study of Software Reliability Growth from the Perspective of Learning Effects," Reliability Engineering and Systems Safety, Vol. 93, No. 10, pp. 1410-1421.
[8]
Chiu, K.-C., Ho, J.-W., and Huang, Y.-S. (2009) "Bayesian Updating of Optimal Release Time for Software Systems," Software Quality Journal, Vol. 17, No. 1, pp. 99-120.
[9]
Cid, J.E.R. and Achcar, J.A. (1999) "Bayesian inference for nonhomogeneous Poisson processes in software reliability models assuming nonmonotonic intensity functions", Computational Statistics & Data Analysis, 32: 147-159.
[10]
Dietmar Pfahl (2001) "An Integrated Approach to Simulation-Based Learning in Support of Strategic and Project Management in Software Organisations" , PhD Theses in Experimental Software Engineering, Fraunhofer-Institut für Experimentelles Software Engineering, 8:27-40.
[11]
Goel, A.L. and Okumoto, K. (1979) "Time-varying fault detection rate model for software and other performance measures", IEEE Transactions on Reliability, 28: 206-211.
[12]
Gokhale, S. S. and Trivedi, K. S. (1999) "A time/structure based software reliability model", Annals of Software Engineering, 8: 85-121.
[13]
Ho, J.W., Fang, C.C. and Huang, Y.S. (2008) "The Determination of Optimal Software Release Times at Different Confidence Levels with Consideration of Learning Effects," Software Testing, Verification and Reliability, 18(4): 221-249. (SCI)
[14]
Hossain, S.A. and Dahiya, R.C. (1993) "Estimating the Parameters of a Non-homogeneous Poisson-Process Model for Software Reliability", IEEE Transactions on Reliability, 42: 604-612.
[15]
Hu, Q.P., Xie, M., Ng, S.H. and Levitin, G. (2007) "Robust recurrent neural network modeling for software fault detection and correction prediction", Reliability Engineering & System Safety, 92: 332-340.
[16]
Huan-Jyh Shyur (2003),"A stochastic software reliability model with imperfect-debugging and change-point",The Journal of Systems and Software, 66,p.135–141
[17]
Huang, C.-Y. (2005) "Performance analysis of software reliability growth models with testing-effort and change-point", Journal of Systems and Software, 76: 181-194.
[18]
Jeske, D.R. and Zhang, X. (2005) "Some successful approaches to software reliability modeling in industry". Journal of Systems and Software, 74: 85-99.
[19]
Jing Zhao, Hong-Wei Liu, Gang Cui and Xiao-Zong Yang (2006),"Software reliability growth model with change-point and environmental function". Journal of Systems and Software, Volume 79, Issue 11, November ,P. 1578-1587
[20]
Kapur, P.K. and Bhalla, V.K. (1992) "Optimal release policies for a flexible software reliability growth model", Reliability Engineering & System Safety, 35: 49-54.
[21]
Karatsas, I., Shreve, S. (1997) Brownian Motion and Stochastic Calculus, 2nd ed. Springer-Verlag: New York.
[22]
Katrina Maxwell, Luk Van Wassenhove, and Soumitra Dutta (1999) "Performance Evaluation of General and Company Specific Models in Software Development Effort Estimation", Management Science , 45: 787-803.
[23]
Kimura, M., Toyota, T. and Yamada, S. (1999) "Economic analysis of software release problems with warranty cost and reliability requirement", Reliability Engineering & System Safety, 66: 49-55.
[24]
Kuo, L., Lee, J.C., Choi, K., and Yang, T.Y. (1997) "Bayes inference for S-shaped software reliability growth models", IEEE Transactions on Reliability, 46: 76-80.
[25]
Kuo, L. and Yang, T.Y. (1996) "Bayesian computation for nonhomogeneous Poisson processes in software reliability", Journal of the American Statistical Association, 91: 763-773.
[26]
Lee, C.H., Kim, Y.T., Park, D.H. (2004) "S-shaped software reliability growth models derived from stochastic differential equations", IIE Transactions, 36: 1193-1199.
[27]
Littlewood, B. (2006) "Comments on ‘Evolutionary neural network modeling for software cumulative failure time prediction", Reliability Engineering & System Safety, 91: 485-486.
[28]
Melo, A.C.V. and Sanchez, A.J. (2008) "Software maintenance project delays prediction using Bayesian networks", Expert Systems with Applications, 34: 908-919.
[29]
Moran, P.A.P. (1969) "Statistical inference with bivariate gamma distribution", Biometrika, 56: 627-634.
[30]
Nalina Suresh, A.N.V. Rao, A.J.G. Babu (1996) "A software reliability growth model", International Journal of Quality & Reliability Management, 13:84-94.
[31]
Ohba, M. (1984a) "Inflexion S-shaped software reliability growth models", in Stochastic Models in Reliability Theory, Osaki, S. and Hatoyama, Y., Eds. Berlin, Germany: Springer-Verlag, 144-162.
[32]
Ohba, M. (1984b) "Software reliability analysis models", IBM Journal of Research and Development, 28: 428-443.
[33]
Özekici, S. and Soyer, R. (2003) "Reliability of software with an operational profile", European Journal of Operational Research, 149: 459-474.
[34]
P.K. Kapur, D.N. Goswami, and A. Bardhan (2007) "A General Software Reliability Growth Model with Testing Effort Dependent Learning Process", International Journal of Modeling and Simulation, 205:4401
[35]
Pham, H. and Zhang, X. (1999) "A software cost model with warranty and risk costs", IEEE Transactions on Computers, 48: 71-75.
[36]
Pham, H. and Zhang, X. (2003) "NHPP software reliability and cost models with testing coverage", European Journal of Operational Research, 145: 445-454.
[37]
Pham, H. (2003) "Software reliability and cost models - Perspectives, comparison, and practice", European Journal of Operational Research, 149: 475-489.
[38]
Shyur, H.-J. (2003) "A stochastic software reliability model with imperfect debugging and change-point", The Journal of Systems and Software, 66: 135-141.
[39]
T. P. Wright. (1936) "Factors Affecting the Cost of Airplanes", Journal of the Aeronautical Sciences, February:3
[40]
Tamura, Y., Yamada, S. (2006) "A flexible stochastic differential equation model in distributed development environment", European Journal of Operational Research, 168: 143-152.
[41]
Tian, L. and Noore, A. (2005) "Evolutionary neural network modeling for software cumulative failure time prediction", Reliability Engineering & System Safety, 87: 45-51.
[42]
William J. Stevenson. (1999) "Production Operations Management", Irwin/McGraw-Hill, 349-358.
[43]
Yamada, M. Kimura, H. Tanaka and S. Osaki. (1994) "Software reliability measurement and assessment with stochastic differential equations", IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E77-A: 109-116.
[44]
Yamada, S., Ohba, M., and Osaki, S.(1983). "S-shaped software reliability modeling for software error detection". IEEE Transactions on Reliability, 32: 475-484.
[45]
Yamada, S., Osaki. S. (1985) "Software reliability growth modeling: Models and applications", IEEE Transactions on Software Engineering, 11: 1431-1437.
[46]
Yamada, S., Tokuno, K. and Osaki, S. (1992) "Imperfect debugging models with fault introduction rate for software reliability assessment", International Journal of Systems Science, 23: 2241-2252.
[47]
Yin, L., Trivedi, K.S. (1999) "Confidence Interval Estimation of NHPP-Based Software Reliability Models", Proceedings of the 10th International Symposium on Software Reliability Engineering, November: 6-11.
[48]
Zhang, X. and Pham, H. (1998) "A software cost model with warranty cost, error removal times and risk costs", IIE Transactions, 30: 1135-1142.
[49]
Zhang, X. and Pham, H. (2006) "Software field failure rate prediction before software deployment", The Journal of Systems and Software, 79: 291-300.
[50]
Zhao, M. (1993) "Change-point problems in software and hardware reliability", Communications in Statistics Theory and Methods, 22: 757-768.
ADDRESS
Science Publishing Group
1 Rockefeller Plaza,
10th and 11th Floors,
New York, NY 10020
U.S.A.
Tel: (001)347-983-5186