Document Type : Research Paper

**Authors**

**Abstract**

Nowadays software systems have very important role in a lot of sensitive and critical applications. Sometimes a small error in software could cause financial or even health loss in critical applications. So reliability assurance as a nun-functional requirement, is very vital. One of the key tasks to ensure error-free operation of the software, is to have a quantitative measurement of the software reliability. So far, many models have been proposed for quantification of the software reliability. Each of these models has its advantages and limitations, so selecting the best proper model for various applications is very crucial. In this article, first, we define the basic concepts of reliability, then we classify different approaches of software reliability modeling and finally, based on the analysis of the advantages and limitations, compare different approaches and mention some challenges and issues.

**Keywords**

[1] I. Sommerville, (2010), "Software Engineering", 9th ed., Harlow, England: Addison-Wesley

[2] R. S. Pressman, (2009), "Software Engineering-A Practitioner’s Approach-Required", 7th ed., New York, USA: McGraw-Hill

[3] International Organization for Standarization,(2001), "ISO Standard 826: Software Engineering – Product Quality, parts 1, 2 and 3", Geneve, Switzerland

[4] E. Hull, K. Jackson, and J. Dick,(2005), "Requirements engineering", 2nd ed., London, England: Springer

[5] H. Pham, (2007)، "System software reliability", New York, USA: Springer-Verlag

[6] F. Febrero, C. Calero, M. A. Moraga, (2014), “A systematic mapping study of software reliability modeling,” Information and software technology, Elsevier, vol. 56, no. 8, pp. 839-849.

[7] M. Rahmani, A. Azadmanesh,(2011), "Exploitation of Quantitative Approaches to Software Reliability", Tech. Rep. cst-2011-002, Computer Science, University of Nebraska, Omaha.

[8] Lyu, M. R., M. Xie, (1996), "Handbook of Software Reliability Engineering", 1st ed., New York, USA: McGraw-Hill.

[9] B. Kitchenham,(2004), “Procedures for performing systematic reviews”, Keele, UK, Keele University, vol. 33, pp. 1-26.

[10] S. Keele,(2007), “Guidelines for performing systematic literature reviews in software engineering”, Technical report, EBSE Technical Report EBSE-2007-01, pp. 1-57.

[11] P. Brereton, B. Kitchenham, D. Budgen, M. Turner, M. Khalil,(2007), “Lessons from applying the systematic literature review process within the software engineering domain”, Journal of systems and software, vol. 80, no. 4, pp. 571-583.

[12] B. Kitchenham, P. Brereton, D. Budgen, M. Turner, J. Bailey, S. Linkman,(2009), “literature reviews in software engineering–a systematic literature review”, Information and software technology, vol. 51, no. 1, pp. 7-15.

[13] B. Kitchenham, R. Pretorius, D. Budgen, P. Brereton, M. Turner, M. Niazi, S. Linkman,(2010), “Systematic literature reviews in software engineering–a tertiary study”, Information and Software Technology, vol. 52, no. 8, pp. 792-805.

[14] F. Q. Da Silva, A. L. Santos, S. Soares, A. C. C. França, C. V. Monteiro, F. F. Maciel,(2011), “Six years of systematic literature reviews in software engineering: An updated tertiary study”, Information and Software Technology, vol. 53, no. 9, pp. 899-913.

[15] J. Pan, (2014), “Software Reliability”, http://users.ece.cmu.edu/~koopman/des_s99/sw_reliability/#metrics.

[16] C. V Ramamoorthy and F. B. Bastani, (1982), “Software Reliability - Status and Perspectives”, Softw. Eng. IEEE Trans., vol. SE-8, no. 4, pp. 354–371.

[17] L. Shanmugam and L. Florence, (2012),“An Overview of Software Reliability Models”, in International Journal of Advanced Research in Computer Science and Software Engineering, vol. 2, no. 10, pp. 36–42.

[18] J. G. Shanthikumar,(1983), “Software reliability models: a review”, journal of Microelectronics and Reliability, Elsevier, vol. 23, no. 5, pp. 903–943.

[19] C. A. Asad, M. I. Ullah, and M. J. Ur-Rehman, (2004),“An approach for software reliability model selection”, in Proceedings ofthe 28th Annual International Computer Software and Applications Conference, pp. 534–539.

[20] S. S. Gokhale, P. N. Marinos, and K. S. Trivedi,(1996), “Important milestones in software reliability modeling”, in 8th International Conference on Software Engineering and Knowledge Engineering (SEKE), Nevada, USA, pp. 345–352.

[21] A. L. Goel,(1985), “Software reliability models: Assumptions, limitations, and applicability”, Softw. Eng. IEEE Trans., no. 12, pp. 1411–1423.

[22] X. Li, (2002), “Software reliability measurement: a survey”, MSc. Thesis, Dept. Computer Science & Software Engineering, Concordia University.

[23] Z. KRAJČUŠKOVÁ,(2007), “Software reliability models,” Proceeding of 17th International Conference on Radioelektronika, IEEE, pp.1-4.

[24] H. Pham, M. Pham,(1991), “Software reliability models for critical applications,” Technical report, Idaho National Engineering Laboratory, EG&G-2663.

[25] P.-H. Seong, (2009), "Reliability and Risk Issues in Large Scale Safety-critical Digital Control Systems", Springer, 1st ed., Berlin, Germany, pp. 85–87.

[26] P. C. J. P. K. Kapur, H. Pham, A. Gupta, (2011), "Software Reliability Assessment with OR Applications", 1st ed., London, England: Springer.

[27] A. K. Pandey, N.K. Goyal, (2013), "Early Software Reliability Prediction a Fuzzy Logic Approach", Springer.

[2] R. S. Pressman, (2009), "Software Engineering-A Practitioner’s Approach-Required", 7th ed., New York, USA: McGraw-Hill

[3] International Organization for Standarization,(2001), "ISO Standard 826: Software Engineering – Product Quality, parts 1, 2 and 3", Geneve, Switzerland

[4] E. Hull, K. Jackson, and J. Dick,(2005), "Requirements engineering", 2nd ed., London, England: Springer

[5] H. Pham, (2007)، "System software reliability", New York, USA: Springer-Verlag

[6] F. Febrero, C. Calero, M. A. Moraga, (2014), “A systematic mapping study of software reliability modeling,” Information and software technology, Elsevier, vol. 56, no. 8, pp. 839-849.

[7] M. Rahmani, A. Azadmanesh,(2011), "Exploitation of Quantitative Approaches to Software Reliability", Tech. Rep. cst-2011-002, Computer Science, University of Nebraska, Omaha.

[8] Lyu, M. R., M. Xie, (1996), "Handbook of Software Reliability Engineering", 1st ed., New York, USA: McGraw-Hill.

[9] B. Kitchenham,(2004), “Procedures for performing systematic reviews”, Keele, UK, Keele University, vol. 33, pp. 1-26.

[10] S. Keele,(2007), “Guidelines for performing systematic literature reviews in software engineering”, Technical report, EBSE Technical Report EBSE-2007-01, pp. 1-57.

[11] P. Brereton, B. Kitchenham, D. Budgen, M. Turner, M. Khalil,(2007), “Lessons from applying the systematic literature review process within the software engineering domain”, Journal of systems and software, vol. 80, no. 4, pp. 571-583.

[12] B. Kitchenham, P. Brereton, D. Budgen, M. Turner, J. Bailey, S. Linkman,(2009), “literature reviews in software engineering–a systematic literature review”, Information and software technology, vol. 51, no. 1, pp. 7-15.

[13] B. Kitchenham, R. Pretorius, D. Budgen, P. Brereton, M. Turner, M. Niazi, S. Linkman,(2010), “Systematic literature reviews in software engineering–a tertiary study”, Information and Software Technology, vol. 52, no. 8, pp. 792-805.

[14] F. Q. Da Silva, A. L. Santos, S. Soares, A. C. C. França, C. V. Monteiro, F. F. Maciel,(2011), “Six years of systematic literature reviews in software engineering: An updated tertiary study”, Information and Software Technology, vol. 53, no. 9, pp. 899-913.

[15] J. Pan, (2014), “Software Reliability”, http://users.ece.cmu.edu/~koopman/des_s99/sw_reliability/#metrics.

[16] C. V Ramamoorthy and F. B. Bastani, (1982), “Software Reliability - Status and Perspectives”, Softw. Eng. IEEE Trans., vol. SE-8, no. 4, pp. 354–371.

[17] L. Shanmugam and L. Florence, (2012),“An Overview of Software Reliability Models”, in International Journal of Advanced Research in Computer Science and Software Engineering, vol. 2, no. 10, pp. 36–42.

[18] J. G. Shanthikumar,(1983), “Software reliability models: a review”, journal of Microelectronics and Reliability, Elsevier, vol. 23, no. 5, pp. 903–943.

[19] C. A. Asad, M. I. Ullah, and M. J. Ur-Rehman, (2004),“An approach for software reliability model selection”, in Proceedings ofthe 28th Annual International Computer Software and Applications Conference, pp. 534–539.

[20] S. S. Gokhale, P. N. Marinos, and K. S. Trivedi,(1996), “Important milestones in software reliability modeling”, in 8th International Conference on Software Engineering and Knowledge Engineering (SEKE), Nevada, USA, pp. 345–352.

[21] A. L. Goel,(1985), “Software reliability models: Assumptions, limitations, and applicability”, Softw. Eng. IEEE Trans., no. 12, pp. 1411–1423.

[22] X. Li, (2002), “Software reliability measurement: a survey”, MSc. Thesis, Dept. Computer Science & Software Engineering, Concordia University.

[23] Z. KRAJČUŠKOVÁ,(2007), “Software reliability models,” Proceeding of 17th International Conference on Radioelektronika, IEEE, pp.1-4.

[24] H. Pham, M. Pham,(1991), “Software reliability models for critical applications,” Technical report, Idaho National Engineering Laboratory, EG&G-2663.

[25] P.-H. Seong, (2009), "Reliability and Risk Issues in Large Scale Safety-critical Digital Control Systems", Springer, 1st ed., Berlin, Germany, pp. 85–87.

[26] P. C. J. P. K. Kapur, H. Pham, A. Gupta, (2011), "Software Reliability Assessment with OR Applications", 1st ed., London, England: Springer.

[27] A. K. Pandey, N.K. Goyal, (2013), "Early Software Reliability Prediction a Fuzzy Logic Approach", Springer.

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[30] S. Mohanta, G. Vinod, A. K. Ghosh, and R. Mall,(2010), “An approach for early prediction of software reliability”, ACM SIGSOFT Softw. Eng. Notes, vol. 35, no. 6, pp. 1–9.

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[34] S. S. Gokhale and K. S. Trivedi,(2006), “Analytical models for architecture-based software reliability prediction: A unification framework”, Reliab. IEEE Trans., vol. 55, no. 4, pp. 578–590.

[35] R. C. Cheung, (1980),“A user-oriented software reliability model”, Softw. Eng. IEEE Trans., no. 2, pp. 118–125.

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[39] G.N. Rodrigues, D.S. Rosenblum, S. Uchitel,(2005), “Using scenarios to predict the reliability of concurrent component-based software systems ” ,in Proceedings of the 8th international conference on Fundamental Approaches to Software Engineering, pp. 111-126.

[40] M.G. Thomason, J.A. Whittaker, (1999),“Rare failure-state in a Markov chain model for software reliability” ,in Proceedings of the 10th international symposiom on Software Reliability Engineering, pp. 12-19.

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[29] Q. P. Hu, Y.-S. Dai, M. Xie, and S. H. Ng, (2006),“Early software reliability prediction with extended ANN model”, in Computer Software and Applications Conferenc, COMPSAC’06. 30th Annual International, vol. 2, pp. 234–239.

[30] S. Mohanta, G. Vinod, A. K. Ghosh, and R. Mall,(2010), “An approach for early prediction of software reliability”, ACM SIGSOFT Softw. Eng. Notes, vol. 35, no. 6, pp. 1–9.

[31] C. Smidts, M. Stutzke, and R. W. Stoddard, (1998),“Software reliability modeling: an approach to early reliability prediction”, Reliab. IEEE Trans., vol. 47, no. 3, pp. 268–278.

[32] Rome Laboratory, (1987),“Methodology for Software Reliability Prediction and Assessment”, Tech. Rep. RADC-TR-87-171.

[33] A. Immonen, E. Niemela, (2007),“Survey of reliability and availability prediction methods from the viewpoint of software architecture,” Software & System Modeling, Springer, vol. 7, no. 1, pp. 49-65.

[34] S. S. Gokhale and K. S. Trivedi,(2006), “Analytical models for architecture-based software reliability prediction: A unification framework”, Reliab. IEEE Trans., vol. 55, no. 4, pp. 578–590.

[35] R. C. Cheung, (1980),“A user-oriented software reliability model”, Softw. Eng. IEEE Trans., no. 2, pp. 118–125.

[36] P. Kubat, (1989),“Assessing reliability of modular software”, Oper. Res. Lett., vol. 8, no. 1, pp. 35–41.

[37] B. Littlewood, (1979), “software reliability model for modular program structure”, IEEE Trans. Reliability, vol. 28, no. 3, pp. 241-246.

[38] R.H. Reussner, H.W. Schimidt, I.H. Poernomo, (2003), “Reliability prediction for component-based software architectures” , J.Sysetem Softw., vol. 66, no. 3, pp. 241-252.

[39] G.N. Rodrigues, D.S. Rosenblum, S. Uchitel,(2005), “Using scenarios to predict the reliability of concurrent component-based software systems ” ,in Proceedings of the 8th international conference on Fundamental Approaches to Software Engineering, pp. 111-126.

[40] M.G. Thomason, J.A. Whittaker, (1999),“Rare failure-state in a Markov chain model for software reliability” ,in Proceedings of the 10th international symposiom on Software Reliability Engineering, pp. 12-19.

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[42] M. L. Shooman,(1976), “Structural models for software reliability prediction”,in Proceedings of the 2nd international conference on Software engineering, pp. 268–280.

[43] S. Krishnamurthy and A. P. Mathur, (1997),“On the estimation of reliability of a software system using reliabilities of its components”, in Proceedings of 8th International Symposium on Software Reliability Engineering, pp. 146–155.

[44] S. M. Yacoub, B. Cukic, and H. H. Ammar,(1999), “Scenario-based reliability analysis of component-based software”, in Proceedings of 10th International Symposium on Software Reliability Engineering, pp. 22–31.

[45] K. Goševa-Popstojanova and K. S. Trivedi, (2001), “Architecture-based approach to reliability assessment of software systems”, Journal of Performance Evaluation, Elsevier, vol. 45, no. 2, pp. 179–204.

[46] M. Xie and C. Wohlin,(1995), “An additive reliability model for the analysis of modular software failure data”, in Proceedings of 6th International Symposium on Software Reliability Engineering, pp. 188–194.

[47] W. W. Everett,(1999), “Software component reliability analysis”, in Proceedings of 3rd IEEE Symposium on Application-Specific Systems and Software Engineering and Technology, pp. 204–211.

[48] M. Klein, et al., (1999),“Attribute-based atchitecture styles”, in Proceedings First Working IFIP Conference on Software Architecture, pp. 225-243.

[49] L. Chung, B. Nixon, E. Yu, J. Mylopoulos,(2000), "Non-functional Requirements in Software Engineering". Kluwer Boston, Dordrecht 439.

[50] R. Kazman, G. Abowd, L. Bass, P. Clements, (1996),“Scenario-based analysis o software architecture ” , IEEE Softw., vol. 13, no. 6, pp. 47-55.

[51] N. Lassing, D. Rijsenbrij, H. van Vilet, (1999),“On software architecture analysis of flexibility, complexity of changes: size isn't everything”, in Proceedings of the 2nd Nordic Software Architecture Workshop.

[52] G. Molter,(1999), “Integrating SAAM in Domain-centric and Reuse-based development process”, in Proceedings of the 2nd Nordic Software Architecture Workshop.

[53] R. Kazman, et al., (1999),“The architecture tradeoff analysis method”, in Proceedings of the 4th IEEE International Conference on Engineering of Complex Computer Systems, pp. 68-78.

[54] S. S. Gokhale and K. S. Trivedi, (1999),“A time/structure based software reliability model”, Annals of Software Engineering, vol. 8, no. 1–4, pp. 85–121.

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[57] H. Pham, (2003),“Software reliability and cost models: Perspectives, comparison, and practice”, Eur. J. Oper. Res., vol. 149, no. 3, pp. 475–489.

[58] H. Pham and X. Zhang,(1997), “An NHPP software reliability model and its comparison”, Int. J. Reliab. Qual. Saf. Eng., vol. 4, no. 03, pp. 269–282.

[59] Z. Jelinski and P. Moranda, (1972), “Software reliability research”, Statistical Computer Performance Evaluation, pp. 465–484.

[60] A. L. Goel and K. Okumoto, (2009),“Time-Dependent Error-Detection Rate Model for Software Reliability and Other Performance Measures”, in IEEE Transactions on Reliability, pp. 206 – 211.

[61] S. Yamada, (2014), "Software reliability modeling Fundamental and Applications", Japan, Springer.

[62] Jinxia An, Jihong Zhu, (2010),“ Software reliability modeling with integrated test coverage,” in Proceeding of Fourth International Conference on Secure Software Integration and Reliability Improvement, IEEE, pp. 106-112.

]63[ دگ یسی زاده ه حگ هانگیری، ت 1386 ، "مدلسازی دماری قا لیت ایمینان نرم افزار"، ر اهلی ن رانس ی المللی تحقیق در ملیاک

ایران، زیره یم، ایرانگ

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[67] M. H. Halstead, (1977),“Elements of software science”, Elsevier, New York, USA.

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[69] S. N. Weiss and E. J. Weyuker, (1988),“An extended domain-based model of software reliability”, Softw. Eng. IEEE Trans., vol. 14, no. 10, pp. 1512–1524.

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[56] H. A. Stiber, (2007), “A family of software reliability growth models”, in Proceeding of 31th Annual International Computer Software and Applications Conference, IEEE, vol. 2, pp. 217-224.

[57] H. Pham, (2003),“Software reliability and cost models: Perspectives, comparison, and practice”, Eur. J. Oper. Res., vol. 149, no. 3, pp. 475–489.

[58] H. Pham and X. Zhang,(1997), “An NHPP software reliability model and its comparison”, Int. J. Reliab. Qual. Saf. Eng., vol. 4, no. 03, pp. 269–282.

[59] Z. Jelinski and P. Moranda, (1972), “Software reliability research”, Statistical Computer Performance Evaluation, pp. 465–484.

[60] A. L. Goel and K. Okumoto, (2009),“Time-Dependent Error-Detection Rate Model for Software Reliability and Other Performance Measures”, in IEEE Transactions on Reliability, pp. 206 – 211.

[61] S. Yamada, (2014), "Software reliability modeling Fundamental and Applications", Japan, Springer.

[62] Jinxia An, Jihong Zhu, (2010),“ Software reliability modeling with integrated test coverage,” in Proceeding of Fourth International Conference on Secure Software Integration and Reliability Improvement, IEEE, pp. 106-112.

]63[ دگ یسی زاده ه حگ هانگیری، ت 1386 ، "مدلسازی دماری قا لیت ایمینان نرم افزار"، ر اهلی ن رانس ی المللی تحقیق در ملیاک

ایران، زیره یم، ایرانگ

[64] T. A. Thayer, G. R. Craig, L. E. Frey, W. L. Hetrick, and M. Lipow, (1976), “Software reliability study”, Tech. Rep. ADA030798.

[65] S. Bologna and W. Ehrenberger, (1978),“Applicability of statistical models for reactor safety software verification”, ENEA Internal report: ENEA RT 47/78, Roma, Italy.

[66] J. R. Brown and M. Lipow, (1975),“Testing for software reliability”, in ACM SIGPLAN Notices, vol. 10, no. 6, pp. 518–527.

[67] M. H. Halstead, (1977),“Elements of software science”, Elsevier, New York, USA.

[68] E. Nelson, (1978), “Estimating software reliability from test data”, Microelectron. Reliab., vol. 17, no. 1, pp. 67–73.

[69] S. N. Weiss and E. J. Weyuker, (1988),“An extended domain-based model of software reliability”, Softw. Eng. IEEE Trans., vol. 14, no. 10, pp. 1512–1524.

[70] F. Grigorjev, N. Lascano, and J. L. Staude, (2003),“A Fault Seeding Experience”, in Proceedings of the 4th Argentine Symposium on Software Engineering (ASSE), Buenos Aires, Argentina.

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June 2017

Pages 285-313

**Receive Date:**01 May 2015**Revise Date:**23 October 2015**Accept Date:**14 December 2015