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A multi-step mathematical model-based predictive strategy for software release timing during testing stage

Year 2024, Volume: 4 Issue: 3, 351 - 369, 30.09.2024
https://doi.org/10.53391/mmnsa.1406374

Abstract

Mathematically precise modeling is important to be established to accurately examine the quantitative relationship between software testing and software reliability. Software testing process is complex since it is concerned with various factors such as test case execution, defect debugging, tester expertise, test case selection, and so forth. For this reason, it is required to be meticulous in formulating the software testing process in a manner which is mathematically concise. The software release life cycle or sequential release timeline, referring to the process related to the development, testing and distribution of a software product comprises several critical stages, and the length of this particular life cycle reveals variations depending on different factors like the type of product, the intended use of it, industry security, general standards and compliance. One consideration software engineers have is related to the release date of the software so that future commitments about the software’s release time can be formulated beforehand. In view of these aspects, a multi-step strategy for predicting software release dates is proposed in the current study along with the following stages: firstly, the proposed technique selects the utmost reliability growth model that very well fits the observed test data halfway through the testing period, and then employs it to forecast the probable date of release. This technique entails approximating the unknown parameters of suitable Software Reliability Growth Models (SRGMs). Finally, the chosen SRGM is used to forecast the release date of the software under test by fitting it to available fault data. The proposed method is straightforward and applied to test on a total of ten actual datasets collected from the literature. The results of the proposed technique reveal that in the majority of the situations, nearly exact approximation of date of release can be made halfway through the testing period. Moreover, the proposed method’s performance is also compared to that of a number of previous strategies present in the literature. The outcomes obtained by our study demonstrate that the proposed strategy may be used to forecast the release date of software in practical situations.

References

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  • [2] Goel, A.L. and Okumoto, K. An analysis of recurrent software errors in a real-time control system. In Proceedings, Proceedings of the 1978 Annual Conference (ACM), pp. 496–501, Washington, DC, USA, (1978, December).
  • [3] Goel, A.L. Software reliability models: assumptions, limitations, and applicability. IEEE Transactions on Software Engineering, SE-11(12), 1411–1423, (1985).
  • [4] Bauer, E., Zhang, X. and Kimber, D.A. Practical System Reliability. John Wiley & Sons: New Jersey, (2009).
  • [5] Huang, C.Y. and Lyu, M.R. Optimal release time for software systems considering cost, testing effort, and test efficiency. IEEE Transactions on Reliability, 54(4), 583–591, (2005).
  • [6] Kapur, P.K., Gupta, D., Gupta, A. and Jha, P.C. Effect of introduction of fault and imperfect debugging on release time. Ratio Mathematica, 18, 62–90, (2008).
  • [7] Singh, Y. and Kumar, P. Determination of software release instant of three-tier client server software system. International Journal of Software Engineering, 1(3), 51–62, (2010).
  • [8] Quadri, S.M.K., Ahmad, N. and Farooq, S.U. Software reliability growth modeling with generalized exponential testing-effort and optimal software release policy. Global Journal of Computer Science and Technology, 11(2), 26-41, (2011).
  • [9] Kapur, P.K., Pham, H., Aggarwal, A.G. and Kaur, G. Two dimensional multi-release software reliability modeling and optimal release planning. IEEE Transactions on Reliability, 61(3), 758–768, (2012).
  • [10] Panwar, P. and Lal, A.K. Predicting total number of failures in a software using NHPP software reliability growth models. In Proceedings, Third International Conference on Soft Computing for Problem Solving (SocProS), pp. 715–727, New Delhi, India, (2014, December).
  • [11] Choudhary, A. and Baghel, A.S. Software reliability prediction using cuckoo search optimization, empirical mode decomposition, and ARIMA model: CS-EEMD-ARIMA based SRGM. International Journal of Open Source Software and Processes, 7(4), 39–54, (2016).
  • [12] Panwar, P. and Kaur, R. Effect of imperfect debugging on prediction of remaining faults in software. In Proceedings, Fifth International Conference on Soft Computing for Problem Solving (SocProS), pp. 175–185, Uttarakhand, India, (2016, December).
  • [13] Shi, Y., Li, M., Arndt, S. and Smidts, C. Metric-based software reliability prediction approach and its application. Empirical Software Engineering, 22, 1579–1633, (2017).
  • [14] Pandey, S. and Kumar, K. Software fault prediction for imbalanced data: A survey on recent developments. Procedia Computer Science, 218, 1815-1824, (2023).
  • [15] Luo, H., Xu, L., He, L., Jiang, L. and Long, T. A novel software reliability growth model based on generalized imperfect debugging NHPP framework. IEEE Access, 11, 71573-71593, (2023).
  • [16] Samal, U., Kushwaha, S. and Kumar, A. A testing-effort based Srgm incorporating imperfect debugging and change point. Reliability: Theory & Applications, 18(1), 86-93, (2023).
  • [17] Pradhan, V., Kumar, A. and Dhar, J. Modeling multi-release open source software reliability growth process with generalized modified weibull distribution. Evolving Software Processes: Trends and Future Directions, 123–133, (2022).
  • [18] Quadri, S.M.K., Ahmad, N. and Peer, M.A. Software optimal release policy and reliability growth modeling. In Proceedings, 2nd National Conference on on Computing for Nation Development (INDIACom), pp. 423–431, New Delhi, India, (2008).
  • [19] Kapur, P.K., Pham, H., Anand, S. and Yadav, K. A unified approach for developing software reliability growth models in the presence of imperfect debugging and error generation. IEEE Transactions on Reliability, 60(1), 331–340, (2011).
  • [20] Huang, C.Y., Lyu, M.R. and Kuo, S.Y. A unified scheme of some nonhomogenous poisson process models for software reliability estimation. IEEE Transactions on Software Engineering, 29(3), 261–269, (2003).
  • [21] Shatnawi, O. Discrete time NHPP models for software reliability growth phenomenon. The International Arab Journal of Information Technology, 6(2), 124-131, (2009).
  • [22] Wood, A. Software reliability growth models. Tandem Technical Report, 96(130056), 900, (1996).
  • [23] Stringfellow, C. and Andrews, A.A. An empirical method for selecting software reliability growth models. Empirical Software Engineering, 7, 319–343, (2002).
  • [24] Andersson, C. A replicated empirical study of a selection method for software reliability growth models. Empirical Software Engineering, 12, 161–182, (2007).
  • [25] Garg, R., Sharma, K., Kumar, R. and Garg, R.K. Performance analysis of software reliability models using matrix method. International Journal of Computer and Information Engineering, 5(2), 113-120, (2010).
  • [26] Sharma, K., Garg, R., Nagpal, C.K. and Garg, R.K. Selection of optimal software reliability growth models using a distance based approach. IEEE Transactions on Reliability, 59(2), 266–276, (2010).
  • [27] Ullah, N., Morisio, M. and Vetrò, A. Selecting the best reliability model to predict residual defects in open source software. Computer, 48(6), 50–58, (2014).
  • [28] Kumar, V., Singh, V.B., Garg, A. and Kumar, G. Selection of optimal software reliability growth models: a fuzzy DEA ranking approach. In Quality, IT and Business Operations, (pp. 347–357). Singapore: Springer, (2018).
  • [29] Li, Q. and Pham, H. A generalized software reliability growth model with consideration of the uncertainty of operating environments. IEEE Access, 7, 84253–84267, (2019).
  • [30] Kumar, V., Saxena, P. and Garg, H. Selection of optimal software reliability growth models using an integrated entropy–Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) approach. Mathematical Methods in the Applied Sciences, 1-21, (2021).
  • [31] Asraful Haque, M. and Ahmad, N. Modified Goel-Okumoto software reliability model considering uncertainty parameter. In Proceedings, Mathematical Modeling, Computational Intelligence Techniques and Renewable Energy (MMCITRE), pp. 369–379. Gandhinagar, India, (2022).
  • [32] Bibyan, R. and Anand, S. Ranking of multi-release software reliability growth model using weighted distance-based approach. Optimization Models in Software Reliability, (pp. 355–373). Singapore, Springer, (2022).
  • [33] Shanmugam, L. and Florence, L. A comparison of parameter best estimation method for software reliability models. International Journal of Software Engineering & Applications, 3(5), 91-102, (2012).
  • [34] Song, K.Y., Chang, I.H. and Lee, S.W. Predictions of MLE and LSE in NHPP Software Reliability Model. Journal of the Chosun Natural Science, 6(2), 111–117, (2013).
  • [35] The MathWorks, Inc., MATLAB 2022 version 9.12.0 (R2022a), Software, Natick, MA, (2022).
  • [36] Yamada, S., Tokuno, K. and Osaki, S. Imperfect debugging models with fault introduction rate for software reliability assessment. International Journal of Systems Science, 23(12), 2241–2252, (1992).
  • [37] Pham, H. Software Reliability. Springer Science & Business Media, Singapore, (2000).
  • [38] Pham, H. System Software Reliability. Springer, London, (2007).
  • [39] Pham, H. and Zhang, X. An NHPP software reliability model and its comparison. International Journal of Reliability, Quality and Safety Engineering, 4(03), 269–282, (1997).
  • [40] Zhang, X., Teng, X. and Pham, H. Considering fault removal efficiency in software reliability assessment. IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans, 33(1), 114–120, (2003).
  • [41] Pham, H., Nordmann, L. and Zhang, Z. A general imperfect-software-debugging model with S-shaped fault-detection rate. IEEE Transactions on Reliability, 48(2), 169–175, (1999).
  • [42] Wood, A. Predicting software reliability. Computer, 29(11), 69–77, (1996).
Year 2024, Volume: 4 Issue: 3, 351 - 369, 30.09.2024
https://doi.org/10.53391/mmnsa.1406374

Abstract

References

  • [1] Musa, J.D. and Okumoto, K. A logarithmic Poisson execution time model for software reliability measurement. In Proceedings, 7th International Conference on Software Engineering, pp. 230–238, Orlando, Florida, (1984, March).
  • [2] Goel, A.L. and Okumoto, K. An analysis of recurrent software errors in a real-time control system. In Proceedings, Proceedings of the 1978 Annual Conference (ACM), pp. 496–501, Washington, DC, USA, (1978, December).
  • [3] Goel, A.L. Software reliability models: assumptions, limitations, and applicability. IEEE Transactions on Software Engineering, SE-11(12), 1411–1423, (1985).
  • [4] Bauer, E., Zhang, X. and Kimber, D.A. Practical System Reliability. John Wiley & Sons: New Jersey, (2009).
  • [5] Huang, C.Y. and Lyu, M.R. Optimal release time for software systems considering cost, testing effort, and test efficiency. IEEE Transactions on Reliability, 54(4), 583–591, (2005).
  • [6] Kapur, P.K., Gupta, D., Gupta, A. and Jha, P.C. Effect of introduction of fault and imperfect debugging on release time. Ratio Mathematica, 18, 62–90, (2008).
  • [7] Singh, Y. and Kumar, P. Determination of software release instant of three-tier client server software system. International Journal of Software Engineering, 1(3), 51–62, (2010).
  • [8] Quadri, S.M.K., Ahmad, N. and Farooq, S.U. Software reliability growth modeling with generalized exponential testing-effort and optimal software release policy. Global Journal of Computer Science and Technology, 11(2), 26-41, (2011).
  • [9] Kapur, P.K., Pham, H., Aggarwal, A.G. and Kaur, G. Two dimensional multi-release software reliability modeling and optimal release planning. IEEE Transactions on Reliability, 61(3), 758–768, (2012).
  • [10] Panwar, P. and Lal, A.K. Predicting total number of failures in a software using NHPP software reliability growth models. In Proceedings, Third International Conference on Soft Computing for Problem Solving (SocProS), pp. 715–727, New Delhi, India, (2014, December).
  • [11] Choudhary, A. and Baghel, A.S. Software reliability prediction using cuckoo search optimization, empirical mode decomposition, and ARIMA model: CS-EEMD-ARIMA based SRGM. International Journal of Open Source Software and Processes, 7(4), 39–54, (2016).
  • [12] Panwar, P. and Kaur, R. Effect of imperfect debugging on prediction of remaining faults in software. In Proceedings, Fifth International Conference on Soft Computing for Problem Solving (SocProS), pp. 175–185, Uttarakhand, India, (2016, December).
  • [13] Shi, Y., Li, M., Arndt, S. and Smidts, C. Metric-based software reliability prediction approach and its application. Empirical Software Engineering, 22, 1579–1633, (2017).
  • [14] Pandey, S. and Kumar, K. Software fault prediction for imbalanced data: A survey on recent developments. Procedia Computer Science, 218, 1815-1824, (2023).
  • [15] Luo, H., Xu, L., He, L., Jiang, L. and Long, T. A novel software reliability growth model based on generalized imperfect debugging NHPP framework. IEEE Access, 11, 71573-71593, (2023).
  • [16] Samal, U., Kushwaha, S. and Kumar, A. A testing-effort based Srgm incorporating imperfect debugging and change point. Reliability: Theory & Applications, 18(1), 86-93, (2023).
  • [17] Pradhan, V., Kumar, A. and Dhar, J. Modeling multi-release open source software reliability growth process with generalized modified weibull distribution. Evolving Software Processes: Trends and Future Directions, 123–133, (2022).
  • [18] Quadri, S.M.K., Ahmad, N. and Peer, M.A. Software optimal release policy and reliability growth modeling. In Proceedings, 2nd National Conference on on Computing for Nation Development (INDIACom), pp. 423–431, New Delhi, India, (2008).
  • [19] Kapur, P.K., Pham, H., Anand, S. and Yadav, K. A unified approach for developing software reliability growth models in the presence of imperfect debugging and error generation. IEEE Transactions on Reliability, 60(1), 331–340, (2011).
  • [20] Huang, C.Y., Lyu, M.R. and Kuo, S.Y. A unified scheme of some nonhomogenous poisson process models for software reliability estimation. IEEE Transactions on Software Engineering, 29(3), 261–269, (2003).
  • [21] Shatnawi, O. Discrete time NHPP models for software reliability growth phenomenon. The International Arab Journal of Information Technology, 6(2), 124-131, (2009).
  • [22] Wood, A. Software reliability growth models. Tandem Technical Report, 96(130056), 900, (1996).
  • [23] Stringfellow, C. and Andrews, A.A. An empirical method for selecting software reliability growth models. Empirical Software Engineering, 7, 319–343, (2002).
  • [24] Andersson, C. A replicated empirical study of a selection method for software reliability growth models. Empirical Software Engineering, 12, 161–182, (2007).
  • [25] Garg, R., Sharma, K., Kumar, R. and Garg, R.K. Performance analysis of software reliability models using matrix method. International Journal of Computer and Information Engineering, 5(2), 113-120, (2010).
  • [26] Sharma, K., Garg, R., Nagpal, C.K. and Garg, R.K. Selection of optimal software reliability growth models using a distance based approach. IEEE Transactions on Reliability, 59(2), 266–276, (2010).
  • [27] Ullah, N., Morisio, M. and Vetrò, A. Selecting the best reliability model to predict residual defects in open source software. Computer, 48(6), 50–58, (2014).
  • [28] Kumar, V., Singh, V.B., Garg, A. and Kumar, G. Selection of optimal software reliability growth models: a fuzzy DEA ranking approach. In Quality, IT and Business Operations, (pp. 347–357). Singapore: Springer, (2018).
  • [29] Li, Q. and Pham, H. A generalized software reliability growth model with consideration of the uncertainty of operating environments. IEEE Access, 7, 84253–84267, (2019).
  • [30] Kumar, V., Saxena, P. and Garg, H. Selection of optimal software reliability growth models using an integrated entropy–Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) approach. Mathematical Methods in the Applied Sciences, 1-21, (2021).
  • [31] Asraful Haque, M. and Ahmad, N. Modified Goel-Okumoto software reliability model considering uncertainty parameter. In Proceedings, Mathematical Modeling, Computational Intelligence Techniques and Renewable Energy (MMCITRE), pp. 369–379. Gandhinagar, India, (2022).
  • [32] Bibyan, R. and Anand, S. Ranking of multi-release software reliability growth model using weighted distance-based approach. Optimization Models in Software Reliability, (pp. 355–373). Singapore, Springer, (2022).
  • [33] Shanmugam, L. and Florence, L. A comparison of parameter best estimation method for software reliability models. International Journal of Software Engineering & Applications, 3(5), 91-102, (2012).
  • [34] Song, K.Y., Chang, I.H. and Lee, S.W. Predictions of MLE and LSE in NHPP Software Reliability Model. Journal of the Chosun Natural Science, 6(2), 111–117, (2013).
  • [35] The MathWorks, Inc., MATLAB 2022 version 9.12.0 (R2022a), Software, Natick, MA, (2022).
  • [36] Yamada, S., Tokuno, K. and Osaki, S. Imperfect debugging models with fault introduction rate for software reliability assessment. International Journal of Systems Science, 23(12), 2241–2252, (1992).
  • [37] Pham, H. Software Reliability. Springer Science & Business Media, Singapore, (2000).
  • [38] Pham, H. System Software Reliability. Springer, London, (2007).
  • [39] Pham, H. and Zhang, X. An NHPP software reliability model and its comparison. International Journal of Reliability, Quality and Safety Engineering, 4(03), 269–282, (1997).
  • [40] Zhang, X., Teng, X. and Pham, H. Considering fault removal efficiency in software reliability assessment. IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans, 33(1), 114–120, (2003).
  • [41] Pham, H., Nordmann, L. and Zhang, Z. A general imperfect-software-debugging model with S-shaped fault-detection rate. IEEE Transactions on Reliability, 48(2), 169–175, (1999).
  • [42] Wood, A. Predicting software reliability. Computer, 29(11), 69–77, (1996).
There are 42 citations in total.

Details

Primary Language English
Subjects Applied Mathematics (Other)
Journal Section Research Articles
Authors

Poonam Panwar 0000-0002-6537-8149

Satish Kumar This is me 0000-0002-6537-8149

Shkauntla Singla This is me 0000-0002-5713-2982

Yeliz Karaca 0000-0001-8725-6719

Publication Date September 30, 2024
Submission Date December 29, 2023
Acceptance Date September 25, 2024
Published in Issue Year 2024 Volume: 4 Issue: 3

Cite

APA Panwar, P., Kumar, S., Singla, S., Karaca, Y. (2024). A multi-step mathematical model-based predictive strategy for software release timing during testing stage. Mathematical Modelling and Numerical Simulation With Applications, 4(3), 351-369. https://doi.org/10.53391/mmnsa.1406374


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