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Open-source Software Reliability Modeling with Stochastic Impulsive Differential Equations

Treść / Zawartość
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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In reality, sudden updates of software, attacks of hackers, influence of the Internet market, etc. can cause a surge in the number of open-source software (OSS) faults (this moment is the time when impulse occurs), which results in impulsive phenomenon. For the existing software reliability models, dynamic process of software fault is considered to be continuous when assessing reliability, but continuity of the process can be disrupted with appearance of random impulses. Thus, to more accurately assess software reliability, we proposed an OSS reliability model with SIDE. In the model, dynamic process of software fault is divided into a continuous and a skipped part, described the continuous part of the process with SDE, and described destruction of the continuity caused by unpredictable random events with random impulses. Finally, the proposed model is verified with two datasets from real OSS project, and the results show that the proposed model is more in line with reality and has better fitting effect than the existing models.
Rocznik
Strony
art. no. 166342
Opis fizyczny
Bibliogr. 30 poz., tab., wykr.
Twórcy
  • School of Mathematics and Statistics, Guizhou University, China
  • School of Mathematics and Statistics, Guizhou University, China
  • School of Data Science, Guizhou Institute of Technology, China
autor
  • School of Mathematics and Statistics, Guizhou University, China
autor
  • School of Data Science, Guizhou Institute of Technology, China
Bibliografia
  • 1. Cai J, Shi Y, Liu B. Inference for A Series System with Dependent Masked Data Under Progressive Interval Censoring. Journal of Applied Statistics, 2017, 44(1): 3-15. https://doi.org/10.1080/02664763.2016.1156658.
  • 2. Calin O. An Informal Introduction to Stochastic Calculus with Applications. World Scientific, 2015: 117-138. https://doi.org/10.1142/9789814678940_0005.
  • 3. Chatterjee S, Chaudhuri B, Bhar C. Optimal Release Time Determination in Intuitionistic Fuzzy Environment Involving Randomized Cost Budget for SDE-based Software Reliability Growth Model. Arabian Journal for Science and Engineering, 2020, 45(4): 2721-2741. https://doi.org/10.1007/s13369-019-04128-7.
  • 4. Chatterjee S, Chaudhuri B, Bhar C. Optimal Release Time Determination Via Fuzzy Goal Programming Approach for SDE-based Software Reliability Growth Model. Soft Computing, 2021, 25(5): 3545-3564. https://doi.org/10.1007/s00500-020-05385-7.
  • 5. Dohi T, Zheng J, Okamura H. Data-driven Software Reliability Evaluation under Incomplete Knowledge on Fault Count Distribution. Quality Engineering, 2020, 32(3): 421-433. https://doi.org/10.1080/08982112.2020.1757705.
  • 6. Erto P, Giorgio M, Lepore A. The Generalized Inflection S-shaped Software Reliability Growth Model. IEEE Transactions on Reliability, 2018, 69(1): 228-244. https://doi.org/10.1109/TR. 2018. 2869466.
  • 7. HE M L, et al. Additive Stochastic Differential Equations Software Reliability Models. Advances in Applied Mathematics, 2022, 11: 6401. https://doi.org/10. 12677/AMM.2022.119677. (In Chinese)
  • 8. Huang Y S, Chiu K C, Chen W M. A Software Reliability Growth Model for Imperfect Debugging. Journal of Systems and Software, 2022, 188: 111267. https://doi.org/10.1016/j.jss.2022.111267.
  • 9. Kelley C T. Iterative Methods for Linear and Nonlinear Equations. Society for Industrial and Applied Mathematics, 1995. ISBN: 0-89871-352-8. https://doi.org/10.1137/1.9781611970944
  • 10. Kyurkchiev N, Markov S. On the Hausdorff Distance between the Heaviside Step Function and Verhulst Logistic Function. Journal of Mathematical Chemistry, 2016, 54(1): 109-119. https://doi.org/10.1007/s10910-015-0552-0.
  • 11. Lang W, Deng S, Shu X B, et al. Existence and Ulam-Hyers-Rassias Stability of Stochastic Differential Equations with Random Impulses. Filomat, 2021, 35(2): 399-407. https://doi.org/10.2298/FIL2102399L.
  • 12. Levy B C. Wiener Process and White Gaussian Noise. Random Processes with Applications to Circuits and Communications. Springer, Cham, 2020: 207-234.https://doi.org/10.1007/978-3-030-22297-0-6.
  • 13. Li L. Software Reliability Growth Fault Correction Model Based on Machine Learning and Neural Network Algorithm. Microprocessors and Microsystems, 2021, 80: 103538. https://doi.org/10.1016/j.micpro.2020.103538.
  • 14. Liu Z, Yang S, Yang M, et al. Software Belief Reliability Growth Model Based on Uncertain Differential Equation. IEEE Transactions on Reliability, 2022. https://doi.org/10.1109/TR.2022.3154770.
  • 15. Nguyen H C, Huynh Q T. New Non‐Homogeneous Poisson Process Software Reliability Model Based on A 3‐arameter S‐shaped Function. IET Software, 2022, 16(2): 214-232. https://doi.org/10.1049/sfw2.12055.
  • 16. Pavlov, N., et al. Some Software Reliability Models: Approximation and Modeling Aspects, LAP LAMBERT Academic Publishing, 2018, ISBN: 978-613-9-82805-0.
  • 17. Pavlov N, Iliev A, Rahnev A, et al. Nonstandard Models in Debugging Theory (Part 2). LAP LAMBERT Academic Publishing, 2018. ISBN: 978-613-9-87794-2.
  • 18. Pavlov N, Iliev A, Rahnev A, et al. Analysis of the Chen’s and Pham’s Software Reliability Models. Cybernetics and Information Technologies, 2018, 18(3): 37-47. https://doi.org/10.2478/cait-2018-0037.
  • 19. Saraf I, Iqbal J, Shrivastava A K, et al. Modelling Reliability Growth for Multi‐version Open Source Software Considering Varied Testing and Debugging Factors. Quality and Reliability Engineering International, 2022, 38(4): 1814-1825. https://doi.org/10.1002/pre.3048.
  • 20. Shen L, Sun J T. Existence and Uniqueness of Solutions for Stochastic Impulsive Differential Equations. Stochastics and Dynamics, 2010, 10(03): 375-383. https://doi.org/10.1142/S0219493710003005.
  • 21. Shen L J, Sun J T. Global Existence of Solutions for Stochastic Impulsive Differential Equations. Acta Mathematica Sinica, English Series, 2011, 27(4): 773-780. https://doi.org/10.1007/s10114-011-8650-9.
  • 22. Sudharson D, Prabha D. A Novel Machine Learning Approach for Software Reliability Growth Modelling with Pareto Distribution Function. Soft Computing, 2019, 23(18): 8379-8387. https://doi.org/10.1007/s00500-019-04047-7.
  • 23. Tamura Y, Yamada S. Optimisation Analysis for Reliability Assessment Based on Stochastic Differential Equation Modelling for Open Source Software. International Journal of Systems Science, 2009, 40(4): 429-438. https: //doi.org/10.1080/00207720802556245.
  • 24. Wang J, Wu Z. Study of The Nonlinear Imperfect Software Debugging Model. Reliability Engineering & System Safety, 2016, 153: 180-192. https://doi.org/10.1016/j.ress.2016.05.003.
  • 25. Wang J. Open Source Software Reliability Model with Nonlinear Fault Detection and Fault Introduction. Journal of Software: Evolution and Process, 2021, 33(12): e2385. https://doi.org/10.1002/smr.2385.
  • 26. Yamada S, Kimura M, Tanaka H, et al. Software Reliability Measurement and Assessment with Stochastic Differential Equations. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 1994, 77(1): 109-116. https://cir.nii.ac.jp/crid/1574231874658900992.
  • 27. Yamada S, Tamura Y. OSS Reliability Measurement and Assessment. Switzerland: Springer International Publishing, 2016. https://doi.org/10.1007/978-3-319-31818-9.
  • 28. Yang J F, Zhao M, Hu W. Web Software Reliability Modeling with Random Impulsive Shocks. Journal of Systems Engineering and Electronics, 2014, 25(2): 349-356. https: //doi.org/10.1109/JSEE.2014.00040.
  • 29. Zhang C, et al. Survey of Software Reliability Growth Model. Journal of Software, 2017, 28(9): 2402-2430. https://doi.org/10.13328/j.cnki.jos.005306. (In Chinese)
  • 30. Zhang Y, Zhao M, Zhang S, et al. An Integrated Approach to Estimate Storage Reliability with Initial Failures Based on E-Bayesian Estimates. Reliability Engineering & System Safety, 2017, 159: 24-36. https://doi.org/10.1016/j.ress.2016.10.024.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-fb88659f-086a-4b15-ba09-7fa3327a798a
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