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A generalized prediction model for improving software reliability using time-series modelling


The primary goal of any prediction model is an accurate estimation. Software reliability is one of the software organization's major research priorities. One of the quantitative indicators of software quality is software reliability. The Software Reliability Model is used to assess the reliability at various stages of testing. The purpose of this work is to investigate the software's dependability using time-series modeling, which is the most efficient tool for evaluating its predictive power. A fault prediction model based on categorizing faults for measuring software reliability known as Seasonal-ARIMA (S-ARIMA) is proposed in this work. The significant attribute for complex software applications is to ensure software reliability and fault tolerance. However, these attributes would inculcate additional overheads such as added costs, implementation delay, and the representation of software solution providers. Therefore, the corporation needs to ensure the reliability of the software before delivering it to the clients. Finding the mistake with a decent degree of precision at the right time aims to limit the consequences. We have analyzed and evaluated three real-time data sets to measure software reliability by the proposed prediction model for software reliability. Based on the results of these datasets, the proposed S-ARIMA model has achieved high reliability and improved accuracy when compared with the ARIMA model in terms of different parameters like mean square error (\(MSE\)), Relative Prediction Accuracy Improvement \(\left( { RPAI_{MSE} } \right)\), and Akanke's Information Criteria (\(AIC\)).

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  1. Alweshah M, Ahmed W, Aldabbas H (2015) Evolution of software reliability growth models: a comparison of auto-regression and genetic programming models. Int J Comput Appl 125(3):20–25

    Google Scholar 

  2. Amin A, Grunske L, Colman A (2013) An approach to software reliability prediction based on time series modeling. J Syst Softw 86(7):1923–1932

    Article  Google Scholar 

  3. Chatterjee S, Nigam S, Singh JB, Upadhyaya LN (2012) Software fault prediction using Nonlinear Autoregressive with Exogenous Inputs (NARX) network. Appl Intell 37(1):121–129

    Article  Google Scholar 

  4. Choraś M, Kozik R, Pawlicki M, Hołubowicz W, Franch X (2019) Software development metrics prediction using time series methods. In: IFIP International Conference on Computer Information Systems and Industrial Management (pp. 311–323). Springer, Cham

  5. Davies R, Coole T, Osipyw D (2014) The application of time series modelling and Monte Carlo simulation: forecasting volatile inventory requirements. Appl Math 05(08):1152

    Article  Google Scholar 

  6. Debusschere V, Bacha S (2012) Hourly server workload forecasting up to 168 hours ahead using seasonal ARIMA model. In: 2012 IEEE international conference on industrial technology (pp. 1127–1131). IEEE

  7. Fan Q, Fan H (2015) Reliability analysis and failure prediction of construction equipment with time series models. J Adv Manag Sci 3(3):203–210

    Article  Google Scholar 

  8. Gupta A, Mohan BR, Sharma S, Agarwal R, Kavya K (2013) Prediction of software anomalies using time series analysis—a recent study. Int J Adv Comput Theory Eng 2(3):101–108

    Google Scholar 

  9. Hossain SA, Dahiya RC (1993) Estimating the parameters of a non-homogeneous Poisson-process model for software reliability. IEEE Trans Reliab 42(4):604–612

    Article  Google Scholar 

  10. Huang CY, Lyu MR (2011) Estimation and analysis of some generalized multiple change-point software reliability models. IEEE Trans Reliab 60(2):498–514

    Article  Google Scholar 

  11. Jain K, Agarwal A, Kumar A (2021) A novel data prediction technique based on correlation for data reduction in sensor networks. In: Proceedings of international conference on artificial intelligence and applications (pp. 595–606). Springer, Singapore

  12. Jeske DR, Pham H (2001) On the maximum likelihood estimates for the Goel-Okumoto software reliability model. Am Stat 55(3):219–222

    MathSciNet  Article  Google Scholar 

  13. Kapur PK, Pham H, Gupta A, Jha PC (2011) Software reliability assessment with OR applications. Springer, London, p 364

    Book  Google Scholar 

  14. Kim YG, Lee SK, Jang SB (2011) Variability management for software product-line architecture development. Int J Software Eng Knowl Eng 21(07):931–956

    Article  Google Scholar 

  15. Kumar P, Singh SK, Choudhary SD (2021) Reliability prediction analysis of aspect-oriented application using soft computing techniques. Mater Today Proc 45:2660–2665

    Article  Google Scholar 

  16. Kumaresan K, Ganeshkumar P (2020) Software reliability prediction model with realistic assumption using time series (S) ARIMA model. J Ambient Intell Humaniz Comput 11(11):5561–5568

    Article  Google Scholar 

  17. Muss JD, Iannino A, Okumoto K (1987) Software reliability: measurement, prediction, application

  18. Park J, Baik J (2015) Improving software reliability prediction through multi-criteria based dynamic model selection and combination. J Syst Softw 101:236–244

    Article  Google Scholar 

  19. Pati J, Shukla KK (2015) A hybrid technique for software reliability prediction. In: Proceedings of the 8th India Software Engineering Conference (pp. 139–146)

  20. Raghuvanshi KK, Agarwal A, Jain K, Singh VB (2021) A time-variant fault detection software reliability model. SN Appl Sci 3(1):1–10

    Article  Google Scholar 

  21. Sahu K, Srivastava RK (2019) Revisiting software reliability. Data Management, Analytics and Innovation, 221–235

  22. Sheta A, Rine D (2006) Modeling incremental faults of software testing process using AR models. In: the Proceeding of 4th International Multi-Conferences on Computer Science and Information Technology (CSIT 2006), Amman, Jordan (Vol. 3)

  23. Sinha S, Goyal NK, Mall R (2019). v. Int J Syst Assur Eng Manag, 10(4):453–474

  24. Sudharson D, Prabha D (2019) A novel machine learning approach for software reliability growth modelling with Pareto distribution function. Soft Comput 23(18):8379–8387

    Article  Google Scholar 

  25. Tohma Y, Tokunaga K, Nagase S, Murata Y (1989) Structural approach to the estimation of the number of residual software faults based on the hypergeometric distribution. IEEE Trans Software Eng 15(3):345–355

    Article  Google Scholar 

  26. Ulrich TA, Boring RL, Lew R (2019) On the use of microworlds for an error seeding method to support human error analysis. In: 2019 Resilience Week (RWS) (Vol. 1, pp. 242–246). IEEE

  27. van Driel WD, Bikker JW, Tijink M, Di Bucchianico A (2020) Software reliability for agile testing. Mathematics 8(5):791

    Article  Google Scholar 

  28. Van Pul M (1992) Simulations on the Jelinski-Moranda model of software reliability; application of some parametric bootstrap methods. Stat Comput 2(3):121–136

    Article  Google Scholar 

  29. Wiper MP, Palacios AP, Marín JM (2012) Bayesian software reliability prediction using software metrics information. Qual Tech Quant Manag 9(1):35–44

    Article  Google Scholar 

  30. Yamada S, Ohba M, Osaki S (1984) S-shaped software reliability growth models and their applications. IEEE Trans Reliab 33(4):289–292

    Article  Google Scholar 

  31. Zhang GP (2003) Time series forecasting using a hybrid ARIMA and neural network model. Neurocomputing 50:159–175

    Article  Google Scholar 

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Correspondence to Khushboo Jain.

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Raghuvanshi, K.K., Agarwal, A., Jain, K. et al. A generalized prediction model for improving software reliability using time-series modelling. Int J Syst Assur Eng Manag (2021).

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  • Akanke's information criteria
  • Fault detection
  • Failure prediction
  • Mean square error
  • Relative prediction accuracy improvement
  • Software reliability
  • Seasonal-ARIMA method
  • Time series analysis