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SOFTWARE RELIABILITY BASED ON RENEWAL PROCESS MODELING FOR ERROR OCCURRENCE DUE TO EACH BUG WITH PERIODIC DEBUGGING SCHEDULE

Published online by Cambridge University Press:  02 June 2020

Sudipta Das Open the ORCID record for Sudipta Das [Opens in a new window] ,
Anup Dewanji  and
Subrata Kundu
Sudipta Das
Affiliation:
Computer Science Department, Ramakrishna Mission Vivekananda Educational and Research Institute, Howrah, India E-mail: jusudipta@gmail.com
Anup Dewanji
Affiliation:
Applied Statistics Unit, Indian Statistical Institute, Kolkata, India
Subrata Kundu
Affiliation:
George Washington University, Washington, DC, USA
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Abstract

The process of software testing usually involves the correction of a detected bug immediately upon detection. In this article, in contrast, we discuss continuous time testing of a software with periodic debugging in which bugs are corrected, instead of at the instants of their detection, at some pre-specified time points. Under the assumption of renewal distribution for the time between successive occurrence of a bug, maximum-likelihood estimation of the initial number of bugs in the software is considered, when the renewal distribution belongs to any general parametric family or is arbitrary. The asymptotic properties of the estimated model parameters are also discussed. Finally, we investigate the finite sample properties of the estimators, specially that of the number of initial number of bugs, through simulation.

Keywords

asymptotic distributionnon-parametric estimationparametric estimationperiodic debuggingrenewal processsoftware testing
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 36 , Issue 1 , January 2022 , pp. 87 - 104
Copyright
Copyright © The Author(s), 2020. Published by Cambridge University Press

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References

Bhuyan, P. & Dewanji, A. (2015). Estimation of system reliability for dynamic stress-strength modeling with cumulative stress and strength degradation. Technical report, Applied Statistics Unit, Indian Statistical Institute, Kolkata 700108.Google Scholar
Boland, P.J. & Singh, H. (2003). A birth-process approach to Moranda's geometric software-reliability model. IEEE Transactions On Reliability 52(2): 168–174.10.1109/TR.2003.813166CrossRefGoogle Scholar
Dai, Y.S., Xie, M., & Poh, K.-L. (2005). Modeling and analysis of correlated software failures of multiple types. IEEE Transactions on Reliability 54(1): 100–106.10.1109/TR.2004.841709CrossRefGoogle Scholar
Dalal, S.R. (2003). Software reliability models: A selective survey and new directions. In Handbook of Reliability Engineering. London: Springer, pp. 201–211.CrossRefGoogle Scholar
Das, S., Dewanji, A., & Sengupta, D. (2016). Discrete time software reliability modeling with periodic debugging schedule. Statistical Methodology 33: 147–159.CrossRefGoogle Scholar
Das, S., Dewanji, A., & Chakraborty, A.K. (2016). Software reliability modeling with periodic debugging. IEEE Transactions On Reliability 65(3): 1449–1456.10.1109/TR.2016.2570572CrossRefGoogle Scholar
Dewanji, A., Nayak, T.K. & Sen, P.K. (1995). Estimating the number of components of a system of superimposed renewal processes. Sankhyā: The Indian Journal of Statistics Series A 57: 486–499.Google Scholar
Dewanji, A., Kundu, S., & Nayak, T.K. (2012). Nonparametric estimation of the number of components of a superposition of renewal processes. Journal of Statistical Planning and Inference 142: 2710–2718.10.1016/j.jspi.2012.03.008CrossRefGoogle Scholar
Goel, A.L. & Okumoto, K. (1981). When to stop testing and start using software? In Proceedings of the 1981 ACM Workshop/Symposium on Measurement and Evaluation of Software Quality, pp. 131–138.Google Scholar
Gokhale, S.S., Lyu, M.R., & Trivedi, K.S. (2006). Incorporating fault debugging activities into software reliability models: A simulation approach. IEEE Transactions on Reliability 55(2): 281–292.10.1109/TR.2006.874911CrossRefGoogle Scholar
Hope, A.C.A. (1968). A simplified monte carlo significance test procedure. Journal of the Royal Statistical Society: Series B (Methodological) 30(3): 582–598.Google Scholar
Huang, C.-Y. & Lyu, M.R. (2011). Estimation and analysis of some generalized multiple change-point software reliability models. IEEE Transactions on Reliability 60(2): 498–514.CrossRefGoogle Scholar
Hwang, S. & Pham, H. (2009). Quasi-renewal time-delay fault-removal consideration in software reliability modeling. IEEE Transactions on Systems Man and Cybernetics 39(1): 200–209.10.1109/TSMCA.2008.2007982CrossRefGoogle Scholar
Jain, M. & Maheshwari, S. (2006). Generalized renewal process (GRP) for the analysis of software reliability growth model. Asia-Pacific Journal of Operational Research 23(2): 215–227.CrossRefGoogle Scholar
Jelinski, Z. & Moranda, P. (1972). Software reliability research. In Freiberger, W. (ed.), Statistical Computer Performance Evaluation. Rhode Island: Academic Press, pp. 465–484.CrossRefGoogle Scholar
Kim, T., Lee, K., & Baik, J. (2015). An effective approach to estimating the parameters of software reliability growth models using a real-valued genetic algorithm. Journal of Systems and Software 102: 134–144.CrossRefGoogle Scholar
Lin, Q. & Pham, H. (2017). Nhpp software reliability model considering the uncertainty of operating environments with imperfect debugging and testing coverage. Applied Mathematical Modelling 51: 68–85.Google Scholar
Liu, Y., Li, D., Wang, L., & Hu, Q. (2016). A general modeling and analysis framework for software fault detection and correction process. Software Testing, Verification and Reliability 26(5): 351–365.CrossRefGoogle Scholar
Lyu, M.R. (1996). Handbook of software reliability engineering, vol. 3. CA: IEEE Computer Society Press.Google Scholar
Moranda, P.B. (1975). Prediction of software reliability and its applications. In Proceedings of the Annual Reliability and maintainability Symposium, pp. 327–332.Google Scholar
Musa, J.D. & Okumoto, K. (1984). A logarithmic Poisson execution time model for software reliability measurement. In Proceedings of the 7th International Conference on Software Engineering. New Jersey, USA: IEEE Press.Google Scholar
Nayak, T.K. (1988). A note on estimating the number of errors in a system by recapture sampling. Statistics & Probability Letters 7(3): 191–194.CrossRefGoogle Scholar
Nishio, Y. & Dohi, T. (2003). Determination of the optimal software release time based on proportional hazards software reliability growth models. Journal of Quality in Maintenance Engineering 9(1): 48–65.10.1108/13552510310466873CrossRefGoogle Scholar
Okamura, H. & Dohi, T. (2017). A generalized bivariate modeling framework of fault detection and correction processes. In IEEE 28th International Symposium on Software Reliability Engineering, pp. 35–45.10.1109/ISSRE.2017.22CrossRefGoogle Scholar
Okamura, H., Dohi, T., & Osaki, S. (2013). Software reliability growth models with normal failure time distributions. Reliability Engineering & System Safety 116: 135–141.10.1016/j.ress.2012.02.002CrossRefGoogle Scholar
Pavlov, N., Spasov, G., Rahnev, A., & Kyurkchiev, N. (2018). A new class of gompertz - type software reliability models. International Electronic Journal of Pure and Applied Mathematics 12(1): 43–57.Google Scholar
Peled, D.A. (2013). Software reliability methods. USA: Springer Science & Business Media.Google Scholar
Pham, H. (2007). System software reliability. New Jersey, USA: Springer Science & Business Media.Google Scholar
Sen, P.K. & Singer, J.M. (1993). Large sample methods in statistics an introduction with application. London: Chapman and Hall.Google Scholar
Shyur, H.J. (2003). A stochastic software reliability model with imperfect-debugging and change-point. Journal of Systems and Software 66(2): 135–141.CrossRefGoogle Scholar
Singpurwalla, N.D. & Wilson, S.P. (1994). Software reliability modeling. International Statistical Review 62(3): 289–317.CrossRefGoogle Scholar
Subrahmaniam, V.T., Dewanji, A., & Roy, B.K. (2015). A semiparametric software reliability model for analysis of a bug-database with multiple defect types. Technometrics 57(4): 576–585.10.1080/00401706.2014.947004CrossRefGoogle Scholar
Wang, L., Hu, Q., & Liu, J. (2016). Software reliability growth modeling and analysis with dual fault detection and correction processes. IIE Transactions 48(4): 359–370.10.1080/0740817X.2015.1096432CrossRefGoogle Scholar
Wu, Y.P., Hu, Q.P., Xie, M., & Ng, S.H. (2007). Modeling and analysis of software fault detection and correction process by considering time dependency. IEEE Transactions on Reliability 56(4): 629–642.CrossRefGoogle Scholar
Xie, M., Hu, Q.P., Wu, Y.P., & Ng, S.H. (2007). A study of the modeling and analysis of software fault-detection and fault-correction processes. Quality and Reliability Engineering International 23(4): 459–470.10.1002/qre.827CrossRefGoogle Scholar
Yamada, S. (2014). Software reliability modeling: Fundamentals and applications, vol. 5. Tokyo, Japan: Springer.10.1007/978-4-431-54565-1CrossRefGoogle Scholar
Yang, J., Liu, Y., Xie, M., & Zhao, M. (2016). Modeling and analysis of reliability of multi-release open source software incorporating both fault detection and correction processes. Journal of Systems and Software 115: 102–110.CrossRefGoogle Scholar