Some Transmuted Software Reliability Models

Nikolay Pavlov; Anton Iliev; Asen Rahnev; Nikolay Kyurkchiev

doi:10.33187/jmsm.434277

EN

Some Transmuted Software Reliability Models

Abstract

The Hausdorff approximation of the shifted Heaviside function $h_{t_0}(t)$ by general transmuted family of cumulative distribution functions is studied and a value for the error of the best approximation is derived in this paper. The outcomes of numerical examples confirm theoretical conclusions and they are derived by the help of CAS Mathematica. Real data set which is proposed by Musa in [4] using general transmuted exponential software reliability model is examined.

Keywords

Hausdorff approximation,General transmuted family,Lower and upper bounds,Shifted Heaviside function $h_{t_0}(t)$

References

[1] J. D. Musa, A. Ianino, K. Okumoto, Software Reliability: Measurement, Prediction, Applications, McGraw–Hill, 1987.
[2] E. A. Owoloko, P. E. Oguntunde, A. O. Adejumo, Performance rating of the transmuted exponential distribution: An analytical approach, Springer Plus, 4 (2015), 8–18.
[3] M. Rahman, B. Al–Zahrani, M. Shahbaz, A general transmuted family of distribution, Pak. J. Stat. Oper. Res., 14 (2) (2018), 451–469.
[4] W. T. Shaw, I. R. Buckley, The alchemy of probability distributions: beyond Gram–Charlier expansions, and skew–kurtotic–normal distribution from a rank transmutation map, UCL discovery repository, (2007).
[5] B. Sendov, Hausdorff Approximations, Boston, Kluwer, 1990.
[6] M. Ohba, Software reliability analysis models, IBM J. Research and Development, 21 (4) (1984).
[7] H. Pham, System Software Reliability, In: Springer Series in Reliability Engineering, London, Springer–Verlag, 2006.
[8] H. Pham, A new software reliability model with vtub–shaped fault–detection rate and the uncertainty of operating environments, Optimization, 63 (10) (2014), 1481–1490.
[9] K. Song, I. Chang, H. Pham, An NHPP Software Reliability Model with S-Shaped Growth Curve Subject to Random Operating Environments and Optimal Release Time, Appl. Sci., 7 (12) (2017).
[10] C. Stringfellow, A. A. Andrews, An empirical method for selecting software reliability growth models, Emp. Softw. Eng., 7 (2012), 319–343.

[11] S. Yamada, Software Reliability Modeling: Fundamentals and Applications, Japan, Springer, 2014.
[12] S. Yamada, Y. Tamura, OSS Reliability Measurement and Assessment, In: Springer Series in Reliability Engineering (H. Pham, Ed.), Springer International Publishing Switzerland, 2016.
[13] I. H. Chang, H. Pham, S. W. Lee, K. Y. Song, A testing coverage software reliability model with the uncertainty of operation environments, International Journal of Systems Science: Operations and Logistics, 1 (4) (2014), 220–227.
[14] K. Y. Song, I. H. Chang, H. Pham, A three–parameter fault–detection software reliability model with the uncertainty of operating environments, Journal of Syst. Sci. Syst. Eng., 26 (2017), 121–132.
[15] D.R. Jeske, X. Zhang, Some successful approaches to software reliability modeling in industry, J. Syst. Softw., 74 (2005), 85–99.
[16] K. Song, H. Pham, A Software Reliability Model with a Weibull Fault Detection Rate Function Subject to Operating Environments, Appl. Sci., 7 (2017), 16 pp.
[17] K. Y. Song, I. H. Chang, H. Pham, Optimal release time and sensitivity analysis using a new NHPP software reliability model with probability of fault removal subject to operating environments, Appl. Sci., 8 (5) (2018), pp. 26.
[18] K. Ohishi, H. Okamura, T. Dohi, Gompertz software reliability model: Estimation algorithm and empirical validation, J. of Systems and Software, 82 (3) (2009), 535–543.
[19] D. Satoh, A discrete Gompertz equation and a software reliability growth model, IEICE Trans. Inform. Syst., E83-D (7) (2000), 1508–1513.
[20] D. Satoh, S. Yamada, Discrete equations and software reliability growth models, in: Proc. 12th Int. Symp. on Software Reliab. and Eng., (2001), 176–184.
[21] S. Yamada, A stochastic software reliability growth model with Gompertz curve, Trans. IPSJ, 33 (1992), 964–969. (in Japanese)
[22] P. Oguntunde, A. Adejumo, E. Owoloko, On the flexibility of the transmuted inverse exponential distribution, Proc. of theWorld Congress on Engineering, July 5–7, 2017, London, 1, 2017.
[23] M. Khan, Transmuted generalized inverted exponential distribution with application to reliability data, Thailand Statistician, 16 (1) (2018), 14–25.
[24] A. Abouammd, A. Alshingiti, Reliability estimation of generalized inverted exponential distribution, J. Stat. Comput. Simul., 79 (11) (2009), 1301–1315.
[25] I. Ellatal, Transmuted generalized inverted exponential distribution, Econom. Qual. Control, 28 (2) (2014), 125–133.
[26] E. P. Virene, Reliability growth and its upper limit, in: Proc. 1968, Annual Symp. on Realib., (1968), 265–270.
[27] S. Rafi, S. Akthar, Software Reliability Growth Model with Gompertz TEF and Optimal Release Time Determination by Improving the Test Efficiency, Int. J. of Comput. Applications, 7 (11) (2010), 34–43.
[28] F. Serdio, E. Lughofer, K. Pichler, T. Buchegger, H. Efendic, Residua–based fault detection using soft computing techniques for condition monitoring at rolling mills, Information Sciences, 259 (2014), 304–320.
[29] S. Yamada, M. Ohba, S. Osaki, S–shaped reliability growth modeling for software error detection, IEEE Trans, Reliab. R–32 (1983), 475–478.
[30] S. Yamada, S. Osaki, Software reliability growth modeling: Models and Applications, IEEE Transaction on Software Engineering, SE–11 (1985), 1431–1437.
[31] A. L. Goel, Software reliability models: Assumptions, limitations and applicability, IEEE Trans. Software Eng., SE–11 (1985), 1411–1423.
[32] J. D. Musa, Software Reliability Data, DACS, RADC, New York, 1980.
[33] Z. Chen, A new two–parameter lifetime distribution with bathtub shape or increasing failure rate function, Stat. and Prob. Letters, 49 (2) (2000), 155–161.
[34] M. Xie, Y. Tang, T. Goh, A modified Weibull extension with bathtub–shaped failure rate function, Reliability Eng. and System Safety, 76 (3) (2002), 279–285.
[35] M. Khan, A. Sharma, Generalized order statistics from Chen distribution and its characterization, J. of Stat. Appl. and Prob., 5 (1) (2016), 123–128.
[36] S. Dey, D. Kumar, P. Ramos, F. Louzada, Exponentiated Chen distribution: Properties and Estimations, Comm. in Stat.–Simulation and Computation, (2017), 1–22.
[37] Y. Chaubey, R. Zhang, An extension of Chen’s family of survival distributions with bathtub shape or increasing hazard rate function, Comm. in Stat.–Theory and Methods, 44 (19) (2015), 4049–4069.
[38] A. Pandey, N. Goyal, Early Software Reliability Prediction. A Fuzzy Logic Approach, In: Studies in Fuzziness and Soft Computing (J. Kacprzyk, Ed.), 303, London, Springer, 2013.
[39] N. D. Singpurwalla, S. P. Wilson, Statistical Methods in Software Engineering. Reliability and Risk, In: Springer Series in Statistics (P. Bickel, Adv.), New York, Springer, 1999.
[40] M. Bisi, N. Goyal, Artificial Neural Network for Software Reliability Prediction, In: Performability Engineering Series (K. Misra and J. Andrews, Eds.), New Jersey, John Wiley & Sons, Inc., 2017.
[41] P. K. Kapur, H. Pham, A. Gupta, P. C. Jha, Software Reliability Assessment with OR Applications, In: Springer Series in Reliability Engineering, London, Springer-Verlag, 2011.
[42] P. Karup, R. Garg, S. Kumar, it Contributions to Hardware and Software Reliability, London, World Scientific, 1999.
[43] M. Lyu (Ed. in Chief), Handbook of Software Reliability Engineering, IEEE Computer Society Press, Los Alamitos, The McGraw-Hill Companies, 1996.
[44] Q. Li, H. Pham, NHPP software reliability model considering the uncertainty of operating environments with imperfect debugging and testing coverage, Applied Mathematical Modelling, 51 (2017), 68-85.
[45] J. Wang, An Imperfect Software Debugging Model Considering Irregular Fluctuation of Fault Introduction Rate, Quality Engineering, 29 (2017), 377–394.
[46] Q. Li, H. Pham, A testing-coverage software reliability model considering fault removal efficiency and error generation, PLoS ONE, 12 (7) (2017).
[47] V. Ivanov, A. Reznik, G. Succi, Comparing the reliability of software systems: A case study on mobile operating systems, Information Sciences, 423 (2018), 398–411.

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Nikolay Pavlov This is me
Bulgaria

Anton Iliev This is me
Bulgaria

Asen Rahnev This is me
Bulgaria

Nikolay Kyurkchiev
Bulgaria

Publication Date

April 20, 2019

Submission Date

June 17, 2018

Acceptance Date

January 15, 2019

Published in Issue

Year 2019 Volume: 2 Number: 1

DOI

https://doi.org/10.33187/jmsm.434277

IZ

https://izlik.org/JA63JU33SM

APA

Pavlov, N., Iliev, A., Rahnev, A., & Kyurkchiev, N. (2019). Some Transmuted Software Reliability Models. Journal of Mathematical Sciences and Modelling, 2(1), 64-70. https://doi.org/10.33187/jmsm.434277

AMA

1.Pavlov N, Iliev A, Rahnev A, Kyurkchiev N. Some Transmuted Software Reliability Models. Journal of Mathematical Sciences and Modelling. 2019;2(1):64-70. doi:10.33187/jmsm.434277

Chicago

Pavlov, Nikolay, Anton Iliev, Asen Rahnev, and Nikolay Kyurkchiev. 2019. “Some Transmuted Software Reliability Models”. Journal of Mathematical Sciences and Modelling 2 (1): 64-70. https://doi.org/10.33187/jmsm.434277.

EndNote

Pavlov N, Iliev A, Rahnev A, Kyurkchiev N (April 1, 2019) Some Transmuted Software Reliability Models. Journal of Mathematical Sciences and Modelling 2 1 64–70.

IEEE

[1]N. Pavlov, A. Iliev, A. Rahnev, and N. Kyurkchiev, “Some Transmuted Software Reliability Models”, Journal of Mathematical Sciences and Modelling, vol. 2, no. 1, pp. 64–70, Apr. 2019, doi: 10.33187/jmsm.434277.

ISNAD

Pavlov, Nikolay - Iliev, Anton - Rahnev, Asen - Kyurkchiev, Nikolay. “Some Transmuted Software Reliability Models”. Journal of Mathematical Sciences and Modelling 2/1 (April 1, 2019): 64-70. https://doi.org/10.33187/jmsm.434277.

JAMA

1.Pavlov N, Iliev A, Rahnev A, Kyurkchiev N. Some Transmuted Software Reliability Models. Journal of Mathematical Sciences and Modelling. 2019;2:64–70.

MLA

Pavlov, Nikolay, et al. “Some Transmuted Software Reliability Models”. Journal of Mathematical Sciences and Modelling, vol. 2, no. 1, Apr. 2019, pp. 64-70, doi:10.33187/jmsm.434277.

Vancouver

1.Nikolay Pavlov, Anton Iliev, Asen Rahnev, Nikolay Kyurkchiev. Some Transmuted Software Reliability Models. Journal of Mathematical Sciences and Modelling. 2019 Apr. 1;2(1):64-70. doi:10.33187/jmsm.434277