A NOTE ON THE LEE–CHANG–PHAM–SONG SOFTWARE RELIABILITY MODEL

TitleA NOTE ON THE LEE–CHANG–PHAM–SONG SOFTWARE RELIABILITY MODEL
Publication TypeJournal Article
Year of Publication2018
AuthorsRAHNEVA OLGA, KISKINOV HRISTO, MALINOVA ANNA, SPASOV GEORGI
JournalNeural, Parallel, and Scientific Computations
Volume26
Issue3
Start Page297
Pagination14
Date Published11/2018
ISSN1061-5369
Keywords41A46
Abstract

In this paper we study the Hausdorff approximation of the shifted Heaviside step function $h_{t_0}(t)$ by sigmoidal function based on the Lee--Chang--Pham--Song cumulative function and find an expression for the error of the best approximation. We give real examples with small on--line data provided by IBM entry software package using the model. The potentiality of the software reliability models is analyzed. Lee--Chang--Pham--Song's idea of including the characteristic $t^{\ast}$ (the time when debugging starts after modifying the code causing syntax errors) in the study of models in debugging theory can be successfully expanded. For instance, for the Goel (1980) software reliability model.

URLhttps://acadsol.eu/npsc/articles/26/3/6.pdf
DOI10.12732/npsc.v26i3.6
Refereed DesignationRefereed
Full Text

REFERENCES

[1] D. H. Lee, I. H. Chang, H. Pham, K. Y. Song, A software reliability model considering the syntax error in uncertainty environments, optimal release time, and sensitivity analysis, Appl. Sci., 8, (2018), 1483.
[2] F. Hausdorff, Set Theory (2 ed.) (Chelsea Publ., New York, (1962 [1957]) Republished by AMS-Chelsea, (2005), ISBN: 978-0-821-83835-8.
[3] M. Ohba, Software reliability analysis models, IBM J. Research and Development, 21, No. 4 (1984).
[4] H. Pham, System Software Reliability, In: Springer Series in Reliability Engineering, Springer-Verlag London Limited (2006).
[5] S. Yamada, Software Reliability Modeling: Fundamentals and Applications, Springer (2014).
[6] S. Yamada, Y. Tamura, OSS Reliability Measurement and Assessment, In: Springer Series in Reliability Engineering (H. Pham, Ed.), Springer International Publishing Switzerland (2016).
[7] N. Pavlov, A. Iliev, A. Rahnev, N. Kyurkchiev, Some software reliability models: Approximation and modeling aspects, LAP LAMBERT Academic Publishing (2018), ISBN: 978-613-9-82805-0.
[8] N. Pavlov, A. Iliev, A. Rahnev, N. Kyurkchiev, Nontrivial Models in Debugging Theory (Part 2), LAP LAMBERT Academic Publishing (2018), ISBN: 978-6139-87794-2.
[9] K. Ohishi, H. Okamura, T. Dohi, Gompertz software reliability model: Estimation algorithm and empirical validation, J. of Systems and Software, 82, No. 3 (2009), 535-543.
[10] D. Satoh, A discrete Gompertz equation and a software reliability growth model, IEICE Trans. Inform. Syst., E83-D, No. 7 (2000), 1508-1513.
[11] D. Satoh, S. Yamada, Discrete equations and software reliability growth models, In: Proc. 12th Int. Symp. on Software Reliab. and Eng., (2001), 176-184.
[12] S. Yamada, A stochastic software reliability growth model with Gompertz curve, Trans. IPSJ, 33, (1992), 964-969. (in Japanese)
[13] P. Oguntunde, A. Adejumo, E. Owoloko, On the flexibility of the transmuted inverse exponential distribution, Proc. of the World Congress on Engineering, July 5-7, 2017, London, U.K., 1, (2017).
[14] W. Shaw, I. Buckley, The alchemy of probability distributions: Beyond GramCharlier expansions and a skew-kurtotic-normal distribution from a rank transmutation map, Research report, (2009).
[15] M. Khan, Transmuted generalized inverted exponential distribution with application to reliability data, Thailand Statistician, 16, No. 1 (2018), 14-25.
[16] A. Abouammd, A. Alshingiti, Reliability estimation of generalized inverted exponential distribution, J. Stat. Comput. Simul., 79, No. 11 (2009), 1301-1315.
[17] I. Ellatal, Transmuted generalized inverted exponential distribution, Econom. Qual. Control, 28, No. 2 (2014), 125-133.
[18] E. P. Virene, Reliability growth and its upper limit, in: Proc. 1968, Annual Symp. on Realib., (1968), 265-270.
[19] 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, No. 11 (2010), 34-43.
[20] 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.
[21] S. Yamada, M. Ohba, S. Osaki, S-shaped reliability growth modeling for software error detection, IEEE Trans, Reliab., R-32, (1983), 475-478.
[22] S. Yamada, S. Osaki, Software reliability growth modeling: Models and Applications, IEEE Transaction on Software Engineering, SE-11, (1985), 1431-1437.
[23] N. Pavlov, G. Spasov, A. Rahnev, N. Kyurkchiev, A new class of Gompertz-type software reliability models, International Electronic Journal of Pure and Applied Mathematics, 12, No. 1 (2018), 43-57.
[24] N. Pavlov, G. Spasov, A. Rahnev, N. Kyurkchiev, Some deterministic reliability growth curves for software error detection: Approximation and modeling aspects, International Journal of Pure and Applied Mathematics, 118, No. 3 (2018), 599611.
[25] N. Pavlov, A. Golev, A. Rahnev, N. Kyurkchiev, A note on the Yamada-exponential software reliability model, International Journal of Pure and Applied Mathematics, 118, No. 4 (2018), 871-882.
[26] N. Pavlov, A. Iliev, A. Rahnev, N. Kyurkchiev, A Note on The ”Mean Value” Software Reliability Model, International Journal of Pure and Applied Mathematics, 118, No. 4 (2018), 949-956.
[27] N. Pavlov, A. Golev, A. Rahnev, N. Kyurkchiev, A note on the generalized inverted exponential software reliability model, International Journal of Advanced Research in Computer and Communication Engineering, 7, No. 3 (2018), 484487.
[28] A. L. Goel, Software reliability models: Assumptions, limitations and applicability, IEEE Trans. Software Eng., SE-11, (1985), 1411-1423.
[29] J. D. Musa, Software Reliability Data, DACS, RADC, New York (1980).
[30] N. Pavlov, A. Iliev, A. Rahnev, N. Kyurkchiev, Transmuted inverse exponential software reliability model, Int. J. of Latest Research in Engineering and Technology, 4, No. 5 (2018), 1-6.
[31] N. Pavlov, A. Iliev, A. Rahnev, N. Kyurkchiev, On the extended Chen’s and Pham’s software software reliability models. Some applications, Int. J. of Pure and Appl. Math., 118, No. 4 (2018), 1053-1067.
[32] N. Pavlov, A. Iliev, A. Rahnev, N. Kyurkchiev, Some deterministic growth curves with applications to software reliability analysis, Int. J. of Pure and Appl. Math., 119, No. 2 (2018), 357-368.
[33] N. Pavlov, A. Iliev, A. Rahnev, N. Kyurkchiev, Investigations of the K-stage Erlangian software reliability growth model, Int. J. of Pure and Appl. Math., 119, No. 3 (2018), 441-449.
[34] N. Pavlov, A. Iliev, A. Rahnev, N. Kyurkchiev, A Note on Ohbas Inflexion Sshaped Software Reliability Growth Model, Collection of scientific works from conference "Mathematics. Informatics. Information Technologies. Application in Education", Pamporovo, Bulgaria, October 10-12, (2018). (to appear)
[35] N. Pavlov, A. Iliev, A. Rahnev, N. Kyurkchiev, Analysis of the Chen’s and Pham’s Software Reliability Models, Cybernetics and Information Technologies, 18, No. 3 (2018), 37-47.
[36] N. Pavlov, A. Iliev, A. Rahnev, N. Kyurkchiev, On Some Nonstandard Software Reliability Models, Dynamic Systems and Applications, 27, No. 4 (2018),757771.
[37] N. Pavlov, A. Iliev, A. Rahnev, N. Kyurkchiev, Application of a new class cumulative lifetime distribution to software reliability analysis, Comm. in Appl. Analysis, 22, No. 4 (2018), 555-565.
[38] V. Kyurkchiev, A. Malinova, O. Rahneva, P. Kyurkchiev, Some Notes on the Extended Burr XII Software Reliability Model, Int. J. of Pure and Appl. Math., 120, No. 1 (2018), 127-136.
[39] V. Kyurkchiev, H. Kiskinov, O. Rahneva, G. Spasov, A Note on the Exponentiated Exponential Poisson Software Reliability Model, Neural, Parallel, and Scientific Computations, 26, No. 3 (2018), 257-267.
[40] N. Kyurkchiev, S. Markov, Sigmoid functions: Some Approximation and Modelling Aspects, LAP LAMBERT Academic Publishing, Saarbrucken (2015), ISBN: 978-3-659-76045-7.
[41] N. Kyurkchiev, A. Iliev, S. Markov, Some techniques for recurrence generating of activation functions, LAP LAMBERT Academic Publishing (2017), ISBN: 978-3-330-33143-3.
[42] N. Pavlov, A. Golev, A. Iliev, A. Rahnev, N. Kyurkchiev, On the KumaraswamyDagum log-logistic sigmoid function with applications to population dynamics, Biomath Communications, 5, No. 1 (2018).
[43] R. Anguelov, N. Kyurkchiev, S. Markov, Some properties of the Blumberg’s hyper-log-logistic curve, BIOMATH, 7, No. 1 (2018).
[44] S. Markov, N. Kyurkchiev, A. Iliev, A. Rahnev, On the approximation of the generalized cut functions of degree p + 1 by smooth hyper-log-logistic function, Dynamic Systems and Applications, 27, No. 4 (2018), 715-728.
[45] S. Markov, A. Iliev, A. Rahnev, N. Kyurkchiev, A note on the Log-logistic and transmuted Log-logistic models. Some applications, Dynamic Systems and Applications, 27, No. 3 (2018), 593-607.
[46] A. Malinova, V. Kyurkchiev, A. Iliev, N. Kyurkchiev, Some new approaches to Kumaraswamy-Lindley cumulative distribution function, Int. J. of Innovative Sci. and Techn., 5 No. 3 (2018), 233-236.
[47] A. Malinova, V. Kyurkchiev, A. Iliev, N. Kyurkchiev, A note on the transmuted Kumaraswamy Quasi Lindley cumulative distribution function, Int. J. for Sci., Res. and Developments, 6 No. 2 (2018), 561-564.
[48] N. Kyurkchiev, A new class activation functions with application in the theory of impulse technics, Journal of Mathematical Sciences and Modelling, 1, No. 1 (2018), 15-20.
[49] S. Markov, N. Kyurkchiev, A. Iliev, A. Rahnev, On the approximation of the cut functions by hyper-log-logistic function, Neural, Parallel and Scientific Computations, 26, No. 2 (2018), 169-182.
[50] N. Kyurkchiev, A. Iliev, Extension of Gompertz-type Equation in Modern Science: 240 Anniversary of the birth of B. Gompertz, LAP LAMBERT Academic Publishing (2018), ISBN: 978-613-9-90569-0.