ON THE EXTENDED CHEN'S AND PHAM'S SOFTWARE RELIABILITY MODELS. SOME APPLICATIONS

The Hausdorff approximation of the impulse function σ∗∗(t) by sigmoidal functions based on the extended Chen’s and Pham’s cumulative functions are studied and an expression for the error of the best approximation is found. The received results are of independent significance in the study of issues related to neural networks and impulse technics. Using programming environment Mathematica we give results of many numerical examples which confirm the theory presented here. We give also real examples with data provided in [4] using extended Chen’s software reliability model and extended Pham’s deterministic software reliability model. Dataset included [5] Year 2000 compatibility modifications, operating system upgrade, and signaling message processing. Some direct comparisons are made. AMS Subject Classification: 41A46

[1]  Tadashi Dohi,et al.  Gompertz software reliability model: Estimation algorithm and empirical validation , 2009, J. Syst. Softw..

[2]  William T. Shaw,et al.  The alchemy of probability distributions: beyond Gram-Charlier expansions, and a skew-kurtotic-normal distribution from a rank transmutation map , 2009, 0901.0434.

[3]  Neeraj Kumar Goyal,et al.  Early Software Reliability Prediction - A Fuzzy Logic Approach , 2013, Studies in Fuzziness and Soft Computing.

[4]  Namig J. Guliyev,et al.  A Single Hidden Layer Feedforward Network with Only One Neuron in the Hidden Layer Can Approximate Any Univariate Function , 2015, Neural Computation.

[5]  Shigeru Yamada.  A stochastic software reliability growth model with Gompertz curve (abstract) , 1992 .

[6]  Shaheda Akthar,et al.  Software Reliability Growth Model with Gompertz TEF and Optimal Release Time Determination by Improving the Test Efficiency , 2010 .

[7]  Shunji Osaki,et al.  Software Reliability Growth Modeling: Models and Applications , 1985, IEEE Transactions on Software Engineering.

[8]  Gianluca Vinti,et al.  Pointwise and uniform approximation by multivariate neural network operators of the max-product type , 2016, Neural Networks.

[9]  Nikolay Pavlov,et al.  A NOTE ON THE YAMADA--EXPONENTIAL SOFTWARE RELIABILITY MODEL , 2018 .

[10]  Gianluca Vinti,et al.  Convergence for a family of neural network operators in Orlicz spaces , 2017 .

[11]  Kyurkchiev Nikolay,et al.  Sigmoid Functions: Some Approximation and Modelling Aspects , 2015 .

[12]  Daisuke Satoh.  A Discrete Gompertz Equation and a Software Reliability Growth Model , 2000 .

[13]  Hoang Pham,et al.  System Software Reliability (Springer Series in Reliability Engineering) , 2007 .

[14]  Mitsuru Ohba,et al.  Software Reliability Analysis Models , 1984, IBM J. Res. Dev..

[15]  A new class activation functions with application in the theory of impulse technics , 2018 .

[16]  Nikolay Pavlov,et al.  Some Software Reliability Models , 2018 .

[17]  Shigeru Yamada,et al.  Discrete equations and software reliability growth models , 2001, Proceedings 12th International Symposium on Software Reliability Engineering.

[18]  Amrit L. Goel,et al.  Software Reliability Models: Assumptions, Limitations, and Applicability , 1985, IEEE Transactions on Software Engineering.

[19]  Hoang Pham,et al.  A Software Reliability Model with a Weibull Fault Detection Rate Function Subject to Operating Environments , 2017 .

[20]  Yoshinobu Tamura,et al.  OSS Reliability Measurement and Assessment , 2016 .

[21]  Zhenmin Chen.  A new two-parameter lifetime distribution with bathtub shape or increasing failure rate function , 2000 .

[22]  Angelika Mueller.  Contributions To Hardware And Software Reliability , 2016 .

[23]  Nikolay Pavlov,et al.  SOME DETERMINISTIC RELIABILITY GROWTH CURVES FOR SOFTWARE ERROR DETECTION: APPROXIMATION AND MODELING ASPECTS , 2018 .

[24]  山田 茂,et al.  Software reliability modeling : fundamentals and applications , 2014 .

[25]  Svetoslav Markov,et al.  On the Hausdorff distance between the Heaviside step function and Verhulst logistic function , 2015, Journal of Mathematical Chemistry.

[26]  Neeraj Kumar Goyal,et al.  Artificial neural network for software reliability prediction , 2017 .

[27]  Xuemei Zhang,et al.  Some successful approaches to software reliability modeling in industry , 2005, J. Syst. Softw..

[28]  Transmuted Generalized Inverted Exponential Distribution , 2013 .

[29]  Transmuted Generalized Inverted Exponential Distribution , 2013 .

[30]  M. J. S. Khan,et al.  Generalized Order Statistics from Chen Distribution and its Characterization , 2016 .

[31]  Nikolay Pavlov,et al.  A NOTE ON THE ``MEAN VALUE'' SOFTWARE RELIABILITY MODEL , 2018 .

[32]  Devendra Kumar,et al.  Exponentiated Chen distribution: Properties and estimation , 2017, Commun. Stat. Simul. Comput..

[33]  Simon P. Wilson,et al.  Statistical methods in software engineering : reliability and risk , 1999 .

[34]  Renato Spigler,et al.  Solving numerically nonlinear systems of balance laws by multivariate sigmoidal functions approximation , 2018 .

[35]  P. C. Jha,et al.  Software Reliability Assessment with OR Applications , 2011 .

[36]  Shigeru Yamada,et al.  S-Shaped Reliability Growth Modeling for Software Error Detection , 1983, IEEE Transactions on Reliability.

[37]  Renato Spigler,et al.  Approximation results for neural network operators activated by sigmoidal functions , 2013, Neural Networks.

[38]  Edwin Lughofer,et al.  Residual-based fault detection using soft computing techniques for condition monitoring at rolling mills , 2014, Inf. Sci..

[39]  Yogendra P. Chaubey,et al.  An Extension of Chen’s Family of Survival Distributions with Bathtub Shape or Increasing Hazard Rate Function , 2015 .

[40]  Thong Ngee Goh,et al.  A modified Weibull extension with bathtub-shaped failure rate function , 2002, Reliab. Eng. Syst. Saf..

[41]  A. M. Abouammoh,et al.  Reliability estimation of generalized inverted exponential distribution , 2009 .

[42]  V. Kyurkchiev,et al.  A Family of Recurrence Generated Functions Based on “Half–Hyperbolic Tangent Activation Function” , 2017 .