A Note on the Exponentiated Exponential–Poisson Software Reliability Model

International journal of pure and applied mathematics, 2018

Dynamic Systems and Applications, 2018

Cybernetics and Information Technologies, 2018

In this paper we study the Hausdorff approximation of the shifted Heaviside step function ht0 (t) by sigmoidal functions based on the Chen’s and Pham’s cumulative distribution functions and find an expression for the error of the best approximation. We give real examples with data provided by IBM entry software package and Apache HTTP Server using Chen’s software reliability model and Pham’s deterministic software reliability model. Some analyses are made.

International journal of pure and applied mathematics, 2018

Abstract: Software reliability modeling is challenging since no single Software Reliability Growth Model (SRGM) is considered suitable in all situations owing to poor goodness of fit, lack of predictive validity of the models and their sensitivity to fluctuations in the number of failures in the data sets. In this paper, we propose a Non- Homogenous Poisson Process Model whose failure intensity function has the same Mathematical form as that of the probability density function (pdf) of a generalized exponential distribution. The performance of the proposed model was verified and also compared with six chosen SRGMs using failure data from 18 software systems and the model is found to be adequate in terms of goodness

Neural, Parallel & Scientific Computations archive, 2018

In this paper we study the Hausdorff approximation of the shifted Heaviside step function ht0(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 (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. AMS Subject Classification: 41A46

International Journal of Latest Research in Engineering and Technology, 2018

In this paper we study the Hausdorff approximation of the Heaviside step function () r ht by sigmoidal curve model based on the transmuted inverse exponential software reliability model and find an expression for the error of the best approximation. Some comparisons are made.

International journal of differential equations and applications, 2019

The determination of compulsory in area of the Software ReliabilityTheory components, such as confidence intervals and confidence bounds, should alsobe accompanied by a serious analysis of the value of the best Hausdorff approximation- the subject of study in the present paper.For example we study the Hausdorff approximation of the shifted Heaviside functionht0(t) by cumulative function based on the extended Song–Chang–Pham’s model [1](see, also [2]).We propose a software module within the programming environment CAS Mathe-matica for the analysis of the considered family of functions.We give real example with dataset using the new extended Song–Chang–Pham’ssoftware reliability model.

Journal of Mathematical Sciences and Modelling, 2019

1990

Properties of software failure times modelled as realizations of order statistics generated by independent but non-identically distributed exponential random variables are developed. Edgeworth and saddle point approximations to central order statistic densities so generated are developed using an exact integral representation of these densities. A comparison of Edgeworth and saddle point approximation with exact densities for two different population types is given. The accuracy of the saddle point approximation, even for very small population sizes (N = 6) and small samples'(n = 2) is excellent. The same technique is used to provide an exact integral representation of the probability that a particular fault appears in a sample of a given size. Some numerical comparisons of Rosen's (1972) approximation of inclusion probabilities with exact values are provided. His simple approximation appears to give excellent results as well. The intimate connection between successive sampl...