Discrete SRGM

Number of software Reliability growth models has been proposed in the literature. A mathematical technique which describes the software testing phenomenon known as the software reliability growth model. Software reliability growth models are used to predict the number of faults and reliability of the software. In the view of this software reliability growth models are basically differentiated as the continuous and discrete models. There is a plenty of development in the continuous models but little towards the discrete models. In this paper we have presented a discrete reliability growth model with different discrete testing effort functions and the same time software release policy is discussed. A new imperfect debugging discrete software reliability growth model with testing effort is proposed. All calculations are done on real data. The results shows the proposed testing effort models are perfectly fit to the data.

In this chapter we discuss the software reliability growth models (SRGMs) that describe the relationship between the number of faults removed and the number of test cases used. Firstly we describe the discrete exponential and S-shaped models in a perfect debugging environment. We also discuss flexible discrete SRGM, which can depict either exponential or S-shaped growth curves, depending upon the parameter values estimated from the past failure data. Further, we describe an SRGM for the fault removal phenomenon in a perfect debugging environment. Most testing processes are imperfect in practice, therefore we also discuss a discrete model that incorporates the impact of imperfect debugging and fault generation into software reliability growth modeling. Faults in the software are generally not of the same type, rather the faults contained in a large software may differ from each other in terms of the amount of time and skill of the removal team required to remove them. Three discrete models: the generalized Erlang model, modeling severity of faults with respect to testing time, and a model with faults of different severity incorporating logistic learning function have been discussed. A discrete model in a distributed environment is also discussed. The above discrete SRGMs assume a constant fault detection rate while testing the software under consideration. In practice, however, the fault detection rate varies because of changes in the testing skill, the system environment, and the testing strategy used to test the software. SRGMs for the fault removal phenomenon, the generalized Erlang model, and the generalized Erlang model with logistic function are discussed, incorporating the concept of change point. It is also shown how equivalent continuous models can be derived. This chapter describes the state-of-the-art in discrete modeling.

To meet highly competitive market challenges along with technological upgrades and changing user requirements, software firms offer newer versions of their products by adding new features and new functionalities. But this also results in increase in the fault content of software. In this paper we propose a discrete software reliability growth model (SRGM) for fault removal process incorporating the effect of up-gradations on the subsequent releases of the software. It is further assumed that faults present in the software are not of the same type and may be classified as simple and hard faults depending upon the effort and time consumed for their removal. The proposed model has been validated on a real life dataset for software with four releases. The results obtained are encouraging and fairly accurate.

Many software reliability growth models have been proposed in the past decade. Those models tacitly assume that testing-effort expenditures are constant throughout software testing. This paper develops realistic software reliability growth models incorporating the effect of testing-effort. The software error detection phenomenon in software testing is modeled by a nonhomogeneous Poisson process. The software reliability assessment measures and the estimation methods of parameters are investigated. Testing-effort expenditures are described by exponential and Rayleigh curves. Least-squares estimators and maximum likelihood estimators are used for the reliability growth parameters. The software reliability data analyses use actual data. The software reliability growth models with testing-effort can consider the relationship between the software reliability growth and the effect of testing-effort. Thus, the proposed models will enable us to evaluate software reliability more realistically.

Software reliability growth model with change-point and environmental function

It is one of the important issues in modern software development to make a highly reliable software system by efficient and economical testing. As one of these solutions, many companies have taken in testing-progress management and quality/reliability assessment based on software reliability growth models. Consequently, many software reliability growth models reflecting various development factors and operational environment of the software system have been proposed. Most of these models have assumed the software system as one domain. That is, the models have assumed that the set of the testing-paths influenced by execution of test-cases is extended with testing-progress and it expands to whole software system finally. However, a software system has the structure that the main-component calls plural sub-components ordinarily. Therefore, unless the main-component is tested, the sub-component called from it is not tested. In this chapter, we propose software reliability growth models based on such components' characteristics. Especially, these models reflecting the different testing-environment for composed components are formulated by nonhomogeneous Poisson processes. Furthermore, using fault-detection data observed in actual development projects, we show numerical examples of software reliability assessment and results of goodness-of-fit comparisons with existing software reliability growth models.

Software reliability assessment for an exponential-S-shaped reliability growth phenomenon

This investigation deals with a N-modules software reliability growth model (SRGM) wherein each module attains multiple types of faults of different severity levels. During the debugging phase, there may arise some new faults due to assumption of imperfect debugging. The reliability growth during the software testing phase governed by a non-homogeneous Poisson Process (NHPP). The proposed study is devoted to analyze the fault debugging phenomenon in all modules of software and to obtain expected number of faults observed, isolated and removed. The software reliability and optimum total cost of the software development during the testing phase are evaluated. The causes of fault occurrences in each module are different. The faults may occur with different failure rates and follow the nonlinear behavior with respect to the testing time. The NHPP model incorporates the testing-effort expenditure required for the faults debugging activities and governed by Weibull and logistic distributions which influence considerably not only the fault observation rate but also the time to isolate the faults and the time to remove the faults from all N-modules. In addition to predict the reliability of N-modular software, this study proposes optimal release policies for the SRGM by minimizing the expected cost subject to budget and testing-effort constraints, while ensuring a prescribed level of reliability and incorporating the effects of testing effort and efficiency. Some specific models are also deduced by setting the appropriate parameters so as to match with the existing models in the literature. Sensitivity results are presented through a numerical experiment to demonstrate the validity of the analytical formulations and the computational tractability of the model. An evolutionary algorithm, namely Particle Swarm Optimization (PSO) based on a dynamic penalty method, is employed to determine the optimal release time.

Multiple Software Reliability Growth Models (SRGM) has been illustrated to inspire designers and software developers to develop quality software. These models implicitly assume that expenditure is constant throughout testing effort. Recently importance was given to the testing phase by the development team and it requires controlled screening closely to raise its overall operational efficiency. Software Reliability Growth Models exhibits a precise relation between the failure patterns with time. Considering this as a basic building block a SRGM which is a Non-Homogeneous Poisson Process in nature is i in this work. The various aspects of our proposed model are testing effort function and fault detection rate (FDR). Mainly in Software Reliability Growth Model it was assumed that fault removal process are perfect which is not true in reality as new faults may get introduced during removal or some faults may not get removed due to its complexity. Thus in this model the concept of imperfect debugging was considered and assists us to justify the software reliability more convincingly through the help of testing effort function.

The software testing process basically aims at building confidence in the software for its use in real world applications. The reliability of a software system is always important to us. As we carry out the error detection and correction phenomenon on our software, the reliability of the software grows. With an aim to model this growth in the software reliability, many formulations in the form of Software Reliability Growth Models have been proposed. Many of these are based on Non-Homogeneous Poisson Process framework. In this paper, a parallel comparison of the performance of the proposed software reliability growth models is carried out, considering linear and exponential fault content functions for study of imperfect debugging situations. The performance of the proposed models has been compared with some famous existing software reliability models and the proposed models have been validated on some real-world datasets. Three goodness-of-fit criteria that include mean square error, predictive-ratio risk and predictive power are used to carry out the performance comparison of the models. Using these comparison criteria on six actual failure datasets, it is concluded that the proposed Model-2 which always outperforms Model-1, fits the actual failure data better and has better predictive power than other considered SRGMs for at least two data sets.

Recent research applies soft computing techniques to fit software reliability growth models. However, runtime performance and the distribution of the distance from an optimal solution over multiple runs must be explicitly considered to justify the practical utility of these approaches, promote comparison, and support reproducible research. This paper presents a meta-optimization framework to design stable and efficient multi-phase algorithms for fitting software reliability growth models. The approach combines initial parameter estimation techniques from statistical algorithms, the global search properties of soft computing, and the rapid convergence of numerical methods. Designs that exhibit the best balance between runtime performance and accuracy are identified. The approach is illustrated through nonhomogeneous Poisson process and covariate software reliability growth models, including a cross-validation step on data sets not used to identify designs. The results indicate the nonhomogeneous Poisson process model considered is too simple to benefit from soft computing because it incurs additional runtime with no increase in accuracy attained. However, a multi-phase design for the covariate software reliability growth model consisting of the bat algorithm followed by a numerical method achieves better performance and converges consistently, compared to a numerical method only. The proposed approach supports higher-dimensional covariate software reliability growth model fitting suitable for implementation in a tool.

The problem of finding the absolute error of stepwise and linear interpolation of the control signal from uniform samples from it using models of composite harmonic half-waves is solved. Previously, during the inspection of the control object, the maximum values of the signal parameters and half-waves are determined: speed, acceleration and sharpness, there are no spectrum parameters. To determine the values of the intervals of uniform sampling of time, two groups of models of "harmonic half-waves" are considered. The first group of models is described by harmonic time functions whose parameters are consistent. The second group of models is described by composite harmonic functions of time, thereby the time parameters of the signals are consistent. It is proved that with an increase in the entropy of the maximum values of the signal parameters, the value of the time sampling interval increases without increasing the interpolation error. Thus, the entropy value of the signal parameters serves as an indicator of their inconsistency. The results of modeling and graphs obtained in the environment of the mathematical package are presented. The results are intended to optimize the loading of input tasks and primary information processing of processors in robust real-time automation systems, for example, used to control high-speed trains when braking in sliding or skidding mode.

To simulate response of concrete members and structures, comprehensive description of concrete behavior is required. This paper presents two groups of models that could be used to simulate behavior of concrete in tension for finite element modeling. The first group of models is based on stress–strain relationships and the second is based on stress–displacement relationships. Six relationships available in literature are investigated to model the response of plain concrete struts of various shapes and the behavior of reinforced concrete frame. Three of these relationships define tension in terms of stress–strain, whereas the other three describe tension in terms of stress–displacement. Comparing model estimates with results from experiments on plain and reinforced concrete members, it is concluded that tensile behavior of concrete can be represented well using stress–strain relationship. Modeling tensile behavior of concrete based on stress–displacement relationships can simulate response of these members, too, but not as well. The stress–strain relationship given by Tsai is the best option to simulate tension in concrete compared to the other stress–strain relationships and stress–displacement relationships considered in this study.

In the literature several models have been derived by different authors in order to predict the solar irradiance intensity over inclined surfaces, however for the most models accuracy at various inclinations have not been verified. The study evaluated the estimation of solar irradiance at different tilt angles by means of different models based on the experimental measurements. For this purpose, two groups of models (isotropic and anisotropic) were carried out: the first group of models was used for estimating the diffuse solar irradiance component, and the second group was used for estimating the global solar irradiance. Five models have been selected and implemented for the estimation of the diffuse solar irradiance component, and five models have been selected for the estimation of global solar irradiance. The results of the analysis were compared with local experimental measurements for diffuse radiation and global irradiance. There are three tilt angles (0°, 30°, 60°) and a two-axis tracking system has been determent for comparison experiments with the model estimated results. The results showed all the selected models generated an error percentage in both the diffuse and global irradiance investigations.

This study presents two different groups of models of bio-inspired hierarchically organized oscillatory mechanical models exhibiting a localization phenomenon, when only certain parts of the system oscillate. The first group of models corresponds to an idealized sympodial tree-type branched structure consisting of branches represented by physical pendula attached mutually via hinges and linear rotational springs. The localization phenomenon is examined analytically and numerically in the structures with a different level of hierarchy, i.e. with a different level of branches, and the corresponding localized modes and their respective natural frequencies are found. The cases of small and large-amplitude vibration are considered. The second group of models has the form of a chain of hierarchically organized block masses attached mutually via tension–extension springs. The case of an arbitrary number of masses attached via linear springs is considered to show which localized modes exist at certain frequencies and the theorem related to the number of localized models is formulated and proven. It is pointed out that localized modes appear also in a system with nonlinear (pure cubic) springs. The results obtained can further be used in theoretical dynamical studies of these systems with different types of excitations, as well as for appropriate biomimetic applications, especially related to their utilization as vibration absorbers.