Software Reliability Growth Model Based on Half Logistic Distribution

Time-dependent error-detection rate model for software reliability and other performance measures: Amrit L. Goel and Kazu Okumoto. IEEE Trans. Reliab., R-28, (3) p. 206, (August 1979)

In reality, the fault detection (or correction) phenomenon and software reliability estimation in the operational phase are different from that in the testing phase. The fault removal continues at a slower rate during the operational phase. In this paper, we will investigate some techniques for software reliability prediction and measurement in the operational phase. We first review how some software reliability growth models (SRGMs) based on non-homogeneous Poisson processes (NHPPs) can be readily derived based on a unified theory for NHPP models. Under this general framework, we can not only verify some conventional SRGMs but also derive some new SRGMs that can be used for software reliability measurement in the operational phase. That is, based on the unified theory, we can incorporate the concept of multiple changepoints into software reliability modeling. We can formularize and simulate the fault detection process in the operational phase. Some numerical illustrations based on real software failure data are also presented. The experimental results show that the proposed models can easily reflect the possible changes of fault detection process and offer quantitative analysis on software failure behavior in field operation.

One of the established trends of research areas and practices in software engineering that dealt with the measurement and enhancement of reliability is software reliability engineering. Stochastic software reliability models find typical usage for analysis. These are the models that perform modeling on failure process of the software and exploit other software metrics or failure data as cornerstone for parameter estimation. The ability of the models for estimating and predicting the current reliability and future failure behavior, respectively, is high. Due to any failures and faults in the system, a product becomes unreliable. The lack of understanding of nature of the software makes the measurement of software reliability as a challenging task. It is not possible to determine a best way to measure the reliability and other aspects of software. This paper proposes an efficient software reliability growth model (SRGM) in which logistic exponential TEF is exploited. This model offers increased failure rate recognition and suitable ways to resolve faults and so on. Our work estimates the SRGM parameters using optimization algorithm. Such estimation can aid in developing precise software reliability model. In order to accomplish the optimization, we use artificial bee colony (ABC) algorithm. As the parameters optimization considerably improves the quality of parameters to be used for reliability growth model, reliability growth can also be improved considerably.

Reliability growth models for hardware and software systems based on nonhomogeneous Poisson processes: A survey

In this paper we consider non-parametric estimation methods for software reliability assessment without specifying the fault distribution, where the underlying stochastic process to describe software fault-counts in the system testing is given by a non-homogeneous Poisson process. A comprehensive approach based on the kernel estimation is provided with several kernel functions and bandwidth estimations. Next, we develop interval estimation methods via the non-parametric bootstrap, and derive the confidence regions of several reliability measures such as the expected cumulative number of software faults, software intensity function, quantitative software reliability as well. The resulting data-driven methodology can give the useful probabilistic information on the software reliability prediction under the incomplete knowledge on fault distribution. In illustrative examples with a real software fault data, it is shown that the proposed methods provide useful software reliability measures under uncertainty from the view point of frequentist analysis.

A software reliability growth model incorporating the amount of test effort expenditures during the software testing phase is described. The time-dependent behavior of test-effort expenditures is described by a Weibull curve due to the flexibility. Assuming that the error detection rate to the amount of test-effort spent during the testing phase is proportional to the current error content, the model is formulated by a nonhomogeneous Poisson process. Using this model, the method of data analysis for software reliability measurement is presented. Also, this model is applied to the prediction of additional test-effort expenditures to obtain the objective number of errors detected by software testing and the determination of the optimum time to stop software testing for release. >

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.

With the increasing use of Open Source Software (OSS) in high speed networking, parallel processing and distributed computing, OSS has emerged as mainstream in the last decade and is now being broadly accepted even by the traditional proprietary software development companies. The major advantages of OSS over traditional software development are less development cost, availability of source code, quality and security. Software reliability—an important attribute of software quality, is defined as the probability that a software will operate free of failures or breakdown for a specified time under specified conditions (IEEE Std. 1633-2016). Investigation of Software reliability with the help of software reliability models (SRM) undertakes the estimation and prediction of the failure phenomenon of a software. In this paper we have investigated whether Non-homogeneous Poisson process (NHPP) based software reliability models fit in the big data open source software fault/bug data. We have extracted real and latest bug/fault data of Hadoop and Spark–open source big data applications, from bug tracking/management tool Jira. For this purpose, we have also compared these models on different goodness-of-fit and prediction criteria based on collected failure data to ascertain whether a best fitted model can also be a best predictor. It is found that the best model fitting the failure data is not a best predictor model.

This paper discusses two-dimensional software reliability measurement technologies, which describe a software reliability growth process depending on two-types of software reliability growth factors: Testing-time and testing-effort factors. From the view point of actual software failure-occurrence mechanism, it is natural to consider that a software reliability growth process depends on not only testing-time factor but also other software reliability growth factors, i.e., testing-effort factors, such as test-execution time, testing-skill of test engineers, testing-coverage. From such reason, the two-dimensional software reliability measurement technologies enable us to conduct more feasible software reliability assessment than the one-dimensional (conventional) software reliability measurement approach, in which it is assumed that the software reliability growth process depends only on testing-time. We discuss two-types of two-dimensional software reliability growth modeling approaches for feasible software reliability assessment, and conduct goodness-of-fit comparisons of our models with existing one-dimensional software reliability growth models. Finally, as one of the examples for two-dimensional software reliability analysis, we show examples of the application of our two-dimensional software reliability growth model by using actual data.

Software reliability growth models based on a nonhomogeneous Poisson process (NHPP) have been considered as one of the most effective among various models since they integrate the information regarding testing and debugging activities observed in the testing phase into the software reliability model. Although most of the existing NHPP models have progressed successfully in their estimation/prediction accuracies by modifying the assumptions with regard to the testing process, these models were developed based on the instantaneous fault-removal assumption. In this paper, we develop a generalized NHPP software reliability model considering quasi-renewal time-delay fault removal. The quasi-renewal process is employed to estimate the time delay due to identifying and prioritizing the detected faults before actual code change in the software reliability assessment. Model formulation based on the quasi-renewal time-delay assumption is provided, and the generalized mean value function (MVF) for the proposed model is derived by using the method of steps. The general solution of the MVFs for the proposed model is also obtained for some specific existing models. The numerical examples, based on a software failure data set, show that the consideration of quasi-renewal time-delay fault-removal assumption improves the descriptive properties of the model, which means that the length of time delay is getting decreased since testers and programmers adapt themselves to the working environment as testing and debugging activities are in progress.

Non-homogeneous Poisson process (NHPP) model with typical reliability growth patterns is an important technology about evaluating software reliability. Two parameters which affect software reliability are original failures number and failure-detected rate. The paper firstly defines the software failure distributed and discusses a few kinds' software reliability models. Non-homogeneous Poisson process model is presented. The models with different parameters are discussed and analyzed. The model's restrict condition and some of parameters, original failures number and failure-detected ratio, are extrapolated. Assessment methodology about key parameters is given.

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.

This paper deals with the effect of interfailure time variability on the modelling of software reliability growth. Some, primarily mathematical arguments, are outlined that cast a doubt on the commonly adopted concept of failures ' occurrence as a Poisson (either homogeneous or non-homogeneous) process. On a contrived (but plausible for the software practice) example the consequences of this assumption, in some cases inappropriate for the software reliability predictions, are illustrated. The idea of “tuning” the reliability growth models based on measurements of the distribution of a single execution time is advocated.Keywordsurn modelsoftware reliability growthPoisson processsoftware execution timeoperational profile

Software reliability in the software development process is an important issue. Software process improvement helps in finishing with reliable software product. In this field, SPC (Statistical process control) is a method of process management through application of statistical analysis, which involves and includes the defining, measuring, controlling, and improving of the processes. In measuring software reliability control charts can be used as efficient and appropriate SPC Tools. The proposed process involves evaluation of the parameter of the mean value function and hence the values of the mean value function at various inter failure times to develop relevant time control chart. In this paper, was proposed a control mechanism, based on time between failures observations using Burr distribution property, which is based on Non Homogenous Poisson Process (NHPP).

The non-homogeneous Poisson process (NHPP) model is a very important class of software reliability models and is widely used in software reliability engineering. NHPPs are characterized by their intensity functions. In the literature it is usually assumed that the functional forms of the intensity functions are known and only some parameters in intensity functions are unknown. The parametric statistical methods can then be applied to estimate or to test the unknown reliability models. However, in realistic situations it is often the case that the functional form of the failure intensity is not very well known or is completely unknown. In this case we have to use functional (non-parametric) estimation methods. The non-parametric techniques do not require any preliminary assumption on the software models and then can reduce the parameter modeling bias. The existing non-parametric methods in the statistical methods are usually not applicable to software reliability data. In this paper we construct some non-parametric methods to estimate the failure intensity function of the NHPP model, taking the particularities of the software failure data into consideration.