A NHPP based software reliability model and optimal release policy with logistic–exponential test coverage under imperfect debugging

Software is used in diverse settings and depends on development and testing environments. Software development should improve the reliability, quality, cost, and stability of software, making the software testing period crucial. We proposed a software reliability model (SRM) that considers the uncertainty of software environments and the fault detection rate function as a Rayleigh distribution, with an explicit mean value function solution in the model. The goodness-of-fit of the proposed model relative to several existing nonhomogeneous Poisson process (NHPP) SRMs is presented based on three software application failure datasets. Further, a cost model is also presented that addresses the error-removal risk level and required time. The optimal testing release policy for minimizing the expected total cost (ETC) is also determined for NHPP SRMs. The impact of the software environment is studied by varying it, and the optimal release times and minimum ETCs are compared. The goodness-of-fit comparison confirmed that the proposed model has more accurate prediction values than other models. Further, whereas the existing models applied to the cost model do not change after a certain operation period, the proposed model yields changes in release time even for long operating periods.

In the software testing process, many factors can affected the failure distribution, such as the testing strategy, running environment and resource allocation, etc. Once these factors are transformed during testing phase, they could result in the failure intensity function increasing or decreasing non-monotonically and abrupt fluctuations at a certain time interval. Especially, in large software systems, detected complex faults and failures are more difficult to isolate, reproduce and remove in comparison of detected simple faults and failures. Therefore, the fault detection rate shows the irregular fluctuation over time in the software testing process. In this paper, we propose an imperfect software debugging model derived from an Ito -type stochastic differential equation (SDE). In the actual testing process, the cumulative number of fault detection can be considered a stochastic event. Thus, we can model fault detection process using SDE. We estimate the parameters of the proposed model using maximum likelihood estimation. We also use five historical fault data sets to test the performance of the proposed model. To show that the proposed model is the best model among all models, we use a new optimal method to select the best model from various software reliability models. Experimental results show that the proposed model has better fitting and predictive performance than non-homogeneous Poisson process models and other perfect software reliability models based on SDE.

A software reliability growth model for imperfect debugging

Owing to release of software in multiple releases, code changes take place in software. Because of this added complexity in software, the testing team may be unable to correct the fault upon detection, leaving the actual fault to reside in the software, termed as imperfect debugging or there may be replacement of original fault by other fault, leading to error generation. Many other factors exist that affect the testing phase of software like strategies of testing, test cases, skill, efficiency, and learning of testing team. All these factors cannot be kept stable during the whole process of testing. They may change at any time moment causing the background processes to experience change, which is known as change‐point. Keeping all these critical testing environment factors under consideration, a new software reliability growth model has been proposed, which is derived from an non homogenous Poisson process (NHPP)based unified scheme for multi‐release two‐stage fault detection/observation and correction/removal software reliability models. The developed model is numerically illustrated on tandem data set for four releases.

In order to incorporate the effect of test coverage, two novel software reliability growth models (SRGMs) are proposed in this paper using failure data and test coverage simultaneously. One is continuous using testing time, and the other is discrete with respect to the number of executed test cases instead of testing time. Since one of the most important factors of the coverage-based SRGMs is the test coverage function (TCF), we first discuss a discrete TCF based on Beta function. Then we develop mean value functions (MVF) of the two models integrating test coverage and imperfect debugging. Finally the proposed TCF and MVFs are evaluated and validated on actual software reliability data collected from real software development projects. The results demonstrate clearly that both the proposed TCF and SRGMs provide better estimation and fitting for the data sets under comparisons.

In order to overcome the limitations of debugging process, insufficient consideration of imperfect debugging and testing-effort (TE) in software reliability modeling and analysis, a software reliability growth model (SRGM) explicitly incorporating imperfect debugging and TE is developed. From the point of view of incomplete debugging and introduction of new fault, software testing process is described and a relatively unified SRGM framework is presented considering TE. The proposed framework models are fairly general models that cover a variety of the previous works on SRGM with ID and TE. Furthermore, a special SRGM incorporating an improved Logistic testing-effort function (TEF) into imperfect debugging modeling is proposed. The effectiveness and reasonableness of the proposed model are verified by published failure data set. The proposed model closer to real software testing has better descriptive and predictive power than other models

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 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.

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.

Software reliability is one of the most important characteristics of software quality. Its measurement and management technologies during the software life-cycle are essential to produce and maintain quality/reliable software systems. In this chapter, we discuss software reliability modeling and its applications. As to software reliability modeling, hazard rate and NHPP models are investigated particularly for quantitative software reliability assessment. Further, imperfect debugging and software availability models are also discussed with reference to incorporating practical factors of dynamic software behavior. And three software management problems are discussed as an application technology of software reliability models: the optimal software release problem, statistical testing-progress control, and the optimal testing-effort allocation problem.

In this paper, we discuss the software performance evaluation method considering the real-time property. The dynamic software reliability growth process is described by the Markovian software reliability model with imperfect debugging. Assuming that the software system can process the multiple tasks simultaneously and that the arrival process of the tasks follows a nonhomogeneous Poisson process (NHPP), we analyze the distribution of the number of tasks whose processes can be completed within a prespecified processing time limit with the infinite server queueing model. We derive several stochastic quantities for software performance measurement considering the real-time property; these are given as the functions of time and the number of debugging activities. Finally, we illustrate several numerical examples of the quantities to investigate the relationship between the software reliability growth characteristics and the system performance.

Software reliability modelling (SRM) is a mathematics technique to estimate some measures of computer system that relate to software reliability. One group of existing models is using non-homogeneous Poisson process (NHPP) whose fault-number and failure-rate are constant or time-dependent functions. A few studies have been manipulated S-shaped curve to construct their models. However, those works remain some limitations. In this study, we introduce a new model that is based on a generalised S-shaped curve and evaluate it by real data set. After installing it in real code of Matlab and using MLE method to estimate parameter with a range of initial solution, we prove that our model converge to the most basic model of NHPP group, Goel-Okumoto model.

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.

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.

Software reliability is one of the most important characteristics of software quality. Its measurement and management technologies during the software life-cycle are essential to produce and maintain quality/reliable software systems. In this paper, we discuss software reliability modeling and its applications. As to software reliability modeling, hazard rate and NHPP models are investigated particularly for quantitative software reliability assessment. Further, imperfect debugging and software availability models are also discussed with reference to incorporating practical factors of dynamic software behavior.