In the software testing phase, software reliability growth models (SRGMs) are commonly used to evaluate the reliability of software systems. Traditional SRGMs are restricted by their assumption of a continuous growth pattern for the failure detection rate (FDR) throughout the testing phase. However, the assumption is compromised by Change-Point phenomena, where FDR fluctuations stem from variations in testing personnel or procedural modifications, leading to reduced prediction accuracy and compromised software reliability assessments. Therefore, the objective of this study is to improve software reliability prediction using a novel approach that combines genetic algorithm (GA) and deep learning-based SRGMs to account for the Change-point phenomenon. The proposed approach uses a GA to dynamically combine activation functions from various deep learning-based SRGMs into a new mutated SRGM called MuSRGM. The MuSRGM captures the advantages of both concave and S-shaped SRGMs and is better suited to capture the change-point phenomenon during testing and more accurately reflect actual testing situations. Additionally, failure data is treated as a time series and analyzed using a combination of Long Short-Term Memory (LSTM) and Attention mechanisms. To assess the performance of MuSRGM, we conducted experiments on three distinct failure datasets. The results indicate that MuSRGM outperformed the baseline method, exhibiting low prediction error (MSE) on all three datasets. Furthermore, MuSRGM demonstrated remarkable generalization ability on these datasets, remaining unaffected by uneven data distribution. Therefore, MuSRGM represents a highly promising advanced solution that can provide increased accuracy and applicability for software reliability assessment during the testing phase.

System scenarios that derived from system design specification play an important role in the reliability engineering of component-based software systems. Several scenario-based approaches have been proposed to predict the reliability of a system at the design time, most of them adopt flat construction of scenarios, which doesn't conform to software design specifications and is subject to introduce state space explosion problem in the large systems. This paper identifies various challenges related to scenario modeling at the early design stages based on software architecture specification. A novel scenario-based reliability modeling and prediction approach is introduced. The approach adopts hierarchical scenario specification to model software reliability to avoid state space explosion and reduce computational complexity. Finally, the evaluation experiment shows the potential of the approach.

In this paper we consider two non-parametric estimation methods for software reliability assessment without specifying the fault-detection time distribution, where the underlying stochastic process to describe software fault-counts in the system testing is given by a non-homogeneous Poisson process. The resulting data-driven methodologies can give the useful probabilistic information on the software reliability assessment under the incomplete knowledge on fault-detection time distribution. Throughout examples with real software fault data, it is shown that the proposed methods provide more accurate estimation results than the common parametric approach.

In this letter we develop a software reliability modeling framework by introducing the Burr XII distributions to software fault-detection time. An extension to deal with software metrics data characterizing the product size, program complexity or testing expenditure is also proposed. Finally, we investigate the goodness-of-fit performance and compare our new models with the existing ones through real data analyses.

We discuss software reliability assessment considering multiple changes of software fault-detection phenomenon. The testing-time when the characteristic of the software failure-occurrence or fault-detection phenomenon changes notably in the testing-phase of a software development process is called change-point. It is known that the occurrence of the change-point influences the accuracy for the software reliability assessment based on a software reliability growth models, which are mainly divided into software failure-occurrence time and fault counting models. This paper discusses software reliability growth modeling frameworks considering with the effect of the multiple change-point occurrence on the software reliability growth process in software failure-occurrence time and fault counting modeling. And we show numerical illustrations for the software reliability analyses based on our models by using actual data.

With the rise of component-based software development, its reliability has attracted much attention from both academic and industry communities. Component-based software development focuses on architecture design, and thus it is important for reliability analysis to emphasize software architecture. Existing approaches to architecture-based software reliability analysis don't model the usage profile explicitly, and they ignore the difference between the testing profile and the practical profile of components, which limits their applicability and accuracy. In response to these issues, a new reliability modeling and prediction approach is introduced. The approach considers reliability-related architecture factors by explicitly modeling the system usage profile, and transforms the testing profile into the practical usage profile of components by representing the profile with input sub-domains. Finally, the evaluation experiment shows the potential of the approach.

Recently, the wavelet-based estimation method has gradually been becoming popular as a new tool for software reliability assessment. The wavelet transform possesses both spatial and temporal resolution which makes the wavelet-based estimation method powerful in extracting necessary information from observed software fault data, in global and local points of view at the same time. This enables us to estimate the software reliability measures in higher accuracy. However, in the existing works, only the point estimation of the wavelet-based approach was focused, where the underlying stochastic process to describe the software-fault detection phenomena was modeled by a non-homogeneous Poisson process. In this paper, we propose an interval estimation method for the wavelet-based approach, aiming at taking account of uncertainty which was left out of consideration in point estimation. More specifically, we employ the simulation-based bootstrap method, and derive the confidence intervals of software reliability measures such as the software intensity function and the expected cumulative number of software faults. To this end, we extend the well-known thinning algorithm for the purpose of generating multiple sample data from one set of software-fault count data. The results of numerical analysis with real software fault data make it clear that, our proposal is a decision support method which enables the practitioners to do flexible decision making in software development project management.

In this paper, we discuss the stochastic modeling for operational software reliability measurement, assuming that the testing environment is originally different from the user operation one. In particular, we introduce the concept of systemability which is defined as the reliability characteristic subject to the uncertainty of the field operational environment into the model. First we introduce the environmental factor to consistently bridge the gap between the software failure-occurrence characteristics during the testing and the operation phases. Then we consider the randomness of the environmental factor, i.e., the environmental factor is treated as a random-distributed variable. We use the Markovian imperfect debugging model to describe the software reliability growth phenomena in the testing and the operation phases. We derive the analytical solutions of the several operational software reliability assessment measures which are given as the functions of time and the number of debuggings. Finally, we show several numerical illustrations to investigate the impacts of the consideration of systemability on the field software reliability evaluation.

An exponential regression-based model with stochastic intensity is developed to describe the software reliability growth phenomena, where the software testing metrics depend on the intensity process. For such a generalized modeling framework, the common maximum likelihood method cannot be applied any more to the parameter estimation. In this paper, we propose to use the pseudo maximum likelihood method for the parameter estimation and to seek not only the model parameters but also the software reliability measures approximately. It is shown in numerical experiments with real software fault data that the resulting software reliability models based on four parametric approximations provide the better goodness-of-fit performance than the common non-homogeneous Poisson process models without testing metric information.

Non-homogeneous Poisson processes (NHPPs) have gained much popularity in actual software testing phases to estimate the software reliability, the number of remaining faults in software and the software release timing. In this paper, we propose a new modeling approach for the NHPP-based software reliability models (SRMs) to describe the stochastic behavior of software fault-detection processes. The fundamental idea is to apply the equilibrium distribution to the fault-detection time distribution in NHPP-based modeling. We also develop efficient parameter estimation procedures for the proposed NHPP-based SRMs. Through numerical experiments, it can be concluded that the proposed NHPP-based SRMs outperform the existing ones in many data sets from the perspective of goodness-of-fit and prediction performance.

The software reliability is the ability of the software to perform its required function under stated conditions for a stated period of time. In this paper, a hybrid methodology that combines both ARIMA and fractal models is proposed to take advantage of unique strength of ARIMA and fractal in linear and nonlinear modeling. Based on the experiments performed on the software reliability data obtained from literatures, it is observed that our method is effective through comparison with other methods and a new idea for the research of the software failure mechanism is presented.

Many existing software reliability models (SRMs) are based on the assumption that fault correction activities take a negligible amount of time and resources, which is often invalid in real-life situations. Consequently, the estimated and predicted software reliability tends to be over-optimistic, which could in turn mislead management in related decision-makings. In this paper, we first make an in-depth analysis of real-life software testing process; then a Markovian SRM considering fault correction process is proposed. Parameter estimation method and software reliability prediction method are established. A numerical example is given which shows that by using the proposed model and methods, the results obtained tend to be more appropriate and realistic.

In this paper, we discuss software performability evaluation considering the real-time property; this is defined as the attribute that the system can complete the task within the stipulated response time limit. We assume that the software system has two operational states from the viewpoint of the end users: one is operating with the desirable performance level according to specification and the other is with degraded performance level. The dynamic software reliability growth process with performance degradation is described by the extended 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, we analyze the distribution of the number of tasks whose processes can be completed within the processing time limit with the infinite server queueing model. We derive several software performability measures 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 measures to investigate the impact of consideration of the performance degradation on the system performability evaluation.

This paper proposes a dynamic capture-recapture (DCR) model to estimate not only the total number of software faults but also quantitative software reliability from observed data. Compared to conventional static capture-recapture (SCR) model and usual software reliability models (SRMs) in the past literature, the DCR model can handle dynamic behavior of software fault-detection processes and can evaluate quantitative software reliability based on capture-recapture sampling of software fault data. This is regarded as a unified modeling framework of SCR and SRM with the Bayesian estimation. Simulation experiments under some plausible testing scenarios show that our models are superior to SCR and SRMs in terms of estimation accuracy.

In this paper we propose a discrete program-size dependent software reliability growth model flexibly describing the software failure-occurrence phenomenon based on a discrete Weibull distribution. We also conduct model comparisons of our discrete SRGM with existing discrete SRGMs by using actual data sets. The program size is one of the important metrics of software complexity. It is known that flexible discrete software reliability growth modeling is difficult due to the mathematical manipulation under a conventional modeling-framework in which the time-dependent behavior of the cumulative number of detected faults is formulated by a difference equation. Our discrete SRGM is developed under an existing unified modeling-framework based on the concept of general order-statistics, and can incorporate the effect of the program size into software reliability assessment. Further, we discuss the method of parameter estimation, and derive software reliability assessment measures of our discrete SRGM. Finally, we show numerical examples of discrete software reliability analysis based on our discrete SRGM by using actual data.

In this paper, we propose a new software reliability growth model which is the mixture of two exponential reliability growth models, one of which has the reliability growth and the other one does not have the reliability growth after the software is released upon completion of testing phase. The mixture of two such models is characterized by a weighted factor p, which is the proportion of reliability growth part within the model. Firstly, this paper discusses an optimal software release problem with regard to the expected total software cost incurred during the warranty period under the proposed software reliability growth model, which generalizes Kimura, Toyota and Yamada's (1999) model with consideration of the weighted factor. The second main purpose of this paper is to apply the Bayesian approach to the optimal software release policy by assuming the prior distributions for the unknown parameters contained in the proposed software reliability growth model. Some numerical examples are presented for the purpose of comparing the optimal software release policies depending on the choice of parameters by the non-Bayesian and Bayesian methods.

Software certification is a notoriously difficult problem. From software reliability engineering perspective, certification process must provide evidence that the program meets or exceeds the required level of reliability. When certifying the reliability of a high assurance system very few, if any, failures are observed by testing. In statistical estimation theory the probability of an event is estimated by determining the proportion of the times it occurs in a fixed number of trials. In absence of failures, the number of required certification tests becomes impractically large. We suggest that subjective reliability estimation from the development lifecycle, based on observed behavior or the reflection of one's belief in the system quality, be included in certification. In statistical terms, we hypothesize that a system failure occurs with the hypothesized probability. Presumed reliability needs to be corroborated by statistical testing during the reliability certification phase. As evidence relevant to the hypothesis increases, we change the degree of belief in the hypothesis. Depending on the corroboration evidence, the system is either certified or rejected. The advantage of the proposed theory is an economically acceptable number of required system certification tests, even for high assurance systems so far considered impossible to certify.

This paper proposes a statistical method to estimate the optimal software release time which minimizes the expected total software cost incurred in both testing and operation phases. It is shown that the underlying cost minimization problem can be reduced to a graphical one. This implies that the software release problem under consideration is essentially equivalent to a time series forecasting for the software fault-occurrence time data. In order to predict the future fault-occurrence time, we apply three extraordinary auto-regressive models by Singpurwalla and Soyer (1985) as the prediction devices as well as the well-known AR and ARIMA models. Numerical examples are devoted to illustrate the predictive performance for the proposed method. We compare it with the classical exponential software reliability growth model based on the non-homogeneous Poisson process, using actual software fault-occurrence time data.

I describe a software reliability growth model that yields accurate parameter estimates even with a small amount of input data. The model is based on a proposed discrete analog of a Gompertz equation that has an exact solution. The difference equation tends to a differential equation on which the Gompertz curve model is defined, when the time interval tends to zero. The exact solution also tends to the exact solution of the differential equation when the time interval tends to zero. The discrete model conserves the characteristics of the Gompertz model because the difference equation has an exact solution. Therefore, the proposed model provides accurate parameter estimates, making it possible to predict in the early test phase when software can be released.

In this paper, we construct a software availability model considering the number of restoration actions. We correlate the failure and restoration characteristics of the software system with the cumulative number of corrected faults. Furthermore, we consider an imperfect debugging environment where the detected faults are not always corrected and removed from the system. The time-dependent behavior of the system alternating between up and down states is described by a Markov process. From this model, we can derive quantitative measures for software availability assessment considering the number of restoration actions. Finally, we show numerical examples of software availability analysis.