Quasi-Bayesian software reliability model with small samples

In traditional Bayesian software reliability models, it was assume that all probabilities are precise. In practical applications the parameters of the probability distributions are often under uncertainty due to strong dependence on subjective information of experts＇ judgments on sparse statistical data. In this paper, a quasi-Bayesian software reliability model using interval-valued probabilities to clearly quantify experts＇ prior beliefs on possible intervals of the parameters of the probability distributions is presented. The model integrates experts＇ judgments with statistical data to obtain more convincible assessments of software reliability with small samples. For some actual data sets, the presented model yields better predictions than the Jelinski-Moranda （JM） model using maximum likelihood （ML）.

Incorporating S-shaped testing-effort functions into NHPP software reliability model with imperfect debugging

Testing-effort（TE） and imperfect debugging（ID） in the reliability modeling process may further improve the fitting and prediction results of software reliability growth models（SRGMs）. For describing the S-shaped varying trend of TE increasing rate more accurately, first, two S-shaped testing-effort functions（TEFs）, i.e.,delayed S-shaped TEF（DS-TEF） and inflected S-shaped TEF（IS-TEF）, are proposed. Then these two TEFs are incorporated into various types（exponential-type, delayed S-shaped and inflected S-shaped） of non-homogeneous Poisson process（NHPP）SRGMs with two forms of ID respectively for obtaining a series of new NHPP SRGMs which consider S-shaped TEFs as well as ID. Finally these new SRGMs and several comparison NHPP SRGMs are applied into four real failure data-sets respectively for investigating the fitting and prediction power of these new SRGMs.The experimental results show that：（i） the proposed IS-TEF is more suitable and flexible for describing the consumption of TE than the previous TEFs;（ii） incorporating TEFs into the inflected S-shaped NHPP SRGM may be more effective and appropriate compared with the exponential-type and the delayed S-shaped NHPP SRGMs;（iii） the inflected S-shaped NHPP SRGM considering both IS-TEF and ID yields the most accurate fitting and prediction results than the other comparison NHPP SRGMs.

Web software reliability modeling with random impulsive shocks

As the web-server based business is rapidly developed and popularized, how to evaluate and improve the reliability of web-servers has been extremely important. Although a large num- ber of software reliability growth models （SRGMs）, including those combined with multiple change-points （CPs）, have been available, these conventional SRGMs cannot be directly applied to web soft- ware reliability analysis because of the complex web operational profile. To characterize the web operational profile precisely, it should be realized that the workload of a web server is normally non-homogeneous and often observed with the pattern of random impulsive shocks. A web software reliability model with random im- pulsive shocks and its statistical analysis method are developed. In the proposed model, the web server workload is characterized by a geometric Brownian motion process. Based on a real data set from IIS server logs of ICRMS website （www.icrms.cn）, the proposed model is demonstrated to be powerful for estimating impulsive shocks and web software reliability.

Singularity of Some Software Reliability Models and Parameter Estimation Method

According to the principle, “The failure data is the basis of software reliability analysis”, we built a software reliability expert system (SRES) by adopting the artificial intelligence technology. By reasoning out the conclusion from the fitting results of failure data of a software project, the SRES can recommend users “the most suitable model” as a software reliability measurement model. We believe that the SRES can overcome the inconsistency in applications of software reliability models well. We report investigation results of singularity and parameter estimation methods of experimental models in SRES.

Singularity of Software Reliability Models LVLM and LVQM

According to the principle, “The failure data is the basis of software reliabilityanalysis”, we built a software reliability expert system (SRES) by adopting the artificialtechnology. By reasoning out the conclusion from the fitting results of failure data of asoftware project, the SRES can recommend users “the most suitable model” as a softwarereliability measurement model. We believe that the SRES can overcome the inconsistency inapplications of software reliability models well. We report investigation results of singularity and parameter estimation methods of models, LVLM and LVQM.

Discrete Software Reliability Growth Modeling for Errors of Different Severity Incorporating Change-point Concept

Several software reliability growth models （SRGM） have been developed to monitor the reliability growth during the testing phase of software development. In most of the existing research available in the literatures, it is considered that a similar testing effort is required on each debugging effort. However, in practice, different types of faults may require different amounts of testing efforts for their detection and removal. Consequently, faults are classified into three categories on the basis of severity： simple, hard and complex. This categorization may be extended to r type of faults on the basis of severity. Although some existing research in the literatures has incorporated this concept that fault removal rate （FRR） is different for different types of faults, they assume that the FRR remains constant during the overall testing period. On the contrary, it has been observed that as testing progresses, FRR changes due to changing testing strategy, skill, environment and personnel resources. In this paper, a general discrete SRGM is proposed for errors of different severity in software systems using the change-point concept. Then, the models are formulated for two particular environments. The models were validated on two real-life data sets. The results show better fit and wider applicability of the proposed models as to different types of failure datasets.

Grey-based approach for estimating software reliability under nonhomogeneous Poisson process

Due to the randomness and time dependence of the factors affecting software reliability, most software reliability models are treated as stochastic processes, and the non-homogeneous Poisson process(NHPP) is the most used one.However, the failure behavior of software does not follow the NHPP in a statistically rigorous manner, and the pure random method might be not enough to describe the software failure behavior. To solve these problems, this paper proposes a new integrated approach that combines stochastic process and grey system theory to describe the failure behavior of software. A grey NHPP software reliability model is put forward in a discrete form, and a grey-based approach for estimating software reliability under the NHPP is proposed as a nonlinear multi-objective programming problem. Finally, four grey NHPP software reliability models are applied to four real datasets, the dynamic R-square and predictive relative error are calculated. Comparing with the original single NHPP software reliability model, it is found that the modeling using the integrated approach has a higher prediction accuracy of software reliability. Therefore, there is the characteristics of grey uncertain information in the NHPP software reliability models, and exploiting the latent grey uncertain information might lead to more accurate software reliability estimation.

Assessment and Prediction of Software Reliability in Mobile Applications

Software reliability is an important quality attribute, and software reliability models are frequently used to measure and predict software maturity. The nature of mobile environments differs from that of PC and server environments due to many factors, such as the network, energy, battery, and compatibility. Evaluating and predicting mobile application reliability are real challenges because of the diversity of the mobile environments in which the applications are used, and the lack of publicly available defect data. In addition, bug reports are optionally submitted by end-users. In this paper, we propose assessing and predicting the reliability of a mobile application using known software reliability growth models (SRGMs). Four software reliability models are used to evaluate the reliability of an open-source mobile application through analyzing bug reports. Our experiment proves it is possible to use SRGMs with defect data acquired from bug reports to assess and predict the software reliability in mobile applications. The results of our work enable software developers and testers to assess and predict the reliability of mobile software applications.

The Applications of Evolutionary Computation in Software Reliability

Software reliability models(SRMs) are the theoretic foundation of software reliability. However, the existence of intrinsic limitation of the preposition in traditional model building confines the applications of SRMs. In this paper, a new method,evolutionary computation,is used to estimate parameters of SRMs .At the same time, new algorithms are also proposed and employed to build SRMs. As the experiment results demonstrate, evolutionary computation method is po'verful and effective.

Reliability Growth Modeling and Optimal Release Policy Under Fuzzy Environment of an N-version Programming System Incorporating the Effect of Fault Removal Efficiency

Failure of a safety critical system can lead to big losses. Very high software reliability is required for automating the working of systems such as aircraft controller and nuclear reactor controller software systems. Fault-tolerant softwares are used to increase the overall reliability of software systems. Fault tolerance is achieved using the fault-tolerant schemes such as fault recovery （recovery block scheme）, fault masking （N-version programming （NVP）） or a combination of both （Hybrid scheme）. These softwares incorporate the ability of system survival even on a failure. Many researchers in the field of software engineering have done excellent work to study the reliability of fault-tolerant systems. Most of them consider the stable system reliability. Few attempts have been made in reliability modeling to study the reliability growth for an NVP system. Recently, a model was proposed to analyze the reliability growth of an NVP system incorporating the effect of fault removal efficiency. In this model, a proportion of the number of failures is assumed to be a measure of fault generation while an appropriate measure of fault generation should be the proportion of faults removed. In this paper, we first propose a testing efficiency model incorporating the effect of imperfect fault debugging and error generation. Using this model, a software reliability growth model （SRGM） is developed to model the reliability growth of an NVP system. The proposed model is useful for practical applications and can provide the measures of debugging effectiveness and additional workload or skilled professional required. It is very important for a developer to determine the optimal release time of the software to improve its performance in terms of competition and cost. In this paper, we also formulate the optimal software release time problem for a 3VP system under fuzzy environment and discuss a the fuzzy optimization technique for solving the problem with a numerical illustration.

An Improved NHPP Model with Time-Varying Fault Removal Delay

In this paper, an improved NHPP model is proposed by replacing constant fault removal time with time-varying fault removal delay in NHPP model, proposed by Daniel R Jeske. In our model, a time-dependent delay function is established to fit the fault removal process. By using two sets of practical data, the descriptive and predictive abilities of the improved NHPP model are compared with those of the NHPP model, G-O model, and delayed S-shape model. The results show that the improved model can fit and predict the data better.

A Study of Quantitative Progress Evaluation Models for Open Source Projects

Open source software (OSS) has become an indispensable part of society, not only for personal use but also for corporate use. Projects developed and operated by OSS are called open source projects, and the number of such projects is increasing. On the other hand, because anyone can participate in an open source project, the progress of the project is uncertain due to differences in project members’ skills, development environments, and time zones of activity. Therefore, many users and companies need to understand the development and operation status of open source project. Then, the developers carefully make decisions on upgrading or installing new OSS. In this paper, we focus on the maintenance effort estimation for open source projects considering uncertainty. Also, we evaluate the project quantitatively using Earned Value Management (EVM). Moreover, we examine the appropriateness of the model for predicting the maintenance effort expeditures. Furthermore, we discuss the appropriateness of this EVM method.

One-Sample Bayesian Predictive Analyses for a Nonhomogeneous Poisson Process with Delayed S-Shaped Intensity Function Using Non-Informative Priors

The delayed S-shaped software reliability growth model (SRGM) is one of the non-homogeneous Poisson process (NHPP) models which have been proposed for software reliability assessment. The model is distinctive because it has a mean value function that reflects the delay in failure reporting: there is a delay between failure detection and reporting time. The model captures error detection, isolation, and removal processes, thus is appropriate for software reliability analysis. Predictive analysis in software testing is useful in modifying, debugging, and determining when to terminate software development testing processes. However, Bayesian predictive analyses on the delayed S-shaped model have not been extensively explored. This paper uses the delayed S-shaped SRGM to address four issues in one-sample prediction associated with the software development testing process. Bayesian approach based on non-informative priors was used to derive explicit solutions for the four issues, and the developed methodologies were illustrated using real data.