Early Stage Software Reliability Estimation with Stochastic Reward Nets

This paper presents software reliability modeling issues at the early stage of a software development for fault tolerant software management system. Based on Stochastic Reward Nets, an effective model of hierarchical view for a fault tolerant software management system is put forward, and an approach that consists of system transient performance analysis is adopted. A quantitative approach for software reliability analysis is given. The results show its usefulness for the design and evaluation of the early-stage software reliability modeling when failure data is not available.

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.

Evaluating the Impact of Prediction Techniques: Software Reliability Perspective

Maintaining software reliability is the key idea for conducting quality research.This can be done by having less complex applications.While developers and other experts have made signicant efforts in this context,the level of reliability is not the same as it should be.Therefore,further research into the most detailed mechanisms for evaluating and increasing software reliability is essential.A signicant aspect of growing the degree of reliable applications is the quantitative assessment of reliability.There are multiple statistical as well as soft computing methods available in literature for predicting reliability of software.However,none of these mechanisms are useful for all kinds of failure datasets and applications.Hence nding the most optimal model for reliability prediction is an important concern.This paper suggests a novel method to substantially pick the best model of reliability prediction.This method is the combination of analytic hierarchy method(AHP),hesitant fuzzy(HF)sets and technique for order of preference by similarity to ideal solution(TOPSIS).In addition,using the different iterations of the process,procedural sensitivity was also performed to validate the ndings.The ndings of the software reliability prediction models prioritization will help the developers to estimate reliability prediction based on the software type.

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.

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.

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.

NHPP-based software reliability model considering testing effort and multivariate fault detection rate

In recent decades,many software reliability growth models（SRGMs） have been proposed for the engineers and testers in measuring the software reliability precisely.Most of them is established based on the non-homogeneous Poisson process（NHPP）,and it is proved that the prediction accuracy of such models could be improved by adding the describing of characterization of testing effort.However,some research work indicates that the fault detection rate（FDR） is another key factor affects final software quality.Most early NHPPbased models deal with the FDR as constant or piecewise function,which does not fit the different testing stages well.Thus,this paper first incorporates a multivariate function of FDR,which is bathtub-shaped,into the NHPP-based SRGMs considering testing effort in order to further improve performance.A new model framework is proposed,and a stepwise method is used to apply the framework with real data sets to find the optimal model.Experimental studies show that the obtained new model can provide better performance of fitting and prediction compared with other traditional SRGMs.

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.

Component-based software reliability process simulation considering imperfect debugging

In view of the flaws of component-based software （CBS） reliability modeling and analysis, the low recognition degree of debugging process, too many assumptions and difficulties in obtaining the solution, a CBS reliability simulation process is presented incorporating the imperfect debugging and the limitation of debugging resources. Considering the effect of imperfect debugging on fault detec- tion and correction process, a CBS integration testing model is sketched by multi-queue muhichannel and finite server queuing model （MMFSQM）. Compared with the analytical method based on pa- rameters and other nonparametric approaches, the simulation approach can relax more of the usual reliability modeling assumptions and effectively expound integration testing process of CBS. Then, CBS reliability process simulation procedure is developed accordingly. The proposed simulation ap- proach is validated to be sound and effective by simulation experiment studies and analysis.

Stochastic differential equation software reliability growth model with change-point

This paper presents software reliability growth models(SRGMs) with change-point based on the stochastic differential equation(SDE).Although SRGMs based on SDE have been developed in a large scale software system,considering the variation of failure distribution in the existing models during testing time is limited.These SDE SRGMs assume that failures have the same distribution.However,in practice,the fault detection rate can be affected by some factors and may be changed at certain point as time proceeds.With respect to this issue,in this paper,SDE SRGMs with changepoint are proposed to precisely reflect the variations of the failure distribution.A real data set is used to evaluate the new models.The experimental results show that the proposed models have a fairly accurate prediction capability.

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.

Software Reliability Growth Model for Imperfect Debugging Process Considering Testing-Effort and Testing Coverage

Because of the inevitable debugging lag,imperfect debugging process is used to replace perfect debugging process in the analysis of software reliability growth model.Considering neither testing-effort nor testing coverage can describe software reliability for imperfect debugging completely,by hybridizing testing-effort with testing coverage under imperfect debugging,this paper proposes a new model named GMW-LO-ID.Under the assumption that the number of faults is proportional to the current number of detected faults,this model combines generalized modified Weibull(GMW)testing-effort function with logistic(LO)testing coverage function,and inherits GMW's amazing flexibility and LO's high fitting precision.Furthermore,the fitting accuracy and predictive power are verified by two series of experiments and we can draw a conclusion that our model fits the actual failure data better and predicts the software future behavior better than other ten traditional models,which only consider one or two points of testing-effort,testing coverage and imperfect debugging.

Empirical Research on the Application of a Structure-Based Software Reliability Model

Reliability engineering implemented early in the development process has a significant impact on improving software quality.It can assist in the design of architecture and guide later testing,which is beyond the scope of traditional reliability analysis methods.Structural reliability models work for this,but most of them remain tested in only simulation case studies due to lack of actual data.Here we use software metrics for reliability modeling which are collected from source codes of post versions.Through the proposed strategy,redundant metric elements are filtered out and the rest are aggregated to represent the module reliability.We further propose a framework to automatically apply the module value and calculate overall reliability by introducing formal methods.The experimental results from an actual project show that reliability analysis at the design and development stage can be close to the validity of analysis at the test stage through reasonable application of metric data.The study also demonstrates that the proposed methods have good applicability.

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）.

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.

A software reliability growth model for component-based software incorporating debugging delay and imperfect debugging

In view of the problems and the weaknesses of component-based software （ CBS ） reliability modeling and analysis, and a lack of consideration for real debugging circumstance of integration tes- ting, a CBS reliability process analysis model is proposed incorporating debugging time delay, im- perfect debugging and limited debugging resources. CBS integration testing is formulated as a multi- queue muhichannel and finite server queuing model （MMFSQM） to illustrate fault detection process （FDP） and fault correction process （FCP）. A unified FCP is sketched, given debugging delay, the diversities of faults processing and the limitations of debugging resources. Furthermore, the impacts of imperfect debugging on fault detection and correction are explicitly elaborated, and the expres- sions of the cumulative number of fault detected and corrected are illustrated. Finally, the results of numerical experiments verify the effectiveness and rationality of the proposed model. By comparison, the proposed model is superior to the other models. The proposed model is closer to real CBS testing process and facilitates software engineer＇ s quantitatively analyzing, measuring and predicting CBS reliability. K

Component-based software reliability analysis incorporating imperfect debugging and change-point

Against the deficiencies of component-based software(CBS) reliability modeling and analysis,for instance,importing too many assumptions,paying less attention to debugging process without considering imperfect debugging and change-point(CP) problems adequately,an approach of CBS reliability process analysis is proposed which incorporates the imperfect debugging and CP.First,perfect/imperfect debugging and CP are reviewed.Based on the queuing theory,a multi-queue multichannel and infinite server queuing model(MMISQM) is presented to sketch the integration test process of CBS.Meanwhile,considering the effects of imperfect debugging and CP,expressions for fault detection and correction are derived based on MMISQM.Numerical results demonstrate that the proposed model can sketch the integration test process of CBS with preferable performance which outperforms other models.

Classification and Appraisement for Nonparametric Software Reliability Models

A taxonomy of software reliability models is developed that the models are classified as parametric and nonparametric models, and the nonparametric models are classified according to the mathematical methods they used. Then, a practical appraising index system for nonparametric software reliability models are put forward. The nonparametric software reliability models are classified into 5 classes, that is time series analysis models, grey theo- ry forecasting models, artificial neural network models, wavelet analysis models and kernel estimation models, and they are evaluated by the practical index system.

A Software Reliability Model for OSS Including Various Fault Data Based on Proportional Hazard-Rate Model

The software reliability model is the stochastic model to measure the software reliability quantitatively. A Hazard-Rate Model is the well-known one as the typical software reliability model. We propose Hazard-Rate Models Considering Fault Severity Levels (CFSL) for Open Source Software (OSS). The purpose of this research is to make the Hazard-Rate Model considering CFSL adapt to baseline hazard function and 2 kinds of faults data in Bug Tracking System (BTS), i.e., we use the covariate vectors in Cox proportional Hazard-Rate Model. Also, we show the numerical examples by evaluating the performance of our proposed model. As the result, we compare the performance of our model with the Hazard-Rate Model CFSL.