Considering the fault dependency concept with debugging time lag in software reliability growth modeling using a power function of testing time

Since the early 1970s tremendous growth has been seen in the research of software reliability growth modeling.In general, software reliability growth models (SRGMs) are applicable to the late stages of testing in software development and they can provide useful information about how to improve the reliability of software products.A number of SRGMs have been proposed in the literature to represent time-dependent fault identification/removal phenomenon;still new models are being proposed that could fit a greater number of reliability growth curves.Often,it is assumed that detected faults axe immediately corrected when mathematical models are developed.This assumption may not be realistic in practice because the time to remove a detected fault depends on the complexity of the fault,the skill and experience of the personnel,the size of the debugging team,the technique,and so on.Thus,the detected fault need not be immediately removed,and it may lag the fault detection process by a delay effect factor.In this paper,we first review how different software reliability growth models have been developed,where fault detection process is dependent not only on the number of residual fault content but also on the testing time,and see how these models can be reinterpreted as the delayed fault detection model by using a delay effect factor.Based on the power function of the testing time concept,we propose four new SRGMs that assume the presence of two types of faults in the software:leading and dependent faults.Leading faults are those that can be removed upon a failure being observed.However,dependent faults are masked by leading faults and can only be removed after the corresponding leading fault has been removed with a debugging time lag.These models have been tested on real software error data to show its goodness of fit,predictive validity and applicability.     

Weibull分布引进故障的软件可靠性增长模型

软件调试是复杂过程,可能会受到很多种因素的影响,例如调试资源分配、调试工具的使用情况、调试技巧等.在软件调试过程中,当检测到的故障被去除时,新的故障可能会被引进.因此,研究故障引进的现象对建立高质量的软件可靠性增长模型具有重要意义.但是到目前为止,模拟故障引进过程仍是一个复杂和困难的问题.虽然有许多研究者开发了一些不完美调试的软件可靠性增长模型,但是一般都是假设故障内容（总数）函数为线性、指数分布或者是与故障去除的数量成正比.这个假设与实际的软件调试过程中故障引进情况并不完全一致.提出一种基于Weibull分布引进故障的软件可靠性增长模型,考虑故障内容（总数）函数服从Weibull分布,并用相关的实验验证了提出的模型的拟合和预测性能.在用两个故障数据集进行的模拟实验中,实验结果指出：提出的模型和其他模型相比,有更好的拟合和预测性能以及更好的鲁棒性.     

一个NHPP类软件可靠性增长模型框架

NHPP类软件可靠性增长模型已经成为软件可靠性工程实践中非常成功的工具,从某些模型的一些共同特征出发,研究了NHPP类软件可靠性增长模型的有限通用框架,提出了一 个既考虑软件测试的不完美性、故障检测率随时间的变化,又考虑了故障改正效率随时间变化的NHPP类软件可靠性增长模型框架。一些已经存在的NHPP类软件可靠性增长模型型是这个框架的特例。     

一个基于响铃形故障检测率函数的软件可靠性增长模型

非齐次泊松过程类软件可靠性增长模型是评价软件产品可靠性指标的有效工具．影响软件可靠性增长模型评估和预测准确性的最重要的两个因素是软件中隐藏的初始故障数和故障检测率．一些非齐次泊松过程类模型假设故障检测率是不随测试时间变化的常量,有些模型假设故障检测率是增函数或减函数．这些假设或忽略了测试者的学习过程,或忽略了越迟被检测到的故障的概率就可能越低的特点．该文将测试者的学习过程和软件固有故障检测率的变化特征相结合,提出了一个铃形的故障检测率函数,建立了一个非齐次泊松过程类软件可靠性增长模型——Bbell—SRGM．在一组失效数据上的实验分析表明：对这组失效数据,Bbell—SRGM模型比G-O模型等的拟合效果更好．     

一个考虑多种排错延迟的NHPP类软件可靠性增长模型

软件可靠性增长模型通常假设软件的测试环境与软件实际运行的现场环境相同,期望利用测试阶段获得的失效数据评估软件在现场运行时的失效行为。多数非齐次泊松过程类软件可靠性增长模型假设软件故障被发现后立即被排除,这点假设无论是在测试环境还是在现场环境下都很难实现。根据故障对测试过程的影响,故障的排错时间可被分为多种。提出了一个考虑多种排错延迟的软件可靠性增长模型,讨论了基于这个模型的故障排除效率函数,指出从用户角度出发讨论软件可靠性时必须考虑重复性故障。     

考虑不完美排错情况的NHPP 类软件可靠性增长模型

针对现有NHPP 类软件可靠性增长模型对故障排错过程中不完美排错情况考虑不完全的现状,提出了一 种新的软件可靠性增长模型.该模型全面考虑了不完美排错的两种情况:既考虑了排错过程中引入新错误的可能性, 又考虑了不完全排错的情况,并且引入了一种故障排除率随时间变化的故障排除率函数,使模型更符合实际情况.利 用公开发表的两组不同的软件失效数据对该模型进行验证的结果表明,与现有的对不完美排错情况考虑不完全的 模型相比,该模型能够取得更好的拟合结果和预测效果.     

不完美排错软件可靠性增长模型效用量化研究

为了进一步提升现有非齐次泊松过程类软件可靠性增长模型的拟合和预测性能,首先从故障总数增长趋势角度对不完美排错模型进行深入研究,提出两个一般性不完美排错框架模型,分别考虑了总故障数量函数与累计检测故障函数间的线性关系与微分关系,并求得累计检测的故障数量与软件中总故障数量函数表达式;其次,在六组真实的失效数据集上对比了提出的两种一般性不完美排错模型和六种不完美排错模型拟合预测性能表现。实例验证结果表明,提出的一般性不完美排错框架模型在大多数失效数据集上都具有优秀的拟合和预测性能,证明了新建模型的有效性和实用性;通过对提出的模型与其他不完美排错模型在数据集上的性能的深入分析,为实际应用中不完美排错模型的选择提出了建议。     

Imperfect debugging models with fault introduction rate for software reliability assessment

In general it is considered to be unrealistic in software reliability modelling to assume that the faults detected by software testing are perfectly removed without introducing new faults. In this paper we propose two software reliability assessment models with imperfect debugging by assuming that new faults are sometimes introduced when the faults originally latent in a software system are corrected and removed during the testing phase. It is assumed that the fault detection rate is proportional to the sum of the numbers of faults remaining originally in the system and faults introduced by imperfect debugging. These two models are described by a nonhomogeneous Poisson process. Several quantitative measures for reliability assessment are derived, and the maximum likelihood estimations of unknown model parameters are presented. Finally, numerical examples of software reliability analysis based on these two models are shown.     

考虑测试环境和实际运行环境的软件可靠性增长模型

软件可靠性增长模型中测试阶段和操作运行阶段环境的不同导致了两个阶段故障检测率的不同.非齐次泊松过程类软件可靠性增长模型是评价软件产品可靠性指标的有效工具.在一些非齐次泊松过程类模型中,有些学者提出了常量的环境因子,用来描述测试环境和运行环境的差别.实际上,环境因子应该是随时间变化的变量.考虑了运行阶段和测试阶段环境的不同,根据实测数据得到了变化的环境因子,并且根据测试阶段的故障检测率和变化的环境因子,转化得到了操作运行阶段的故障检测率.考虑到故障的排除效率和故障引入率,从而建立了一个既考虑运行环境和测试环境差别,又考虑故障排除效率和故障引入率的非齐次泊松过程类软件可靠性增长模型（PTEO-SRGM）.在两组失效数据上的实验分析表明,对这组失效数据,PTEO-SRGM模型比G-O模型等模型的拟合效果和预测能力更好.     

考虑不完美排错情况的NHPP 类软件可靠性增长模型

针对现有NHPP类软件可靠性增长模型对故障排错过程中不完美排错情况考虑不完全的现状,提出了一种新的软件可靠性增长模型.该模型全面考虑了不完美排错的两种情况:既考虑了排错过程中引入新错误的可能性,又考虑了不完全排错的情况,并且引入了一种故障排除率随时间变化的故障排除率函数,使模型更符合实际情况.利用公开发表的两组不同的软件失效数据对该模型进行验证的结果表明,与现有的对不完美排错情况考虑不完全的模型相比,该模型能够取得更好的拟合结果和预测效果.     

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.     

考虑测试工作量与覆盖率的软件可靠性模型

为了进一步提升现有非齐次泊松过程类软件可靠性增长模型的拟合与预计精度,首先,提出一个同时考虑测试工作量与测试覆盖率的NHPP类软件可靠性建模框架.在此基础上,将变形S型测试工作量函数(IS-TEF)以及Logistic测试覆盖率函数(LO-TCF)带入该建模框架,建立了一个新的软件可靠性增长模型,即IS-LO-SRGM.同时,还对利用该框架进行建模过程中的两个重要问题进行了描述与分析,即如何确定具体的TEF和TCF以及模型参数估计.然后,在两组真实的失效数据集上,利用该建模框架建立了最为合适的增长模型,即IS-LO-SRGM,并将该模型与8种经典NHPP模型进行对比.实例验证结果表明,所提出的IS-LO-SRGM模型具有最为优秀的拟合与预计性能,从而证明新建模框架的有效性和实用性.最后,对不完美排错情况进行了初步的讨论与建模分析.     

A new fuzzy rule based algorithm for estimating software faults in early phase of development

Estimation of reliability and the number of faults present in software in its early development phase, i.e., requirement analysis or design phase is very beneficial for developing reliable software with optimal cost. Software reliability prediction in early phase of development is highly desirable to the stake holders, software developers, managers and end users. Since, the failure data are unavailable in early phase of software development, different reliability relevant software metrics and similar project data are used to develop models for early software fault prediction. The proposed model uses the linguistic values of software metrics in fuzzy inference system to predict the total number of faults present in software in its requirement analysis phase. Considering specific target reliability, weightage of each input software metrics and size of software, an algorithm has been proposed here for developing general fuzzy rule base. For model validation of the proposed model, 20 real software project data have been used here. The linguistic values from four software metrics related to requirement analysis phase have been considered as model inputs. The performance of the proposed model has been compared with two existing early software fault prediction models.     

可靠性模型中故障检测率研究述评

故障检测率FDR（Fault Detection Rate）是可靠性研究的关键要素,对于测试环境构建、故障检测效率提升、可靠性建模和可靠性增长具有重要作用,对于提高系统可靠性与确定发布时间具有重要现实意义.首先,对基于NHPP（Non-Homogeneous Poisson Process,非齐次泊松过程）类的软件可靠性增长模型SRGM（Software Reliability Growth Mode）进行概述,给出了建模本质、功用与流程.基于此,引出可靠性建模与研究中的关键参数——FDR,给出定义,对测试环境描述能力进行分析,展示不同模型的差异.着重剖析了FDR与失效强度、冒险率（风险率）的区别,得出三者之间的关联性表述.全面梳理了FDR的大类模型,分别从测试覆盖函数视角、直接设定角度、测试工作量函数参与构成方式三个方面进行剖析,继而提出统一的FDR相关的可靠性模型.考虑到对真实测试环境描述能力需要,建立不完美排错框架模型,衍生出不完美排错下多个不同FDR参与的可靠性增长模型.进一步,在12个真实描述应用场景与公开发表的失效数据集上进行实验,验证不同FDR模型相关的可靠性模型效用,对差异性进行分析与讨论.结果表明,FDR模型自身的性能可以支撑可靠性模型性能的提升.最后,指出了未来研究趋势和需要解决的问题.     

Analysis of Software Fault Removal Policies Using a Non-Homogeneous Continuous Time Markov Chain

Software reliability is an important metric that quantifies the quality of a software product and is inversely related to the residual number of faults in the system. Fault removal is a critical process in achieving desired level of quality before software deployment in the field. Conventional software reliability models assume that the time to remove a fault is negligible and that the fault removal process is perfect. In this paper we examine various kinds of fault removal policies, and analyze their effect on the residual number of faults at the end of the testing process, using a non-homogeneous continuous time Markov chain. The fault removal rate is initially assumed to be constant, and it is subsequently extended to cover time and state dependencies. We then extend the non-homogeneous continuous time Markov chain (NHCTMC) framework to include imperfections in the fault removal process. A method to compute the failure intensity of the software in the presence of explicit fault removal is also proposed. The fault removal scenarios can be easily incorporated using the state-space view of the non-homogeneous Poisson process.     

考虑故障相关的软件可靠性增长模型研究

软件可靠性增长模型是用来评估和预测软件可靠性的重要工具.目前,绝大多数的软件可靠性增长模型并没有考虑故障之间的相关性,也没有考虑测试环境和运行环境的区别.文中提出了一种随机过程类非齐次泊松过程(NHPP)中的考虑故障相关性、测试环境和运行环境差别的模型.在两组失效数据上的实验分析表明:对这两组失效数据,文中提出的模型比其他一些非齐次泊松过程类模型的拟合效果和预测效果更好.     

Enhancing and measuring the predictive capabilities of testing-effort dependent software reliability models

Software testing is necessary to accomplish highly reliable software systems. If the project manager can conduct well-planned testing activities, the consumption of related testing-resources will be cost-effective. Over the past 30 years, many software reliability growth models (SRGMs) have been proposed to estimate the reliability growth of software, and they are mostly applicable to the late stages of testing in software development. Thus far, it appears that most SRGMs do not take possible changes of testing-effort consumption rates into consideration. However, in some cases, the policies of testing-resource allocation could be changed or adjusted. Thus, in this paper, we will incorporate the important concept of multiple change-points into Weibull-type testing-effort functions. The applicability and performance of the proposed models are demonstrated through two real data sets. Experimental results show that the proposed models give a fairly accurate prediction capability. Finally, based on the proposed SRGM, constructive rules are developed for determining optimal software release times.