A general modeling and analysis framework for software fault detection and correction process

Software reliability growth modeling plays an important role in software reliability evaluation. To incorporate more information and provide more accurate analysis, modeling software fault detection and correction processes has attracted widespread research attention recently. In modeling software correction processes, the assumption of fault correction time is relaxed from constant delay to random delay. However, stochastic distribution of fault correction time brings more difficulties in modeling and corresponding parameter estimation. In this paper, a framework of software reliability models containing both information from software fault detection process and correction process is studied. Different from previous extensions on software reliability growth modeling, the proposed approach is based on Markov model other than a nonhomogeneous Poisson process model. Also, parameter estimation is carried out with weighted least‐square estimation method, which emphasizes the influence of later data on the prediction. Two data sets from practical software development projects are applied with the proposed framework, which shows satisfactory performance with the results. Copyright © 2016 John Wiley & Sons, Ltd.     

运用MATLAB进行军用软件可靠性评估

军用软件的可靠性已成为影响武器装备系统质量的关键因素。介绍了非齐次泊松过程类软件可靠性增长模型的原理以及如何运用MATLAB绘制软件故障数据曲线、模型参数估计及分布拟合检验,进而建立可靠性增长模型,进行可靠性评估。     

Software Reliability Growth Modeling: Models and Applications

This paper summarizes existing software reliability growth models (SRGM's) described by nonhomogeneous Poisson processes. The SRGM's are classified in terms of the software reliability growth index of the error detection rate per error. The maximum-likelihood estimations based on the SRGM's are discussed for software reliability data analysis and software reliability evaluation. Using actual software error data observed by software testing, application examples of the existing SRGM's are illustrated.     

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。     

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.     

Statistical inference for general-order-statistics andnonhomogeneous-Poisson-process software reliability models

There are many software reliability models that are based on the times of occurrences of errors in the debugging of software. It is shown that it is possible to do asymptotic likelihood inference for software reliability models based on order statistics or nonhomogeneous Poisson processes, with asymptotic confidence levels for interval estimates of parameters. In particular, interval estimates from these models are obtained for the conditional failure rate of the software, given the data from the debugging process. The data can be grouped or ungrouped. For someone making a decision about when to market software, the conditional failure rate is an important parameter. The use of interval estimates is demonstrated for two data sets that have appeared in the literature     

基于PSO的软件可靠性模型参数估计方法

软件可靠性建模是一个重要的研究领域,现有的软件可靠性模型基本上是非线性函数模型,估计这些模型的参数比较困难。粒子群优化是一类适合求解非线性优化问题的随机优化方法,提出一种基于粒子群优化的软件可靠性模型估计参数方法,该方法的关键是构造合适的适应函数。用该方法分别估计了5个实际软件系统的指数软件可靠性模型以及对数泊松执行时间模型,实验结果表明：该方法参数估计的精度高,对模型的适应性强。     

故障检测率不规则变化的软件可靠性模型

传统的NHPP(non-homogeneous Poisson process)模型在实际的测试当中被证明是成功的.但是,由于传统的NHPP模型用的是理想的假设,例如,假设故障检测率是常数、平稳变化和规律变化,模型的性能在实际的测试环境中总是受到损害.因此,提出一个基于NHPP的软件可靠增长模型,并且考虑故障检测率的不规则变化情况,这种变化符合故障检测率在实际的软件测试过程中的变化.通过相关的实验验证了所提出的NHPP模型的拟合和预测能力.实验结果表明:在用实际的故障数据进行拟合和预测的过程中,所提出的模型与传统的NHPP模型相比,有更好的拟合和预测性能.同时,也给出了所提出模型相应的置信区间.     

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。     

A Bayesian analysis of the logarithmic-Poisson execution time modelbased on expert opinion and failure data

We propose a Bayesian approach for predicting the number of failures in a piece of software, using the logarithmic-Poisson model, a nonhomogeneous Poisson process (NHPP) commonly used for describing software failures. A similar approach can be applied to other forms of the NHPP. The key feature of the approach is that now we are able to use, in a formal manner, expert knowledge on software testing, as for example, published information on the empirical experiences of other researchers. This is accomplished by treating such information as expert opinion in the construction of a likelihood function which leads us to a joint distribution. The procedure is computationally intensive, but for the case of the logarithmic-Poisson model has been codified for use on a personal computer. We illustrate the working of the approach via some real live data on software testing. The aim is not to propose another model for software reliability assessment. Rather, we present a methodology that can be invoked with existing software reliability models     

一种基于离散时间的NHPP软件可靠性增长模型

基于非齐次泊松过程的软件可靠性增长模型按时间域可分为连续时间模型和离散时间模型两类。现有的软件可靠性增长模型大多都是针对连续时间构造的,在一定程度上忽视了对离散时间模型的研究。利用概率生成函数构建两种基于离散时间的软件可靠性增长模型——基本模型和扩展模型,具有很大的实用性和必要性。构建的扩展模型以不完美排错情形作为基础,考虑到了由于故障排除而有可能引入新故障的问题,同时还考虑到了在软件排错过程中由于测试团队的熟练程度而引起的软件故障排除率的相对变化情况,这使得提出的模型更加符合实际。最后利用两组公开发表的     

NHPP models with Markov switching for software reliability

We describe the use of a latent Markov process governing the parameters of a nonhomogeneous Poisson process (NHPP) model for characterizing the software development defect discovery process. Use of a Markov switching process allows us to characterize non-smooth variations in the rate at which defects are found, better reflecting the industrial software development environment in practice. Additionally, we propose a multivariate model for characterizing changes in the distribution of defect types that are found over time, conditional on the total number of defects. A latent Markov chain governs the evolution of probabilities of the different types. Bayesian methods via Markov chain Monte Carlo facilitate inference. We illustrate the efficacy of the methods using simulated data, then apply them to model reliability growth in a large operating system software component-based on defects discovered during the system testing phase of development.     

Software-Reliability Modeling: The Case for Deterministic Behavior

Software-reliability models (SRMs) are used for the assessment and improvement of reliability in software systems. These models are normally based on stochastic processes, with the nonhomogeneous Poisson process being one of the most prominent model forms. An underlying assumption of these models is that software failures occur randomly in time. This assumption has never been quantitatively tested. Our contribution in this paper is to conduct an experimental investigation that contrasts random processes with nonlinear deterministic processes as a model for software failures. We study two sets of real-world software-reliability data using the techniques of chaotic time-series analysis. We have found that both appear to arise from a deterministic process, rather than a stochastic process, and that both show some evidence of chaotic dynamics. In addition, we have conducted a series of k-steps-ahead forecasting experiments in the datasets, pitting a number of well-known stochastic SRMs against radial basis function networks (RBFNs), which are deterministic in nature. The out-of-sample prediction results from the RBFNs showed an improvement of roughly 25% over the best of the stochastic models, for both of our datasets. Finally, we propose a causal model to explain these results, which hypothesizes that faults in a program are distributed over a fractal subset of the program's input space     

A software cost model with imperfect debugging,random life cycle and penalty cost

The paper develops a cost model with an imperfect debugging and random life cycle as well as a penalty cost that is used to determine the optimal release policies for a software system. The software reliability model, based on the nonhomogeneous Poisson process, allows for three different error types: critical, major and minor errors. The model also allows for the introduction of any of these errors during the removal of an error. Using the software reliability model presented, the cost model with multiple error types and imperfect debugging is developed. This cost also considers the penalty cost due to delay for a scheduled delivery time and the length of the software life cycle is random with a known distribution. The optimal software release policies that minimize the expected software system costs (subject to the various constraints) or maximize the software reliability subject to a cost constraint, are then determined. Numerical examples are provided to illustrate the results.     

软件可靠性专家系统(SRES)中经验模型的奇异性问题与参数估计方法

本文作者以“一切让数据说明问题”为原则,采用人工智能技术,开发出软件可靠性专家系统ＳＲＥＳ（ＳｏｆｔｗａｒｅＲｅｌｉｂｉｌｉｔｙＥｘｐｅｒｔＳｙｓｔｅｍ）根据统一的标准,通过统一组软件可靠性模型ＳＲＭ（ＳｏｆｔｗａｒｅＲｅｌｉａｂｉｌｉｔｙＭｏｄｅｌｓ）的拟合结果,经过推理,得出一个“最适”模型,推荐给用户,作为估测该软件系统的一个“标准模型”同时为软件开发方和使用方所接受,以解决软件可靠性模型应     

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。     

Cost–reliability optimum release policies for a software system under penalty cost

Optimum software release policies are considered, minimizing the expected software cost simultaneously with the reliability requirement. Cost here also includes the penalty cost which is incurred by the manufacturer for not delivering the software at scheduled delivery time. The underlying software reliability growth models (SRGMs) are based on the non-homogeneous Poisson process (NHPP). Numerical results are also presented.     

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．