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。     

A mathematical modeling framework for software reliability testing†

Software reliability testing refers to various software testing activities that are driven to achieve a quantitative reliability goal given a priori or lead to a quantitative reliability assessment for the software under test. In this paper we develop a modeling framework for the software reliability testing process, comprising a simplifying model and a generalized model. In both models the software testing action selection process and the defect removal mechanism are explicitly described. Both the discrete-time domain and the continuous-time domain are involved. The generalized model is more accurate or realistic than the simplifying model since the former avoids the assumption that defects are equally detectable and the assumption that defects are removed upon being detected. However simulation examples show that the simplifying model really captures some of essential features of the software testing process after a short initial testing stage. The modeling framework is practically realistic, mathematically rigorous, and quantitatively precise. It demonstrates that the relationship between software testing and delivered software reliability, which was poor understood, can well be formulated and quantified. Rigorous examinations show that several common assumptions adopted in software reliability modeling, including the independence assumption, the exponentiality assumption, and the NHPP assumption, are theoretically false in general. This paper sets a good starting point to further formalize and quantify the software testing process and its relation to delivered software reliability.     

A quasi-renewal process for software reliability and testing costs

This paper models software reliability and testing costs using a new tool: a quasi-renewal process. It is assumed that the cost of fixing a fault during software testing phase, consists of both deterministic and incremental random parts, increases as the number of faults removed increases. Several software reliability and cost models by means of quasi-renewal processes are derived in which successive error-free times are independent and increasing by a fraction. The maximum likelihood estimates of parameters associated with these models are provided. Based on the valuable properties of quasi-renewal processes, the expected software testing and debugging cost, number of remaining faults in the software, and mean error-free time after testing are obtained. A class of related optimization problem is then contemplated and optimum testing policies incorporating both reliability and cost measures are investigated. Finally, numerical examples are presented through a set of real testing data to illustrate the models results     

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.     

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.     

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。     

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.     

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．     

结合故障相关的软件构件NHPP可靠性模型研究

传统的NHPP类模型是评价软件可靠性的重要模型之一。通过将故障关联融入到NHPP模型中,改进了传统的GO模型。并分析了时间域模型和基于构件模型的不足,提出一种结合两种模型的方法,同时考虑了故障排除和软件体系的方面的问题,使软件可靠性模型更加接近于实际的软件系统。     

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     

Does software reliability growth behavior follow a non-homogeneous Poisson process

It is widely believed in software reliability community that software reliability growth behavior follows a non-homogeneous Poisson process (NHPP) based on analyzing the behavior of the mean of the cumulative number of observed software failures. In this paper we present two controlled software experiments to examine this belief. The behavior of the mean of the cumulative number of observed software failures and that of the corresponding variance are examined simultaneously. Both empirical observations and statistical hypothesis testing suggest that software reliability behavior does not follow a non-homogeneous Poisson process in general, and does not fit the Goel–Okumoto NHPP model in particular. Although this new finding should be further tested on other software experiments, it is reasonable to cast doubt on the validity of the NHPP framework for software reliability modeling. The importance of the work presented in this paper is not only for the new finding which is distinctly different from existing popular belief of software reliability modeling, but also for the adopted research approach which is to examine the behavior of the mean and that of the corresponding variance simultaneously on basis of controlled software experiments.     

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.     

潜伏故障点不完美覆盖的软件可靠性增长模型

现有的基于测试覆盖率的非齐次泊松过程（NHPP）类软件可靠性增长模型绝大多数都没有考虑到潜伏故障点不完美覆盖的情况。提出了一种考虑潜伏故障点不完美覆盖的软件可靠性NHPP增长模型,称之为UPNHPP模型。在一组失效数据上的实验分析表明,对这组数据,UPNHPP模型与其他模型相比有更好的拟合效果。     

A time/structure based software reliability model

The past 20 years have seen the formulation of numerous analytical software reliability models for estimating the reliability growth of a software product. The predictions obtained by applying these models tend to be optimistic due to the inaccuracies in the operational profile, and saturation effect of testing. Incorporating knowledge gained about some structural attribute of the code, such as test coverage, into the time-domain models can help alleviate this optimistic trend. In this paper we present an enhanced non-homogeneous Poisson process (ENHPP) model which incorporates explicitly the time-varying test-coverage function in its analytical formulation, and provides for defective fault detection and test coverage during the testing and operational phases. It also allows for a time varying fault detection rate. The ENHPP model offers a unifying framework for all the previously reported finite failure NHPP models via test coverage. We also propose the log-logistic coverage function which can capture an increasing/decreasing failure detection rate per fault, which cannot be accounted for by the previously reported finite failure NHPP models. We present a methodology based on the ENHPP model for reliability prediction earlier in the testing phase. Expressions for predictions in the operational phase of the software, software availability, and optimal software release times subject to various constraints such as cost, reliability, and availability are developed based on the ENHPP model. We also validate the ENHPP model based on four different coverage functions using five failure data sets. This revised version was published online in June 2006 with corrections to the Cover Date.     

A unified scheme of some Nonhomogenous Poisson process models for software reliability estimation

In this paper, we describe how several existing software reliability growth models based on Nonhomogeneous Poisson processes (NHPPs) can be comprehensively derived by applying the concept of weighted arithmetic, weighted geometric, or weighted harmonic mean. Furthermore, based on these three weighted means, we thus propose a more general NHPP model from the quasi arithmetic viewpoint. In addition to the above three means, we formulate a more general transformation that includes a parametric family of power transformations. Under this general framework, we verify the existing NHPP models and derive several new NHPP models. We show that these approaches cover a number of well-known models under different conditions.     

基于排错等待延迟的广义动态集成神经网络模型

软件可靠性增长模型在可靠性评估与保障中具有重要作用,针对软件测试过程中的故障检测和排错等待延迟问题,提出了一种考虑故障排错等待延迟的广义动态集成神经网络模型(RWD-SRGM)。该模型考虑软件工程的多样性,利用神经网络方法构建广义动态集成模型,并考虑排错等待延迟现象完成故障检测和预测。通过2组真实失效数据集(DS1和DS2)的实验,将所提模型与现有的软件可靠性增长模型进行了比较,结果显示考虑故障排错等待延迟的神经网络模型拟合效果最优,表现出了更好的软件可靠性评估性能和模型通用性。     

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.