一种基于马尔可夫模型的软件可靠性评估方法

针对目前软件可靠性不易评估的特点,建立一种基于马儿可夫链的软件可靠性评估模型。该模型在软件运行流程图的框架下,利用一定的统计学方法,使用线性代数方法来计算软件运行流程中各个状态的概率,建立软件可靠性评估模型,从而计算软件的可靠性;最后,利用软件设计时的判别准则来判断软件是否符合需求。     

A Bayes nonparametric framework for software-reliability analysis

This paper presents a Bayes nonparametric approach for tracking and predicting software reliability. We use the common assumptions on the software operational environment to get a stochastic model where the successive times between software failures are exponentially distributed; their failure rates have Markov priors. Under these general assumptions we give Bayes estimates of the parameters that assess and predict the software reliability. We give algorithms (based on Monte-Carlo methods) to compute these Bayes estimates. Our approach allows the reliability analyst to construct a personal software reliability model simply by specifying the available prior knowledge; afterwards the results in this paper can be used to get Bayes estimates of the useful reliability parameters. Examples of possible prior physical knowledge concerning the software testing and correction environments are given. The maximum-entropy principle is used to translate this knowledge to prior distributions on the failure-rate process. Our approach is used to study some simulated and real failure data sets     

A software-reliability growth model for N-version programmingsystems

This paper presents a NHPP-based SRGM (software reliability growth model) for NVP (N-version programming) systems (NVP-SRGM) based on the NHPP (nonhomogeneous Poisson process). Although many papers have been devoted to modeling NVP-system reliability, most of them consider only the stable reliability, i.e., they do not consider the reliability growth in NVP systems due to continuous removal of faults from software versions. The model in this paper is the first reliability-growth model for NVP systems which considers the error-introduction rate and the error-removal efficiency. During testing and debugging, when a software fault is found, a debugging effort is devoted to remove this fault. Due to the high complexity of the software, this fault might not be successfully removed, and new faults might be introduced into the software. By applying a generalized NHPP model into the NVP system, a new NVP-SRGM is established, in which the multi-version coincident failures are well modeled. A simplified software control logic for a water-reservoir control system illustrates how to apply this new software reliability model. The s-confidence bounds are provided for system-reliability estimation. This software reliability model can be used to evaluate the reliability and to predict the performance of NVP systems. More application is needed to validate fully the proposed NVP-SRGM for quantifying the reliability of fault-tolerant software systems in a general industrial setting. As the first model of its kind in NVP reliability-growth modeling, the proposed NVP SRGM can be used to overcome the shortcomings of the independent reliability model. It predicts the system reliability more accurately than the independent model and can be used to help determine when to stop testing, which is a key question in the testing and debugging phase of the NVP system-development life cycle     

Reliability growth models for hardware and software systems based on nonhomogeneous Poisson processes: A survey

We summarize the reliability growth models for hardware and software systems described by a stochastic process, where the underlying stochastic process is assumed to be a nonhomogeneous Poisson process (NHPP). The background of reliability growth modelling based on an NHPP is surveyed. The Duane model, which was first postulated as a reliability growth model and is commonly used, is first explained. Secondly, the Weibull growth and modified Weibull growth models for hardware systems and the exponential type growth and gamma type growth models for error detection for software systems are discussed. The parameter estimates can be obtained by maximum likelihood estimation. Finally, the goodness-of-fit tests based on chi-square, Cramér-von Mises and Kolmogorov-Smirnov statistics are presented for the reliability growth models based on an NHPP.     

Modeling and analysis of correlated software failures of multiple types

Most software reliability models assume independence of successive software runs. It is a strict assumption, and usually not valid in reality. Goseva-Popstojanova & Trivedi (2000) presented an interesting study on failure correlation among successive software runs. In this paper, by extending their results, a software reliability model is developed based on a Markov renewal process for the modeling of the dependence among successive software runs, where more than one type of failure is allowed in general formulation. Meanwhile, the cases of restarting with repair, and without repair, are considered. Although such a model is more complex than the traditional approach based on reliability growth, it incorporates more information about the failures, and system structure. A numerical example is also shown to illustrate the procedure, and provide some comparison.     

Analytical Models for Architecture-Based Software Reliability Prediction: A Unification Framework

Traditional approaches to software reliability modeling are black box-based; that is, the software system is considered as a whole, and only its interactions with the outside world are modeled without looking into its internal structure. The black box approach is adequate to characterize the reliability of monolithic, custom, built-to-specification software applications. However, with the widespread use of object oriented systems design & development, the use of component-based software development is on the rise. Software systems are developed in a heterogeneous (multiple teams in different environments) fashion, and hence it may be inappropriate to model the overall failure process of such systems using one of the several software reliability growth models (black box approach). Predicting the reliability of a software system based on its architecture, and the failure behavior of its components, is thus essential. Most of the research efforts in predicting the reliability of a software system based on its architecture have been focused on developing analytical or state-based models. However, the development of state-based models has been mostly ad hoc with little or no effort devoted towards establishing a unifying framework which compares & contrasts these models. Also, to the best of our knowledge, no attempt has been made to offer an insight into how these models might be applied to real software applications. This paper proposes a unifying framework for state-based models for architecture-based software reliability prediction. The state-based models we consider are the ones in which application architecture is represented either as a discrete time Markov chain (DTMC), or a continuous time Markov chain (CTMC). We illustrate the DTMC-based, and CTMC-based models using examples. A detailed discussion of how the parameters of each model may be estimated, and the life cycle phases when the model may be applied is also provided     

Analysis of incorporating logistic testing-effort function intosoftware reliability modeling

This paper investigates a SRGM (software reliability growth model) based on the NHPP (nonhomogeneous Poisson process) which incorporates a logistic testing-effort function. SRGM proposed in the literature consider the amount of testing-effort spent on software testing which can be depicted as an exponential curve, a Rayleigh curve, or a Weibull curve. However, it might not be appropriate to represent the consumption curve for testing-effort by one of those curves in some software development environments. Therefore, this paper shows that a logistic testing-effort function can be expressed as a software-development/test-effort curve and that it gives a good predictive capability based on real failure-data. Parameters are estimated, and experiments performed on actual test/debug data sets. Results from applications to a real data set are analyzed and compared with other existing models to show that the proposed model predicts better. In addition, an optimal software release policy for this model, based on cost-reliability criteria, is proposed     

Optimal release time for software systems considering cost, testing-effort, and test efficiency

In this paper, we study the impact of software testing effort & efficiency on the modeling of software reliability, including the cost for optimal release time. This paper presents two important issues in software reliability modeling & software reliability economics: testing effort, and efficiency. First, we propose a generalized logistic testing-effort function that enjoys the advantage of relating work profile more directly to the natural flow of software development, and can be used to describe the possible testing-effort patterns. Furthermore, we incorporate the generalized logistic testing-effort function into software reliability modeling, and evaluate its fault-prediction capability through several numerical experiments based on real data. Secondly, we address the effects of new testing techniques or tools for increasing the efficiency of software testing. Based on the proposed software reliability model, we present a software cost model to reflect the effectiveness of introducing new technologies. Numerical examples & related data analyzes are presented in detail. From the experimental results, we obtain a software economic policy which provides a comprehensive analysis of software based on cost & test efficiency. Moreover, the policy can also help project managers determine when to stop testing for market release at the right time.     

A testing-effort dependent software reliability model and its application

We discuss a software reliability growth model with testing-effort based on a nonhomogeneous Poisson process and its application to a testing-effort control problem. The time-dependent behaviour of testing-effort expenditures which is incorporated into software reliability growth is expressed by a Weibull curve due to the flexibility in describing a number of testing-effort expenditure patterns. Using several sets of actual software error data, the model fitting and examples of a testing-effort control problem are illustrated.     

随机Petri网在软件可靠性分析中的应用

软件可靠性模型对于软件可靠性估测起着核心的作用。目前所提出的模型大多有着一定的应用条件和适用范围,不能适应复杂多变的应用环境的要求,在客观上为软件可靠性模型的应用提出了新的问题。提出了一种基于随机Petri网的软件可靠性分析方法,该方法有利于降低可靠性描述与分析的复杂度,提高评价和预测可靠性的精确度。同时指出该方法在应用中会遇到的某些问题及其解决方法。     

基于Markov过程的硬/软件综合系统可靠性分析

现代大型监控系统通常是一个复杂的硬/软件综合系统,其可靠性分析对于系统的设计、评估具有重要意义.综合考虑硬件、软件特点以及两者之间的相互作用关系,提出一种基于Markov过程的综合系统可靠性分析模型,模型中将系统失效分为硬件失效、软件失效与硬/软件结合失效.实际应用中,由于系统的状态数较大,提出利用循环网络方法对Markov状态转移方程进行求解,从而方便地得到系统处于各状态的瞬时概率与稳态概率.通过分析硬/软件综合系统可靠度、可用度与系统可靠性参数之间的关系,指出硬/软件结合失效将影响系统可用度,忽略硬/软件结合失效将导致可靠性估计值偏离实际值.     

组合导航设备实时多任务软件可靠性分配

本文对软件的复杂性、强度及重要度进行了分析,针对实时多任务软件的具体特点,提出了一种基于任务模块的软件可靠性指标分配模型以及计算方法。针对某一组合导航系统应用软件,采用上述模型进行软件可靠性指标分配计算。结果表明,在保证系统可靠性的前提下,能够实现各子任务可靠性指标的合理分配。     

Optimal allocation and control problems for software-testingresources

Two kinds of software-testing management problems are considered: testing-resource allocation to best use specified testing resources during module testing, and a testing-resource control problem concerning how to spend the allocated amount of testing-resource expenditures during it. A software reliability growth model based on a nonhomogeneous Poisson process is introduced. The model describes the time-dependent behavior of software errors detected and testing-resource expenditures spent during the testing. The optimal allocation and control of testing resources among software modules can improve reliability and shorten the testing stage. Based on the model, numerical examples of these two software testing management problems are presented     

A New Methodology for Predicting Software Reliability in the Random Field Environments

This paper presents a new methodology for predicting software reliability in the field environment. Our work differs from some existing models that assume a constant failure detection rate for software testing and field operation environments, as this new methodology considers the random environmental effects on software reliability. Assuming that all the random effects of the field environments can be captured by a unit-free environmental factor,$eta$, which is modeled as a random-distributed variable, we establish a generalized random field environment (RFE) software reliability model that covers both the testing phase and the operating phase in the software development cycle. Based on the generalized RFE model, two specific random field environmental reliability models are proposed for predicting software reliability in the field environment: the$gamma$-RFE model, and the$beta$-RFE model. A set of software failure data from a telecommunication software application is used to illustrate the proposed models, both of which provide very good fittings to the software failures in both testing and operation environments. This new methodology provides a viable way to model the user environments, and further makes adjustments to the reliability prediction for similar software products. Based on the generalized software reliability model, further work may include the development of software cost models and the optimum software release policies under random field environments.     

Why failure rates observe Zipf's law in operational software

The author proposes a model showing how software developers, when attempting to produce software of a given reliability level with a minimum of resources, create software whose fault content observes Phillip's and Zipf's laws. He also proposes a software reliability model based on Zipf's law that fits Adam's reliability data on nine software systems with an average correlation coefficient of 0.986. He concludes that software, when and only when optimally developed, displays operational reliability patterns conforming to Zipf's law     

A stochastic model of fault introduction and removal duringsoftware development

Two broad categories of human error occur during software development: (1) development errors made during requirements analysis, design, and coding activities; (2) debugging errors made during attempts to remove faults identified during software inspections and dynamic testing. This paper describes a stochastic model that relates the software failure intensity function to development and debugging error occurrence throughout all software life-cycle phases. Software failure intensity is related to development and debugging errors because data on development and debugging errors are available early in the software life-cycle and can be used to create early predictions of software reliability. Software reliability then becomes a variable which can be controlled up front, viz, as early as possible in the software development life-cycle. The model parameters were derived based on data reported in the open literature. A procedure to account for the impact of influencing factors (e.g., experience, schedule pressure) on the parameters of this stochastic model is suggested. This procedure is based on the success likelihood methodology (SLIM). The stochastic model is then used to study the introduction and removal of faults and to calculate the consequent failure intensity value of a small-software developed using a waterfall software development     

Reliability analysis of real-time fault-tolerant task models

One notable advantage of Model-Driven Architecture (MDA) method is that software developers could do sufficient analysis and tests on software models in the design phase, which helps construct high confidence on the expected software behaviors and performance, especially for safety-critical real-time software. Most existing literature of reliability analysis ignores the effects from those deadline requirements of tasks which are critical properties for real-time software and thus cannot be ignored. Considering the contradictory relationship between the deadline requirements and time costs of fault tolerance in real-time tasks, in this paper, we present a novel reliability model, which takes schedulability as one of the major factors affecting the reliability, to analyze reliability of the task execution model in real-time software design phase. The tasks in this reliability model has no restrictions on their distributions and thus could be distributed on a multiprocessor or on a distributed system. Furthermore, the tasks also define arrival rates of faults and fault-tolerant mechanisms to model the occurrences of non-permanent faults and the corresponding time costs of fault handling. By analyzing the probability of tasks still being schedulable in the worst-case execution scenario with faults occurring, reliability and schedulability are combined into an unified analysis framework, and two algorithms for reliability analysis are given. To make this reliability model more pragmatic, we also present an estimation technique for estimating the fault arrival rate of each task. We show through two case studies respectively the detailed derivation process under static-priority scheduling in a multiprocessor system and in the design process of avionics software, and then analyze the factors affecting the reliability analysis by setting up simulation experiments. When no assumptions of fault occurrences made on the task model, this reliability model regresses to a generic schedulability model.     

基于Bayes网的软件可靠性模型研究与系统设计

传统的软件可靠性预测主要是概率方法,但其存在假设与实际不符的缺点。利用Bayes网,充分利用专家知识和清晰表达相关因素关系的优点,构建了基于Bayes网的软件可靠性预测模型。该模型不仅考虑软件不完全排错和排错时间,同时把软件可靠性因素也考虑在内,增强了其准确和有效性,并基于BN Tookit软件包以MATLAB语言通过实例给以验证。为弥补MATLAB的GUI设计不方便的缺点,给出了VC和MATLAB混合编程实现软件可靠性预测的系统设计思路。     

软件可靠性衡量体系设计

提出了一套软件可靠性衡量体系,重点研究了衡量体系中的软件可靠性建模和软件可靠性评估方法。研究了适用于软件测试阶段的Musa模型以及模型的使用前提条件、模型表示、数据要求和参数估计;同时针对软件可靠性评估的主观性和受多因素影响的特点,提出采用模糊综合评判法进行评估,给出了评估步骤和方法;最后通过实例说明如何进行可靠性建模和评估。     

考虑测试覆盖率和故障排除效率的软件可靠性增长模型

软件测试覆盖率直观地描述了软件测试的程度,现有的基于测试覆盖率的软件可靠性增长模型绝大多数都没有考虑故障的排除效率.论文把软件测试覆盖率和故障排除效率引入到软件可靠性评估过程中,建立了一个既考虑测试覆盖率,又考虑故障排除效率的非齐次泊松过程类软件可靠性增长模型,在一组失效数据上的实验分析表明:对这组失效数据,论文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更好.