The determination of optimal software release times at different confidence levels with consideration of learning effects

As most software reliability models do not clearly explain the variance in the mean value function of cumulative software errors, they might not be effective in deducing the confidence interval regarding the mean value function. In such cases, software developers cannot estimate the possible risk variation in software reliability by using the randomness of the mean value function, thus reducing the decision‐making reliability when determining an optimal software release time. In this paper, the method of stochastic differential equations is used to build a software reliability model, which is validated based on practical data previously used in six published papers. Moreover, the estimation of the parameters of the proposed model, which can be defined as the autonomous error‐detected factor and the learning factor, is also illustrated, and the results of model validation empirically confirm that the proposed model is able to account for a fairly large portion of the variance of the mean value function. Additionally, the confidence intervals of the mean value function regarding software faults are employed to assist software developers in determining the optimal release times at different confidence levels. Finally, a numerical example is given to verify the effectiveness of the proposed model. Copyright © 2008 John Wiley & Sons, Ltd.     

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.     

软件可靠性增长模型的不确定性量化研究

数量激增的软件系统被开发出来为用户提供了极大便利性,但也给系统开发带来了极大的不确定性.故障调试过程中的故障检测率FDR（Fault Detection Rate）是不规律变化的,且通常被描述为白色噪音.白色噪音具有马儿可夫性,但是在实践中,噪音出现非马尔可夫性是普通现象,而噪音呈现马尔可夫性仅仅是例外.在许多真实情况下,白色噪声的理想化假设是不足的：真正的不规则因素总是非马尔可夫相关性的.我们提出了一个新的模型来量化调试过程相关的环境不确定性因素.基于广泛应用于软件故障检测过程的非齐次泊松过程（Non-Homogeneous Poisson Process,简称NHPP）模型,我们将环境的不确定性考虑为任意分布和时间相关性的噪声.通过与一些现有模型的比较,新的框架表现出更接近实际观测数据的特征.除了常用的关注故障数的平均值,我们提供了公式来计算其累积密度函数（CDF）和概率密度函数（PDF）,来获得调试过程的完整统计信息.     

基于区间预测模型的污水处理厂传感器故障检测

污水处理厂配备许多传感器用于监测出水水质。传感器的正常工作与否对保证出水水质至关重要。给出了一种污水处理出水变量传感器故障检测方法。该方法根据入水和出水数据,采用径向基函数神经网络构造出水变量预测模型;使用参数线性集员辨识算法得到网络输出权值的集合描述,从而使预测模型能够给出出水变量的置信区间;以此置信区间为基础获得传感器的故障检测策略。由于置信区间描述了出水变量的存在范围,当传感器测量值超出置信区间,则可推断传感器发生故障。此外,在设计传感器故障检测策略时还考虑了污水处理过程异常的影响。实验结果证实所提方法的有效性。     

Evaluation of several nonparametric bootstrap methods to estimate confidence intervals for software metrics

Sample statistics and model parameters can be used to infer the properties, or characteristics, of the underlying population in typical data-analytic situations. Confidence intervals can provide an estimate of the range within which the true value of the statistic lies. A narrow confidence interval implies low variability of the statistic, justifying a strong conclusion made from the analysis. Many statistics used in software metrics analysis do not come with theoretical formulas to allow such accuracy assessment. The Efron bootstrap statistical analysis appears to address this weakness. In this paper, we present an empirical analysis of the reliability of several Efron nonparametric bootstrap methods in assessing the accuracy of sample statistics in the context of software metrics. A brief review on the basic concept of various methods available for the estimation of statistical errors is provided, with the stated advantages of the Efron bootstrap discussed. Validations of several different bootstrap algorithms are performed across basic software metrics in both simulated and industrial software engineering contexts. It was found that the 90 percent confidence intervals for mean, median, and Spearman correlation coefficients were accurately predicted. The 90 percent confidence intervals for the variance and Pearson correlation coefficients were typically underestimated (60-70 percent confidence interval), and those for skewness and kurtosis overestimated (98-100 percent confidence interval). It was found that the Bias-corrected and accelerated bootstrap approach gave the most consistent confidence intervals, but its accuracy depended on the metric examined. A method for correcting the under-/ overestimation of bootstrap confidence intervals for small data sets is suggested, but the success of the approach was found to be inconsistent across the tested metrics.     

Interval fuzzy modeling applied to Wiener models with uncertainties.

This correspondence addresses the problem of interval fuzzy model identification and its use in the case of the robust Wiener model. The method combines a fuzzy identification methodology with some ideas from linear programming theory. On a finite set of measured data, an optimality criterion which minimizes the maximum estimation error between the data and the proposed fuzzy model output is used. The min-max optimization problem can then be seen as a linear programming problem that is solved to estimate the parameters of the fuzzy model in each fuzzy domain. This results in lower and upper fuzzy models that define the confidence interval of the observed data. The model is called the interval fuzzy model and is used to approximate the static nonlinearity in the case of the Wiener model with uncertainties. The resulting model has the potential to be used in the areas of robust control and fault detection.     

How to improve the calibration of cost models

One of software engineering's long-standing problems is to estimate the cost of a software project. Using the volume or size of a program to estimate the cost is a common practice in many software development organizations. However, in many situations one is unable to observe the value of this variable at the beginning of the project; one has to estimate it. In this paper we introduce a fairly general model which permits a surrogate or a proxy variable to be observed instead of the actual size. Under this model we obtain estimation of software cost at the given value of a surrogate variable. A confidence interval is also provided under this model     

软件可靠性增长G-O模型的改进

在传统的软件可靠性增长G-O模型中,故障检测率和初始的故障总数是影响软件可靠性的2个重要因素.为了提高软件可靠性评估的可信性,考虑到在软件纠错的过程中可能会引入新的错误,把模型中潜在的故障总数和故障检测率看作随时间变化的函数,提出了改进的G-O模型,给出了解析方法,并将改进前后的G-O模型进行了对比,通过实例进行了验证...     

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.     

基于Kullback-Leibler距离的闭环系统传感器微小故障诊断

在闭环控制系统中,当故障幅值较小时,由故障带来的影响会被控制量所掩盖.因此,闭环系统中的微小故障诊断实现更为复杂.本文针对闭环系统中的传感器故障,提出了基于Kullback-Leibler(KL)距离的微小故障在线检测与估计方法.本文首先介绍了KL距离的定义及其在多变量故障检测中的应用,然后提出了结合KL距离与快速移动窗口主成分分析(MWPCA)的在线微小故障检测与估计模型.在高斯分布的假设下,利用系统输入输出残差构造MWPCA的数据矩阵,然后通过在线更新数据矩阵主成分的均值与方差实现KL距离的在线更新,最终实现闭环系统中传感器的在线故障检测与估计.仿真实验表明,该方法能有效实现具有低故障—噪声比(FNR)特性的微小故障诊断.     

故障检测率对软件可靠性影响实证分析

故障检测率是软件可靠性模型的主要参数之一,不同形式的故障检测率具有不同的作用。聚焦于故障检测率对软件可靠性的影响,提出基于信息熵与优劣距离决策算法的单可靠性模型单失效数据集多故障检测率与多可靠性增长模型多失效数据集多故障检测率2种实证分析方案,旨在全面地分析故障检测率的影响。经过实验分析,对于单一可靠性模型单一数据集,故障检测率对软件可靠性的影响主要与失效数据集相关,在不同数据集上不同故障检测率函数的性能差异较大;在多可靠性模型多数据集上,幂函数与S型故障检测率对应的软件可靠性模型的综合性能较好,指数型故障检测率对应的软件可靠性模型的综合性能较差。本文的研究对于软件可靠性建模中的模型参数选择、最优发布时间的确定等具有较强的指导作用。     

Software size estimation of object-oriented systems

The strengths and weaknesses of existing size estimation techniques are discussed. The nature of software size estimation is considered. The proposed method takes advantage of a characteristic of object-oriented systems, the natural correspondence between specification and implementation, in order to enable users to come up with better size estimates at early stages of the software development cycle. Through a statistical approach the method also provides a confidence interval for the derived size estimates. The relation between the presented software sizing model and project cost estimation is also considered     

基于节点相似性的WSNs故障检测方法研究

针对目前多数无线传感器网络分布式故障检测的算法都以假设故障节点数据为离群值为基础,存在局限性的问题。提出一种基于节点相似度比较的无线传感器网络故障检测方法,簇头节点根据簇内节点数据的时空相关性,进行节点相似性度量,实时调整节点可信水平,并采用最优函数计算出当前实验的最优阈值(0.8)进行故障节点的判断。通过仿真实验证明:针对不同的故障模型,算法保持了良好的故障检测能力,一定程度上解决通用性问题。     

瑞利分布的可靠性分析

基于逐步增加Ⅱ型截尾样本,研究了瑞利分布可靠性指标的贝叶斯估计及其容许性。在不同的损失函数下给出了分布参数、可靠度函数、失效率函数的贝叶斯估计及参数的最短可信区间估计,并证明了贝叶斯估计具有容许性。最后运用蒙特卡洛方法对各结果的均方误差进行了比较。     

Neural networks for modelling and fault detection of the inter-stand strip tension of a cold tandem mill

This paper deals with the multilayered approach of the high-order neural network applied in a robust fault detection scheme. To introduce dynamic properties in these networks, a dynamic high-order neural unit is presented. It is shown that these networks can approximate any function with less parameters than in the case of multi-layer perceptron neural network. Such networks have good modelling properties, which make them useful for designing residuals in fault detection of dynamic processes. A method of computing a variable threshold derived from the confidence interval prediction is applied in order to obtain robustness in the fault detection process. Application of these networks for system identification and robust fault detection of the inter-stand strip tension of a continuous five stands cold mill is presented in the final part.     

基于构件的可信软件系统冗余机制及可靠性分析

在高可信软件的设计和开发中,软件容错是提高系统可信性的一种实现技术之一. 容错性就是指软件在故障出现时保证提供服务的能力,对退化故障进行容错的一种处理方式就是依靠冗余技术. 本文在分析结构冗余及其对可信性的影响的基础上,在基于构件的可信软件系统中提出了对核心构件进行冗余的机制,包括单个构件的双模冗余结构、组合构件的双模冗余结构和构件的三取二冗余及其扩展结构,并给出了其故障检测和判断方法. 同时,在各种冗余结构的基础上对系统可靠性能进行分析.     

基于SαS分布参数估计的系统鲁棒故障检测

因为复杂系统难以建立精确的数学模型,基于模型的故障检测方法在实际复杂控制系统中应用时往往难以获得很好的效果。针对这类数学模型未知的非线性系统,提出了一种基于SαS分布参数估计的系统故障检测方法。首先应用预测方法对系统输出序列进行预测建模,利用预测误差放大信号的脉冲突变,然后利用SαS分布的参数估计方法对预测误差序列的参数α进行估计,获得α的变化曲线,根据α的变化可以直观地判断出故障的发生。该方法对大幅值的有色噪声污染的信号仍然有很好的检测鲁棒性。以轴承系统的故障检测为例进行仿真实验,通过分析轴承振动信号故障条件下α曲线的变化情况,判断轴承的故障状态。仿真结果证实了该方法有效且可行。     

一种结合Bayes估计的NHPP航班查询软件可靠性评估方法

从航班查询系统故障的监控日志出发,分析了航班查询系统的故障数与其发生的时间间隔区间的关系,建立了NHPP模型。为了使NHPP模型能够更加准确地反映时间对航班查询系统的故障数的影响,对航班查询系统的寿命总体分布函数F(t)进行贝叶斯估计。当不重复采样时,贝叶斯估计取F(t)的先验分布为DP(α,P0),使得F(t)后验分布容易分析计算,从而使NHPP模型的估计更为精确。利用实际监控数据进行仿真,对模型进行了实现,结果表明了该模型对可靠性评估有较高的准确度。     

Design of a bilinear fault detection observer for singular bilinear systems

A bilinear fault detection observer is proposed for a class of continuous time singular bilinear systems subject to unknown input disturbance and fault. By singular value decomposition on the original system, a bilinear fault detection observer is proposed for the decomposed system via an algebraic Riccati equation, and the domain of attraction of the state estimation error is estimated. A design procedure is presented to determine the fault detection threshold. A model of flexible joint robot is used to demonstrate the effectiveness of the proposed method.     

Confidence estimation methods for neural networks: a practicalcomparison

Feedforward neural networks, particularly multilayer perceptrons, are widely used in regression and classification tasks. A reliable and practical measure of prediction confidence is essential. In this work three alternative approaches to prediction confidence estimation are presented and compared. The three methods are the maximum likelihood, approximate Bayesian, and the bootstrap technique. We consider prediction uncertainty owing to both data noise and model parameter misspecification. The methods are tested on a number of controlled artificial problems and a real, industrial regression application, the prediction of paper "curl". Confidence estimation performance is assessed by calculating the mean and standard deviation of the prediction interval coverage probability. We show that treating data noise variance as a function of the inputs is appropriate for the curl prediction task. Moreover, we show that the mean coverage probability can only gauge confidence estimation performance as an average over the input space, i.e., global performance and that the standard deviation of the coverage is unreliable as a measure of local performance. The approximate Bayesian approach is found to perform better in terms of global performance.