Statistical software reliability prediction and its applicability based on mean time between failures

One of the most important issues for a development manager may be how to predict the reliability of a software system at an arbitrary testing time. In this paper, using the software failure-occurrence time data, we discuss a method of software reliability prediction based on software reliability growth models described by an NHPP (nonhomogeneous Poisson process). From the applied software reliability growth models, the conditional probability distribution of the time between software failures is derived, and its mean and median are obtained as reliability prediction measures. Finally, based on several numerical examples, we compare the performance between these measures from the view point of software reliability prediction in the testing phase.     

多台系统可靠性增长试验方法研究

提出了一种解决多台系统同步投试、同步停止试验和同步改进问题的新模型——指数模型．该模型充分考虑了增长过程中的各种可得信息,包括各改进阶段的失效数、未失效数和失效时间等数据．如果多台系统经过多次同步改进,并且单台系统的可靠性增长符合AMSAA模型,就可以合理地认为在每两个相邻的改进时刻之间,每台系统的失效时间服从指数分布．采用非参数方法得到多台系统在各同步停止试验时刻的可靠度,并利用最小二乘法拟合求得该模型中参数a和b的点估计值,以及参数b的置信限．通过在工程实例中对所提模型和几种已有模型计算结果的比较,说明了所提模型在解决多台系统同步可靠性增长问题中的合理性．     

Sensitivity analysis of release time of software reliability models incorporating testing effort with multiple change-points

To accurately model software failure process with software reliability growth models, incorporating testing effort has shown to be important. In fact, testing effort allocation is also a difficult issue, and it directly affects the software release time when a reliability criteria has to be met. However, with an increasing number of parameters involved in these models, the uncertainty of parameters estimated from the failure data could greatly affect the decision. Hence, it is of importance to study the impact of these model parameters. In this paper, sensitivity of the software release time is investigated through various methods, including one-factor-at-a-time approach, design of experiments and global sensitivity analysis. It is shown that the results from the first two methods may not be accurate enough for the case of complex nonlinear model. Global sensitivity analysis performs better due to the consideration of the global parameter space. The limitations of different approaches are also discussed. Finally, to avoid further excessive adjustment of software release time, interval estimation is recommended for use and it can be obtained based on the results from global sensitivity analysis.     

Effect of change point and imperfect debugging in software reliability and its optimal release policy

This article presents a software reliability growth model based on non-homogeneous Poisson process. The main focus of this article is to deliver a method for software reliability modelling incorporating the concept of time-dependent fault introduction and fault removal rate with change point. Also in this article, a cost model with change point has been developed. Based on the cost model optimal release policy with change point has been discussed. Maximum likelihood technique has been applied to estimate the parameters of the model. The proposed model has been validated using some real software failure data. Comparison has been made with models incorporating change point and without change point. The application of the proposed cost model has been shown using some numerical examples.     

Cost–benefit modelling for reliability growth

Decisions during the reliability growth development process of engineering equipment involve trade-offs between cost and risk. However slight, there exists a chance an item of equipment will not function as planned during its specified life. Consequently the producer can incur a financial penalty. To date, reliability growth research has focussed on the development of models to estimate the rate of failure from test data. Such models are used to support decisions about the effectiveness of options to improve reliability. The extension of reliability growth models to incorporate financial costs associated with ‘unreliability’ is much neglected. In this paper, we extend a Bayesian reliability growth model to include cost analysis. The rationale of the stochastic process underpinning the growth model and the cost structures are described. The ways in which this model can be used to support cost–benefit analysis during product development are discussed and illustrated through a simple case.     

Dynamic fuzzy reliability models of degraded hold-down structures for folded solar array

The hold-down structures are of considerable importance to the launch of solar array. Due to the difficulties in obtaining sufficient load specimen, it is imprecise to construct the stress as random variables. Therefore, dynamic fuzzy reliability models are developed in this paper, which resolve the problems in dealing with the interaction between the fuzzy stress process and the stochastic strength process. Even for a deterministic fuzzy stress process, the influences of material statistical properties on reliability can be affected by the level α of fuzzy stress. Meanwhile, the level α relates to investment in the collection of information about the fuzzy stress on hold-down bar. Hence, the models can be used for the economic analysis and optimal design of hold-down bar. Finally, key fuzzy parameters of stress, which have significant influences on both the reliability behavior and the effects of material statistical properties on reliability, are identified and some suggestions for the reliability enhancement of hold-down bar are provided in this paper.     

Assessing the reliability of a nanocomponent using nanocrack growth

In nanoscience and nanotechnology, much attention has been given to the dual problem of designing nanocomponents with novel physical properties and how such nanocomponents can be fabricated. Receiving less attention has been the question of the nanocomponent's reliability; how does a nanocomponent fail and how long does a nanocomponent survive under typical operating conditions? High reliability is necessary to guarantee the advancement and utilization of nanocomponents due to the fact that they account for a high proportion of costs of newly designed nanosystems as well as multiscale systems. A nanocomponent is a component that is made of atoms, and its reliability is determined by these atoms. There are situations where it is hard or impossible to extract information from a nanocomponent about its relationship to its atoms. In this article, we assess the nanocomponent's reliability by using its physical properties. Specifically, it is known that nanocrack growth involves considerable statistical variability and such variability should be accounted for assessing growth. In this paper, we first provide a stochastic nanocrack growth model and then evaluate the reliability of a nanocomponent based on this model. Various properties of this model are obtained. We also evaluate the reliability of a nanocomponent under different assumptions on our proposed growth model. This paper is a modification of the extensive literature on modeling fatigue cracks in materials on a larger scale, applied to nanoscale where growth is not a function of cumulative stress on the component but related to the time to first exceedance of a threshold. Copyright © 2013 John Wiley & Sons, Ltd.     

Enhancing software reliability modeling and prediction through the introduction of time-variable fault reduction factor

Over the past three decades, many software reliability models with different parameters, reflecting various testing characteristics, have been proposed for estimating the reliability growth of software products. We have noticed that one of the most important parameters controlling software reliability growth is the fault reduction factor (FRF) proposed by Musa. FRF is generally defined as the ratio of net fault reduction to failures experienced. During the software testing process, FRF could be influenced by many environmental factors, such as imperfect debugging, debugging time lag, etc. Thus, in this paper, we first analyze some real data to observe the trends of FRF, and consider FRF to be a time-variable function. We further study how to integrate time-variable FRF into software reliability growth modeling. Some experimental results show that the proposed models can improve the accuracy of software reliability estimation. Finally, sensitivity analyses of various optimal release times based on cost and reliability requirements are discussed. The analytic results indicate that adjusting the value of FRF may affect the release time as well as the development cost.     

可靠性系列知识讲座 第四讲:可靠性增长试验的统计分析与设计

新产品的研制工作要经历若干个阶段,每个阶段都是在前一阶段的基础上针对产品在设计、材料或工艺等方面的缺点采取改进措施,以便产品的可靠度得到提高。本文在一般公认的假定—次序约束下,综合利用各阶段的数据给出了最后阶段产品可靠度的点估计和置信下限,它比只利用最后阶数据得到的点估计和置信下限更为合理。此处,还对可靠性增长试验的设计提出了有价值的建议。     

软件可靠性M-O模型和逆线性模型的参数估计

Musa-Okumoto模型和逆线性模型是研究软件可靠性的重要模型，给出了在分组数据下，M－O模型和逆线性模型中参数的最大似然估计及其存在的充分性条件，指出了[4]中的错误，并且给出了一个实例。     

Dependency analysis in reliability studies

The reliability of engineering systems, especially safety systems,is acknowledged to be significantly affected by the dependencyof the components and subsystems. The factors that cause thedependency range from the design of the system to the maintenanceprocedures employed. Assessing the effect of dependency hasbeen a concern in both reliability theory and statistics. Mostinterest has centred on wmmoncause, or common-mode, failurebut other forms, such as time between failures, can play a majorrole. The engineering and statistical approaches to dependency havetended to diverge, and misconceptions in both assessment andmodelling have arisen. This paper constructively reviews thevarying approaches employed, and indicates future benefits thatmight accrue by the proper use of statistical methodologies.In this exploration, the pitfalls asscciated with some of thetechniques are highlighted. One of the major problems encounteredin assessing dependency is that the information d for assessmentwmes from maintenance records or incident reports which arcnot collected specifically for dependency studies. Other aspectsare the naivety of some of the models employed, which includecut-off assessment, the beta-factor, and multiple-parametermodels. Another feature, which seems to be overlooked by practitioners,is failures that are timedependent. Complementary to these practical approaches, there are a numberof statistical m e t h d that could be applied. In the recentliterature, there has been considerable work on developing multivariatemodels. There are also a variety of stochastic processes thatmight be employed. The paper examines how such models can bepractically applied to the data available, to produce a morecomprehensive understanding of dependency in the field of reliability.Particular emphasis is given to methods for identification ofdependency between components and systems, especially thosecapable of detecting time-dependent failures.     

A cross entropy approach to design of reliable networks

One of the most important parameters determining the performance of communication networks is network reliability. The network reliability strongly depends on not only topological layout of the communication networks but also reliability and availability of the communication facilities. The selection of optimal network topology is an NP-hard problem so that computation time of enumeration-based methods grows exponentially with network size. This paper presents a new solution approach based on cross-entropy method, called NCE, to design of communication networks. The design problem is to find a network topology with minimum cost such that all-terminal reliability is not less than a given level of reliability. To investigate the effectiveness of the proposed NCE, comparisons with other heuristic approaches given in the literature for the design problem are carried out in a three-stage experimental study. Computational results show that NCE is an effective heuristic approach to design of reliable networks.     

AMSAA-BISE可靠性增长模型不能成立

阐述周源泉、翁朝曦提出的AMSAA-BISE模型存在的问题,提出一个近似计算模型,并给出数值例加以说明.     

冲击次数为复合Poisson-Geometric过程的系统损伤模型及其可靠性指标

针对系统损伤模型,引入双参数的复合Poisson-Geometric过程来刻画损伤次数,是普通复合Poisson过程的一种推广,扩大其实际应用背景.针对此分布下的损伤模型,着重研究了其平均损伤、可靠度和平均寿命等可靠性指标,作为特例,给出了当损伤值满足指数分布时,各个指标的表达式.     

一种新的基于不完全排错的最优软件发行策略

软件的最优发行管理问题是软件可靠性研究的一个关键问题.现有的最优软件发行模型大都假定软件排错过程是完全的,并且在排错过程中没有新的故障引入,这种假设在很多情况下是不合理的.本文提出了一种新的最优软件发行管理模型,该模型既考虑了软件的不完全排错过程,又考虑了在排错过程中可能会引入新的故障,同时还考虑了由于排错经验的不断积累,软件的完全排错概率会增加的情况.本文同时给出了该模型的解.     

Application of fuzzy time series in prediction of time between failures &; faults in software reliability assessment

Since last seventies, various software reliability growth models (SRGMs) have been developed to estimate different measures related to quality of software like: number of remaining faults, software failure rate, reliability, cost, release time, etc. Most of the exiting SRGMs are probabilistic. These models have been developed based on various assumptions. The entire software development process is performed by human being. Also, a software can be executed in different environments. As human behavior is fuzzy and the environment is changing, the concept of fuzzy set theory is applicable in developing software reliability models. In this paper, two fuzzy time series based software reliability models have been proposed. The first one predicts the time between failures (TBFs) of software and the second one predicts the number of errors present in software. Both the models have been developed considering the software failure data as linguistic variable. Usefulness of the models has been demonstrated using real failure data.     

基于L-M方法的液压油源系统的可靠性分析

本文结合液压伺服系统的工程实际,运用了L-M方法,对恒压油源系统进行可靠性分析与建模,并给出了系统可靠度的定量评估结果,最后利用该模型对试验模拟数据进行分析,这对工程设计具有重要的指导作用。     

考虑n中连续取k失效准则的树状系统可靠性求解方法

树状网络系统在管道运输,网络通信中较为常见,对其进行可靠性评估对系统设计及优化具有重要意义。针对树状冗余系统,在n中连续取k失效准则下,通过有限马尔可夫嵌入法并对其进行变形,研究了树状系统可靠性求解方法。本文对树状系统建模加以定义,提出了基于层数参数,层-节点向量,父-子节点矩阵三元参数的树状系统表示方法,研究了变形有限马尔可夫嵌入法的树状系统n中连续取k失效准则下的可靠性求解方法,给出了三个数值算例应用并分析了算法的运算复杂度。最后,本文对比讨论了基于概率母函数法的树状系统在n中连续取k准则下系统可靠性求解方法的研究,得出结论本文算法针对树状冗余系统n中连续取k失效准则下系统可靠性求解应用范围更广,求解效率较高。     

带休假且有优先修理权的三部件串并联可修系统的分析

研究修理工带多重休假且有优先修理权的三部件串并联可修系统,其中假定系统只有一个修理工,部件可修复如新,部件1对其它部件有抢占优先修理权,其它两部件先坏先修,且打断的修理时间可以累积计算,运用补充变量的方法,在寿命分布为指数分布,维修分布为连续型分布的假定下,求得了系统的瞬态和稳态的可用度和可靠性指标,并给出一个特例.