One-Sample Bayesian Predictive Analyses for a Nonhomogeneous Poisson Process with Delayed S-Shaped Intensity Function Using Non-Informative Priors

The delayed S-shaped software reliability growth model (SRGM) is one of the non-homogeneous Poisson process (NHPP) models which have been proposed for software reliability assessment. The model is distinctive because it has a mean value function that reflects the delay in failure reporting: there is a delay between failure detection and reporting time. The model captures error detection, isolation, and removal processes, thus is appropriate for software reliability analysis. Predictive analysis in software testing is useful in modifying, debugging, and determining when to terminate software development testing processes. However, Bayesian predictive analyses on the delayed S-shaped model have not been extensively explored. This paper uses the delayed S-shaped SRGM to address four issues in one-sample prediction associated with the software development testing process. Bayesian approach based on non-informative priors was used to derive explicit solutions for the four issues, and the developed methodologies were illustrated using real data.

Nonlinear Modeling for a Two-Stage Degradation System Based on Nonhomogeneous Poisson Process

The degradation process modeling is one of research hotspots of prognostic and health management(PHM),which can be used to estimate system reliability and remaining useful life(RUL).In order to study system degradation process,cumulative damage model is used for degradation modeling.Assuming that damage increment is Gamma distribution,shock counting subjects to a homogeneous Poisson process(HPP)when degradation process is linear,and shock counting is a non-homogeneous Poisson process(NHPP)when degradation process is nonlinear.A two-stage degradation system is considered in this paper,for which the degradation process is linear in the first stage and the degradation process is nonlinear in the second stage.A nonlinear modeling method for considered system is put forward,and reliability model and remaining useful life model are established.A case study is given to validate the veracities of established models.

Incorporating S-shaped testing-effort functions into NHPP software reliability model with imperfect debugging

Testing-effort（TE） and imperfect debugging（ID） in the reliability modeling process may further improve the fitting and prediction results of software reliability growth models（SRGMs）. For describing the S-shaped varying trend of TE increasing rate more accurately, first, two S-shaped testing-effort functions（TEFs）, i.e.,delayed S-shaped TEF（DS-TEF） and inflected S-shaped TEF（IS-TEF）, are proposed. Then these two TEFs are incorporated into various types（exponential-type, delayed S-shaped and inflected S-shaped） of non-homogeneous Poisson process（NHPP）SRGMs with two forms of ID respectively for obtaining a series of new NHPP SRGMs which consider S-shaped TEFs as well as ID. Finally these new SRGMs and several comparison NHPP SRGMs are applied into four real failure data-sets respectively for investigating the fitting and prediction power of these new SRGMs.The experimental results show that：（i） the proposed IS-TEF is more suitable and flexible for describing the consumption of TE than the previous TEFs;（ii） incorporating TEFs into the inflected S-shaped NHPP SRGM may be more effective and appropriate compared with the exponential-type and the delayed S-shaped NHPP SRGMs;（iii） the inflected S-shaped NHPP SRGM considering both IS-TEF and ID yields the most accurate fitting and prediction results than the other comparison NHPP SRGMs.

Grey-based approach for estimating software reliability under nonhomogeneous Poisson process

Due to the randomness and time dependence of the factors affecting software reliability, most software reliability models are treated as stochastic processes, and the non-homogeneous Poisson process(NHPP) is the most used one.However, the failure behavior of software does not follow the NHPP in a statistically rigorous manner, and the pure random method might be not enough to describe the software failure behavior. To solve these problems, this paper proposes a new integrated approach that combines stochastic process and grey system theory to describe the failure behavior of software. A grey NHPP software reliability model is put forward in a discrete form, and a grey-based approach for estimating software reliability under the NHPP is proposed as a nonlinear multi-objective programming problem. Finally, four grey NHPP software reliability models are applied to four real datasets, the dynamic R-square and predictive relative error are calculated. Comparing with the original single NHPP software reliability model, it is found that the modeling using the integrated approach has a higher prediction accuracy of software reliability. Therefore, there is the characteristics of grey uncertain information in the NHPP software reliability models, and exploiting the latent grey uncertain information might lead to more accurate software reliability estimation.

Software Reliability Growth Model for Imperfect Debugging Process Considering Testing-Effort and Testing Coverage

Because of the inevitable debugging lag,imperfect debugging process is used to replace perfect debugging process in the analysis of software reliability growth model.Considering neither testing-effort nor testing coverage can describe software reliability for imperfect debugging completely,by hybridizing testing-effort with testing coverage under imperfect debugging,this paper proposes a new model named GMW-LO-ID.Under the assumption that the number of faults is proportional to the current number of detected faults,this model combines generalized modified Weibull(GMW)testing-effort function with logistic(LO)testing coverage function,and inherits GMW's amazing flexibility and LO's high fitting precision.Furthermore,the fitting accuracy and predictive power are verified by two series of experiments and we can draw a conclusion that our model fits the actual failure data better and predicts the software future behavior better than other ten traditional models,which only consider one or two points of testing-effort,testing coverage and imperfect debugging.

An Improved NHPP Model with Time-Varying Fault Removal Delay

In this paper, an improved NHPP model is proposed by replacing constant fault removal time with time-varying fault removal delay in NHPP model, proposed by Daniel R Jeske. In our model, a time-dependent delay function is established to fit the fault removal process. By using two sets of practical data, the descriptive and predictive abilities of the improved NHPP model are compared with those of the NHPP model, G-O model, and delayed S-shape model. The results show that the improved model can fit and predict the data better.

考虑不完美排错情况的NHPP类软件可靠性增长模型

针对现有NHPP类软件可靠性增长模型对故障排错过程中不完美排错情况考虑不完全的现状,提出了一种新的软件可靠性增长模型.该模型全面考虑了不完美排错的两种情况:既考虑了排错过程中引入新错误的可能性,又考虑了不完全排错的情况,并且引入了一种故障排除率随时间变化的故障排除率函数,使模型更符合实际情况.利用公开发表的两组不同的软件失效数据对该模型进行验证的结果表明,与现有的对不完美排错情况考虑不完全的模型相比,该模型能够取得更好的拟合结果和预测效果.

基于NHPP类模型的Web软件可靠性分析

结合Web软件运行的实际情况,提出一种基于BurrX测试工作量函数(TEF)的非齐次泊松过程类软件可靠性增长模型(SRGM),并将其应用到Web软件可靠性分析中。TEF能直接体现Web软件工作量与日历时间之间的关系,解决Web软件因工作量高度不均衡导致的问题。实验结果表明,与G-O模型相比,SRGM具有较好的Web软件可靠性评估效果,能较准确地描述Web软件运行的失效过程。

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失效数据集对两种模型与指数模型和S型模型进行对比验证,验证结果表明提出的两种模型具有更好的拟合能力和预测效果。

Discrete Software Reliability Growth Modeling for Errors of Different Severity Incorporating Change-point Concept

Several software reliability growth models （SRGM） have been developed to monitor the reliability growth during the testing phase of software development. In most of the existing research available in the literatures, it is considered that a similar testing effort is required on each debugging effort. However, in practice, different types of faults may require different amounts of testing efforts for their detection and removal. Consequently, faults are classified into three categories on the basis of severity： simple, hard and complex. This categorization may be extended to r type of faults on the basis of severity. Although some existing research in the literatures has incorporated this concept that fault removal rate （FRR） is different for different types of faults, they assume that the FRR remains constant during the overall testing period. On the contrary, it has been observed that as testing progresses, FRR changes due to changing testing strategy, skill, environment and personnel resources. In this paper, a general discrete SRGM is proposed for errors of different severity in software systems using the change-point concept. Then, the models are formulated for two particular environments. The models were validated on two real-life data sets. The results show better fit and wider applicability of the proposed models as to different types of failure datasets.

NHPP软件可靠性模型的推广

在一般的意义上对一类非齐次泊松过程模型作了推广,用多项式函数来拟合纠错经验函数,在一定程度上简化了模型的选择.给出了上述推广的可行性的证明,并对模型参数的性质进行了讨论.

劣化系统周期预防性维修策略的优化

以长期运行费用率为评估指标,研究了劣化系统的周期预防性维修策略。假定开展的周期预防性维修介于最小维修和完全维修之间,维修间隔期间的故障过程用非齐次泊松过程进行描述,在此基础上采用比例寿命回退模型对预防性维修效果进行建模,给出了最佳预防性维修周期T和预防性维修次数N的计算方法以及参数应当满足的条件,同时结合实际情况给出了(N,T)策略的优化求解算法,最后通过数值算例,验证了所提方法的可行性。

考虑软件不同失效过程偏差的软件可靠性模型

软件可靠性分析是根据软件失效数据等信息,通过合理建模来对软件可靠性进行预计和评价.现有的基于随机过程的可靠性模型一般采用均值过程来描述软件失效数据,然而,软件失效数据的模型化实质上应该是使其成为某个随机过程的一个样本轨迹.文中建立了考虑软件不同失效过程偏差的软件可靠性模型,用NHPP过程表示失效过程均值函数的变化趋势,ARMA过程表示实际失效过程对均值过程的偏差序列.在两组公开发表的真实数据集上对模型的实验表明,新模型较之一些广泛使用的NHPP软件可靠性模型在拟合能力及适用性上有明显的提高,并且保持了较好的预测能力.

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.

一种考虑缺陷关联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(NHPP-SRGMs)是评价软件产品可靠性指标的有效工具,但大多数该类模型都未考虑软件缺陷关联这一测试过程中普遍存在的现象。该文在考虑软件缺陷关联关系的基础上对缺陷进行分类,提出一个改进的NHPP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,改进的模型具有较好的拟合效果和预测能力。

引入错误严重性分级的软件可靠性模型

在对G-O模型的基本假设进行改进的基础上,将软件错误严重性分级引入G-O模型,建立了引入错误严重性分级的软件可靠性模型G-NHPP.按严重程度将软件错误严重性分为致命错误、严重错误和一般错误三类,从基本假设、模型度量、参数估计、数据要求等四个方面对软件可靠性模型G-NHPP进行了分析,使用序列似然比PLR图、U-结构图、Y-结构图的图形法和误差平方和、均方误差值、Akaike信息准则、预测风险率4种参数的数值法对软件可靠性模型G-NHPP进行了分析验证.验证结果表明,所建立的G-NHPP模型比G-O模型和J-M模型更接近实际,该模型具有良好的拟合效果和评估能力.

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。

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.

考虑不完美排错情况的软件可靠性过程仿真

针对传统非齐次泊松过程(NHPP)类软件可靠性分析方法存在忽略对软件测试中的故障排除过程的问题,提出了一种新的描述软件测试中的实际可靠性增长过程的仿真方法。该方法采用排队论建模软件测试中可能存在的故障排除行为。排队模型全面考虑了故障排除中可能存在的不完全排错,甚至是引入新故障的情况,并考虑了排错资源的局限性问题。以排队模型作为仿真模型,开发出仿真过程实现对软件可靠性过程的仿真。利用公开发表的一组软件失效数据对仿真方法进行的验证表明,与现有的仿真方法相比,该方法由于更全面地考虑了软件测试过程,因此取得更好的拟合结果。

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。