MULTIVARIATE SURVIVAL DISTRIBUTIONS OF AGE AND RESIDUAL LIFETIME PROCESSES IN NONHOMOGENEOUS POISSON PROCESS

Let {V(t),t≤0} be the nonhomogeneous Poisson process with cumulative intensituy parameter A(t). |δ,t≥0 the, age process, and y, t≥0} the residual lifetime process. In the present-paper the expressions of n-dimensional survival distribution functions of the processes {δ and γ, and their Lebesgue decompositions are derived.

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.

One-Sample Bayesian Predictive Analyses for an Exponential Non-Homogeneous Poisson Process in Software Reliability

The Goel-Okumoto software reliability model, also known as the Exponential Nonhomogeneous Poisson Process,is one of the earliest software reliability models to be proposed. From literature, it is evident that most of the study that has been done on the Goel-Okumoto software reliability model is parameter estimation using the MLE method and model fit. It is widely known that predictive analysis is very useful for modifying, debugging and determining when to terminate software development testing process. However, there is a conspicuous absence of literature on both the classical and Bayesian predictive analyses on the model. This paper presents some results about predictive analyses for the Goel-Okumoto software reliability model. Driven by the requirement of highly reliable software used in computers embedded in automotive, mechanical and safety control systems, industrial and quality process control, real-time sensor networks, aircrafts, nuclear reactors among others, we address four issues in single-sample prediction associated closely with software development process. We have adopted Bayesian methods based on non-informative priors to develop explicit solutions to these problems. An example with real data in the form of time between software failures will be used to illustrate the developed methodologies.

Two-Sample Bayesian Predictive Analyses for an Exponential Non-Homogeneous Poisson Process in Software Reliability

The Goel-Okumoto software reliability model is one of the earliest attempts to use a non-homogeneous Poisson process to model failure times observed during software test interval. The model is known as exponential NHPP model as it describes exponential software failure curve. Parameter estimation, model fit and predictive analyses based on one sample have been conducted on the Goel-Okumoto software reliability model. However, predictive analyses based on two samples have not been conducted on the model. In two-sample prediction, the parameters and characteristics of the first sample are used to analyze and to make predictions for the second sample. This helps in saving time and resources during the software development process. This paper presents some results about predictive analyses for the Goel-Okumoto software reliability model based on two samples. We have addressed three issues in two-sample prediction associated closely with software development testing process. Bayesian methods based on non-informative priors have been adopted to develop solutions to these issues. The developed methodologies have been illustrated by two sets of software failure data simulated from the Goel-Okumoto software reliability model.

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。

基于非齐次泊松过程的高压断路器剩余电寿命预测及可靠性分析

高压断路器可保护电力设备和电网免受过电流和短路的损害,其正常运行对于特高压线路来说至关重要。从高压断路器相对电寿命曲线入手,分情况建立了断路器电触头可靠性数学模型,基于非齐次泊松过程对可靠性模型进行仿真验证,获取了更加符合实际退化过程的可靠性模型,实现了断路器剩余电寿命及可靠性值的定量预测,为断路器运行状态评估、故障诊断及检修策略制定提供了借鉴和参考。

非齐次Poisson跳-扩散再装股票期权的定价

文章假定股票价格过程遵循非齐次Poisson跳跃扩散过程,并且股票预期收益率μ(t)、波动率σ(t)和无风险收益率r(t)均为时间的函数,在风险中性定价模型中,得到了再装股票期权的定价;比较了时间依赖参数下与参数为常数下的定价公式,并讨论了当有红利率为δ(t)时的期权定价公式。

随机弹性在非齐次Poisson过程中的作用

将弹性引入到非齐次Poisson过程中,探讨了累积强度函数对时间的弹性和概率母函数对累积强度的弹性,并通过实例检验了强度弹性的实用性和正确性。

基于区域失效的数据中心和5G基站冷却设备可靠性预测方法研究

对数据中心和5G基站用冷却设备在不同安装区域的现场失效大数据进行分析,通过极大似然法建立寿命分布模型,其寿命分布最优拟合符合威布尔三参数分布规律,故障复发符合非齐次泊松过程,按区域聚类可靠性呈现显著性差异。对典型区域失效数据按可修复系统和不可修复系统分别进行可靠性预测,按可修复系统的预测结果与实际维修数据相关性良好。建立的基于区域失效的寿命分布、故障复发及可靠性预测方法适用于数据中心和5G基站用冷却设备的使用现场失效大数据分析,故障预测及维修备件、包修策略制定。

软件可靠性中NHPP模型趋势检验的U-图方法

对软件可靠性中一类重要的模型——非齐次泊松过程（ＮＨＰＰ）模型的趋势检验，构造了一列检验的统计量，独立同分布于均匀分布Ｕ（０，１）．并由柯尔莫哥洛夫检验判定所选择的可靠性增长趋势模型的合适性．本文方法可适用于完全数据和不完全数据．这里报告的方法，可以作为选择软件可靠性模型时的一种判断依据，以定量地评判选择的软件可靠性模型的优劣．

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。

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.

广义非齐次复合Poisson过程及其应用

给出了广义非齐次复合泊松过程的定义,并且在讨论它的概率母函数(矩母函数,特征函数)的基础之上,进而深入讨论了它的若干性质,举例说明了它在实际问题中的应用.

基于非齐次复合Poisson过程的正交异性钢桥面板细节疲劳裂纹随机扩展研究

传统的正交异性钢桥面板疲劳损伤评估常采用确定性和可靠性分析方法,忽略了疲劳裂纹扩展的随机性影响,针对这一问题,提出钢桥面板细节疲劳随机扩展分析方法。本文以南溪长江大桥为工程背景,基于长期车辆荷载监测数据,建立了车辆荷载非齐次复合Poisson过程模型。建立钢桥面板有限元模型,采用瞬态分析方法将随机车辆荷载转化成细节疲劳应力,基于线弹性断裂力学理论推导U肋-顶板焊接细节疲劳裂纹扩展时变微分方程,实现宏观关系式疲劳应力幅次数-疲劳损伤至微观表达式应力时间序列-疲劳损伤转换,讨论了车载次序及超载对疲劳裂纹扩展的影响。研究结果表明,非齐次复合泊松过程模型能够较好描述随机车流运营状态,车辆荷载的次序对疲劳裂纹扩展速率的影响不可忽略,重车排序靠前时能够促使疲劳裂纹扩展增速,南溪长江大桥细节点的车辆超载迟滞效应修正系数取值0.804。

非时齐复合Poisson风险模型的破产特征量分析

该文将经典风险模型推广到非时齐复合Poisson风险模型.首先,运用经典方法和时变方法,计算了该模型下的破产特征量,且得到了更新方程的解析表达式.其次,定义了时变后相应模型的一个广义的Gerber-Shiu函数,验证了时变方法对非时齐Poisson风险模型的有效性.最后,当单次索赔量服从指数分布时,计算了相应的破产概率和Gerber-Shiu函数.

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.

K阶非齐次Poisson过程

探讨了Ｋ阶非齐次Ｐｏｉｓｓｏｎ过程的分布，研究了其等待时间的分布，以及等待时间的各阶矩之间的关系．

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.