基于屏蔽数据的部件可靠性指标的贝叶斯估计

基于屏蔽数据,在单元的屏蔽与失效不独立的情形下,研究系统中Burr XII部件可靠性指标的估计问题。在三种不同的损失函数下,推算出部件寿命参数及可靠性指标的贝叶斯估计。最后利用随机模拟对两种估计方法进行比较分析,并讨论屏蔽概率和屏蔽水平对估计结果的影响。     

基于Copula函数的屏蔽数据并-串联系统可靠性分析

讨论了失效相依屏蔽数据系统的可靠性分析问题.通过引入Copula函数描述部件寿命变量之间的相依关系,建立屏蔽数据并-串联系统可靠性模型,推导出并-串联系统的一些概率结果.在此基础上,基于逐步Ⅰ型混合截尾的系统失效数据,获得了模型参数及可靠性指标的极大似然估计和bootstrap区间估计.最后,运用蒙特卡罗模拟验证了方法的可行性和有效性.     

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在已有讨论竞争失效数据统计分析的文献中, 大多数都假设失效机理之间相互独立. 本文使用copula作为连接函数来考查加速寿命试验中的竞争失效模型. 通过模拟, 把失效机理相关时得到的结果与失效机理独立时得到的结果做了比较. 最后分析了文献中的一个实际数据.     

基于隐藏故障和竞争失效的多态系统视情维修策略

针对具有隐藏故障和竞争失效模式的多态系统维修策略问题,提出了一种综合考虑隐藏故障损失成本、竞争失效模式、不完美检测、不完美维修等因素的多态系统维修建模方法。首先,描述了多态系统及其失效准则,并给出具体的视情维修策略;其次,推导了系统因隐藏故障而导致的损失成本,并对缺陷状态的不完美检测和不完美维修情形进行了数学描述;然后,分析计算了竞争失效模式下系统的两种更新情形及其发生概率,并基于此构建了多态系统的维修模型-期望成本率;最后,通过数值算例验证了所构建维修模型的有效性,分析结果表明,通过优化维修模型能够找到系统的最佳检测策略,从而有效降低维修成本。     

平方损失下屏蔽数据并联系统的经验贝叶斯分析

在部件寿命服从逆威布尔分布时,研究了屏蔽数据两部件并联系统的可靠性分析问题.基于截尾样本,将经典统计方法和贝叶斯理论相结合,推导出模型参数及系统可靠性指标的经验贝叶斯估计,最后给出数值模拟.     

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．     

恒应力加速寿命试验中无失效数据的处理

对恒应力加速寿命试验中W eibu ll分布无失效数据,合理地构造了失效概率的两种先验分布,并结合现场试验数据,利用极大似然方法和Bayes方法对该组无失效数据进行了处理,所得结果表明本文给出的方法是正确可行的.     

逐步Ⅰ型混合截尾下指数-威布尔分布竞争失效模型的统计分析（英文）

本文基于指数-威布尔分布研究逐步Ⅰ型混合截尾竞争失效模型的统计推断问题.根据模型假设和竞争失效数据,推导出未知参数和产品可靠度的极大似然估计;考虑极大似然估计的渐近正态性质,计算出观测Fisher信息阵,从而获得未知参数和可靠度的渐近置信区间.由于贝叶斯后验密度函数不具有封闭形式,利用MCMC方法给出未知参数和可靠度的近似贝叶斯估计以及最大后验密度可信区间.最后通过模拟研究对估计方法作出解释并给出数值结果.结果表明极大似然方法和贝叶斯方法可以对逐步Ⅰ型混合截尾竞争失效模型进行统计推断.     

基于超图的多冲击共因失效模型

复杂冗余系统的共因失效一直是工程中亟待解决的问题.针对传统共因失效模型的缺点,利用超图概念和矩阵相似度的原理,在充分考虑了不同共同原因冲击耦合问题的基础上,提出了一种新的共因失效模型.该模型从实际统计数据出发,不需要专家分析,可以精确计算出不同共同原因冲击对系统的影响,且在实际应用中更加简单.     

成分数据相关系数的计算方法

成分数据具有非常复杂的数学性质,很多传统的统计分析方法对其是失效的,因此,在研究中必须采用特殊处理和专门技术.着重讨论了成分数据相关系数的计算方法,由于普通数据的相关系数计算方法只适用于两组单变量数据,而传统的典型相关分析又鉴于成分数据的特殊性质而不能直接使用,故结合logratio变换和典型相关分析技术,提出了一种针对成分数据的相关系数计算方法,成功地解决了这一问题.     

About conditional masking probability models

We study the existing models for right-censored competing risks data and with masked failure cause. By introducing a new random variable hidden behind the current models, we give a practical interpretation of the symmetry assumption made by almost all researchers in this field. We further point out that the drawback of the symmetry assumption is that it has a strong restriction on the underlying distribution function to be studied. Moreover, we correct an assumption in the current models.     

A statistical study of time-sharing systems

Time-sharing systems are discussed in which competing users can achieve access only on a chance basis, depending on the availability of a system channel at the time of attempted access. A simple statistical method is presented for evaluating the relative merits of different time-sharing configurations. Calculated results for a variety of user demand levels in a representative system are shown in graphic and tabular form.     

An applied cell mapping method for optimal control problems

From the application point of view, a series of modifications are proposed for the cell mapping method discussed in Ref. 1 for the optimal control analysis of dynamical systems. The cell order around the target set is rearranged. A set of common discriminate principles is used for the selection of the optimal one among competing control strategies of the same cost. Inequality constraints of the system are taken into account. The number of elements in the set of allowable time intervals is not prescribed, but left open. These modifications seem to make the cell mapping method more efficient for analyzing feedback systems and for obtaining their global optimal control information. The algorithms presented in this paper could broaden the application of the cell mapping approach of Ref. 1 to a wider class of engineering problems.     

Estimating advertisers' values for paid search clickthroughs

Paid search is an important form of online advertisement. Clickthroughs from slots are bid for by advertisers. The process of formulating bids is a complex one involving bidders in competing against other advertisers in multiple auctions. It would be helpful in managing the bidding process if it were possible to determine the values placed on a clickthrough by different advertisers. The theory of two models for estimating advertiser values and associated parameters is presented. The models are applied to a set of data for searches on the term Personal Loans. The results of the model that fits the data better are evaluated. The utility of the model to practitioners is discussed. Some issues raised by the results about the role of bidding agents and the discriminatory power of Customer Relationship Management systems are considered. Ways to develop the preferred model are outlined. It is suggested that the model has implications for evaluating forecasting methods for use in paid search auctions.     

Random partition masking model for censored and masked competing risks data

We consider the parametric estimation with right-censored competing risks data and with masked failure cause. We propose a new model, called the random partition masking (RPM) model. The existing model based on the so called symmetry assumption, but the RPM model does not need the symmetry assumption. We propose a wide class of parametric distribution families of the failure time and cause, which does not need the assumption of independence between the components of the system. We also study the asymptotic properties of the maximum likelihood estimator under the new model, and apply our procedure to a medical and an industrial data sets.     

Data-driven recursive least squares methods for non-affined nonlinear discrete-time systems

Aiming at identifying nonlinear systems, one of the most challenging problems in system identification, a class of data-driven recursive least squares algorithms are presented in this work. First, a full form dynamic linearization based linear data model for nonlinear systems is derived. Consequently, a full form dynamic linearization-based data-driven recursive least squares identification method for estimating the unknown parameter of the obtained linear data model is proposed along with convergence analysis and prediction of the outputs subject to stochastic noises. Furthermore, a partial form dynamic linearization-based data-driven recursive least squares identification algorithm is also developed as a special case of the full form dynamic linearization based algorithm. The proposed two identification algorithms for the nonlinear nonaffine discrete-time systems are flexible in applications without relying on any explicit mechanism model information of the systems. Additionally, the number of the parameters in the obtained linear data model can be tuned flexibly to reduce computation complexity. The validity of the two identification algorithms is verified by rigorous theoretical analysis and simulation studies.     

Direct and iterative methods for interval parametric algebraic systems producing parametric solutions

This paper deals with interval parametric linear systems with general dependencies. Motivated by the so‐called parameterized solution introduced by Kolev, we consider the enclosures of the solution set in a revised affine form. This form is advantageous to a classical interval solution because it enables us to obtain both outer and inner bounds for the parametric solution set and, thus, intervals containing the endpoints of the hull solution, among others. We propose two solution methods, a direct method called the generalized expansion method and an iterative method based on interval‐affine Krawczyk iterations. For the iterative method, we discuss its convergence and show the respective sufficient criterion. For both methods, we perform theoretical and numerical comparisons with some other approaches. The numerical experiments, including also interval parametric linear systems arising in practical problems of structural and electrical engineering, indicate the great usefulness of the proposed methodology and its superiority over most of the existing approaches to solving interval parametric linear systems.     

Challenging assumptions of notational transparency: the case of vectors in engineering mathematics

ABSTRACT

The notation for vector analysis has a contentious nineteenth century history, with many different notations describing the same or similar concepts competing for use. While the twentieth century has seen a great deal of unification in vector analysis notation, variation still remains. In this paper, the two primary notations used for expressing the components of a vector are discussed in historical and current context. Popular mathematical texts use the two notations as if they are transparent and interchangeable. In this research project, engineering students’ proficiency at vector analysis was assessed and the data were analyzed using the Rasch measurement method. Results indicate that the students found items expressed in unit vector notation more difficult than those expressed in parenthesis notation. The expert experience of notation as transparent and unproblematically symbolic of underlying processes independent of notation is shown to contrast with the student experience where the less familiar notation is experienced as harder to work with.     

Multiscale approach to computation of three-dimensional gas mixture flows in engineering microchannels

A multiscale approach to computing real gas flows in engineering microchannels on high-performance computer systems in a wide range of Knudsen numbers is described. The numerical implementation of the approach combines the solution of quasigasdynamic equations and the molecular dynamics method. Following the approach, the parameters of the real gas equation of state are found at the molecular level, the kinetic gas properties are calculated, and the form of boundary conditions on the microchannel walls are determined. The technique is verified by computing several test problems. The results agree well with available theoretical and experimental data.     

An Akaike information criterion for multiple event mixture cure models

We derive the proper form of the Akaike information criterion for variable selection for mixture cure models, which are often fit via the expectation–maximization algorithm. Separate covariate sets may be used in the mixture components. The selection criteria are applicable to survival models for right-censored data with multiple competing risks and allow for the presence of a non-susceptible group. The method is illustrated on credit loan data, with pre-payment and default as events and maturity as the non-susceptible case and is used in a simulation study.