Bayesian inference based on partial monitoring of components with applications to preventive system maintenance

Consider a binary, monotone system of n components. The assessment of the parameter vector, θ, of the joint distribution of the lifetimes of the components and hence of the reliability of the system is often difficult due to scarcity of data. It is therefore important to make use of all information in an efficient way. For instance, prior knowledge is often of importance and can indeed conveniently be incorporated by the Bayesian approach. It may also be important to continuously extract information from a system currently in operation. This may be useful both for decisions concerning the system in operation as well as for decisions improving the components or changing the design of similar new systems. As in Meilijson [12], life‐monitoring of some components and conditional life‐monitoring of some others is considered. In addition to data arising from this monitoring scheme, so‐called autopsy data are observed, if not censored. The probabilistic structure underlying this kind of data is described, and basic likelihood formulae are arrived at. A thorough discussion of an important aspect of this probabilistic structure, the inspection strategy, is given. Based on a version of this strategy a procedure for preventive system maintenance is developed and a detailed application to a network system presented. All the way a Bayesian approach to estimation of θ is applied. For the special case where components are conditionally independent given θ with exponentially distributed lifetimes it is shown that the weighted sum of products of generalized gamma distributions, as introduced in Gåsemyr and Natvig [7], is the conjugate prior for θ. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 551–577, 2001.     

Convolutions and generalization of logconcavity: Implications and applications

Additive convolution of unimodal and α‐unimodal random variables are known as an old classic problem which has attracted the attention of many authors in theory and applied fields. Another type of convolution, called multiplicative convolution, is rather younger. In this article, we first focus on this newer concept and obtain several useful results in which the most important ones is that if is logconcave then so are and for some suitable increasing functions ?. This result contains and as two more important special cases. Furthermore, one table including more applied distributions comparing logconcavity of f(x) and and two comprehensive implications charts are provided. Then, these fundamental results are applied to aging properties, existence of moments and several kinds of ordered random variables. Multiplicative strong unimodality in the discrete case is also introduced and its properties are investigated. In the second part of the article, some refinements are made for additive convolutions. A remaining open problem is completed and a conjecture concerning convolution of discrete α‐unimodal distributions is settled. Then, we shall show that an existing result regarding convolution of symmetric discrete unimodal distributions is not correct and an easy alternative proof is presented. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 109–123, 2016     

0.13 μm标准CMOS工艺的高可靠流水线模数转换器

针对航空航天电子系统对高性能模数转换器的需求,采用0. 13μm标准互补金属氧化物半导体工艺,设计可以在极端温度和空间辐射环境中稳定可靠工作的12位分辨率、50 MS/s采样率的流水线模数转换器。通过采用无采样保持电路以及抗辐射电路和版图加固等技术,在减小功耗的同时有效地削弱总剂量辐射效应的影响。测试结果表明:在-55～125℃温度范围内以及150 krad(Si)的总剂量辐照条件下,得到大于64 dB的信噪比、大于73. 5 dB的无杂散动态范围和最大0. 22 dB的微分非线性。     

基于复合等效可信度加权的Bayes融合评估方法

在小子样试验评估时,为避免大量先验信息湮没实际飞行试验的信息,融合先验补充样本时通常会进行数学相容性检验并加权.首先分析了小子样情形下直接根据数据计算数学相容性可能造成的不稳定性,为改善这种情况,根据不同试验类型的不同试验环境,对不同试验类型下的误差进行分析和折合,定义了物理等效可信度;并结合物理等效可信度和数学相容性检验,得到先验样本的复合等效可信度权重,基于正态逆伽玛分布计算了Bayes融合评估的后验结果;通过比较Bayes估计后验方差与不磁合先验信息的估计后验方差,根据先验信息参与融合后是否能减小后验方差来判断先验样本是否应该参与融合.理论分析和仿真说明,基于复合等效可信度的加权方法是合理的.     

Monitoring poisson count data with probability control limits when sample sizes are time varying

This article considers the problem of monitoring Poisson count data when sample sizes are time varying without assuming a priori knowledge of sample sizes. Traditional control charts, whose control limits are often determined before the control charts are activated, are constructed based on perfect knowledge of sample sizes. In practice, however, future sample sizes are often unknown. Making an inappropriate assumption of the distribution function could lead to unexpected performance of the control charts, for example, excessive false alarms in the early runs of the control charts, which would in turn hurt an operator's confidence in valid alarms. To overcome this problem, we propose the use of probability control limits, which are determined based on the realization of sample sizes online. The conditional probability that the charting statistic exceeds the control limit at present given that there has not been a single alarm before can be guaranteed to meet a specified false alarm rate. Simulation studies show that our proposed control chart is able to deliver satisfactory run length performance for any time‐varying sample sizes. The idea presented in this article can be applied to any effective control charts such as the exponentially weighted moving average or cumulative sum chart. © 2013 Wiley Periodicals, Inc. Naval Research Logistics 60: 625–636, 2013     

基于加权网络模型的指挥节点重要度评估方法

指挥节点重要度评估是研究指挥网络可靠性和抗毁性的重要内容。通过定义加权网络节点重要度贡献矩阵,提出了一种利用节点重要度评价矩阵确定加权网络关键节点的相对重要度的方法,该方法能充分考虑节点的位置信息、邻接节点的重要度贡献关系;结合作战任务对社区的依赖度,设计了节点全局重要度评估算法,并利用该算法对典型网络节点重要度进行了分析,结果表明算法有效、可行。     

Deterministic and stochastic scheduling with teamwork tasks

We study a class of new scheduling problems which involve types of teamwork tasks. Each teamwork task consists of several components, and requires a team of processors to complete, with each team member to process a particular component of the task. Once the processor completes its work on the task, it will be available immediately to work on the next task regardless of whether the other components of the last task have been completed or not. Thus, the processors in a team neither have to start, nor have to finish, at the same time as they process a task. A task is completed only when all of its components have been processed. The problem is to find an optimal schedule to process all tasks, under a given objective measure. We consider both deterministic and stochastic models. For the deterministic model, we find that the optimal schedule exhibits the pattern that all processors must adopt the same sequence to process the tasks, even under a general objective function GC = F(f₁(C₁), f₂(C₂), … , f_n(C_n)), where f_i(C_i) is a general, nondecreasing function of the completion time C_i of task i. We show that the optimal sequence to minimize the maximum cost MC = max f_i(C_i) can be derived by a simple rule if there exists an order f₁(t) ≤ … ≤ f_n(t) for all t between the functions {f_i(t)}. We further show that the optimal sequence to minimize the total cost TC = ∑ f_i(C_i) can be constructed by a dynamic programming algorithm. For the stochastic model, we study three optimization criteria: (A) almost sure minimization; (B) stochastic ordering; and (C) expected cost minimization. For criterion (A), we show that the results for the corresponding deterministic model can be easily generalized. However, stochastic problems with criteria (B) and (C) become quite difficult. Conditions under which the optimal solutions can be found for these two criteria are derived. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004     

一种图像去模糊正则化恢复算法参数确定方法

为了解决模糊正则化恢复算法中参数确定问题,提出一种正则化参数确定方法,该方法根据降质图像特征计算正则化参数.分析了目前普遍应用的全变分正则化方法和该问题的改进拉格朗日迭代解法(SALSA),分析不同正则化参数对恢复效果的影响,提出的正则化参数确定方法与噪声和原图像梯度大小相关.对不同梯度和噪声图像的不同正则化参数恢复效果进行对比,得到提出的正则化参数确定方法能使恢复图像的改进信噪比处于最大值附近.从实验视觉效果得出,该参数确定方法能够抑制降质图像的噪声并能够尽量恢复原图像细节信息.     

加权随机模拟的时变可靠性分析方法

针对结构时变可靠性的随机模拟分析方法计算代价大的问题,在极值方法的基础上提出基于加权随机模拟的时变可靠性分析策略。时变可靠性分析需要计算在不同时间处的失效概率,通常需要进行多次可靠性分析,计算代价巨大。所提方法通过对常规静态可靠性的随机模拟方法进行改进拓展,运用加权策略分别发展了加权蒙特卡洛法和加权重要抽样法,使之能够高效分析计算时变可靠性问题。所提方法仅需一次常规可靠性分析模拟,即可得到时变失效概率函数估计。采用管状悬臂梁和十杆桁架两个算例进行验证。结果表明,基于加权思想的分析方法在能确保精确度的前提下能够大幅度减小计算量,提高计算效率。