Exact bayesian estimation of system reliability from component test data

System reliability is often estimated by the use of components' reliability test results when system test data are not available, or are very scarce. A method is proposed for computing the exact posterior probability density function, cumulative distribution function, and credible intervals for system reliability in a Bayesian setting, with the use of components' prior probability distributions and current test results. The method can be applied to series, parallel, and many mixed systems. Although in theory the method involves evaluating infinite series, numerical results show that a small number of terms from the infinite series are sufficient in practice to provide accurate estimates of system reliability. Furthermore, because the coefficients in the series follow some recurrence relations, our results allow us to calculate the reliability distribution of a large system from that of its subsystems. Error bounds associated with the proposed method are also given. Numerical comparisons with other existing approaches show that the proposed method is efficient and accurate. © 1997 John Wiley & Sons, Inc.     

基于贝叶斯模型的装备剩余寿命预测研究

为了解决武器装备日益复杂及维修工作日趋繁重的问题,运用贝叶斯模型预测装备修理后的剩余寿命,为合理安排其修理计划提供依据。替代传统的指数分布,用威布尔分布描述系统寿命特征,并运用极大似然方法和贝叶斯方法估计威布尔分布的两个未知参数,给出其置信区间。在此基础上,对先验样本和后验样本两种不同情况,分别运用贝叶斯模型预测装备修理后的剩余寿命,并给出实例。结果表明了该方法的有效性。     

一种新的非线性/非高斯滤波方法

自主滤波方法是一种递归式贝叶斯估计方法 ,该方法采用一组抽样值来近似目标状态的概率密度函数 ,可用于非线性系统模型和观测模型、非高斯观测噪声条件下的滤波。将该算法与扩展卡尔曼滤波方法进行了比较 ,仿真结果表明 ,该算法性能优于扩展卡尔曼滤波方法     

The reliability of a series system of repairable subsystems: A bayesian approach

Consider the problem of estimating the reliability of a series system of (possibly) repairable subsystems when test data and historical information are available at the component, subsystem, and system levels. Such a problem is well suited to a Bayesian approach. Martz, Waller, and Fickas [Technometrics, 30 , 143–154 (1988)] presented a Bayesian procedure that accommodates pass/fail (binomial) data at any level. However, other types of test data are often available, including (a) lifetimes of nonrepayable components, and (b) repair histories for repairable subsystems. In this article we describe a new Bayesian procedure that accommodates pass/fail, life, and repair data at any level. We assume a Weibull model for the life data, a censored Weibull model for the pass/fail data, and a power-law process model for the repair data. Consequently, the test data at each level can be represented by a two-parameter likelihood function of a certain form, and historical information can be expressed using a conjugate family of prior distributions. We discuss computational issues, and use the procedure to analyze the reliability of a vehicle system. © 1994 John Wiley & Sons, Inc.     

基于贝叶斯原理的放大转发中继联合信道估计

在贝叶斯原理的框架下,依据放大转发中继联合信道等价于两段瑞利信道相叠加的特征,将其概率密度分布这一先验知识与接收端的训练序列相结合,得到了最小均方和最大后验两种估计方法。由于两种方法的准确贝叶斯CRB难以求解获得闭合表达式,从最大熵原理出发,结合复高斯分布性质,推导了MLE准则下的CRB相对应的近似贝叶斯CRB,以衡量不同方法的估计精度。仿真结果表明相比于原有的MLE方法,最大后验估计方法在低信噪比下性能改善明显。     

Approximate probability distributions for the extreme spread

The extreme spread, or greatest distance between all pairs of impact points on a target, is often used as a rapid measure of dispersion or precision of shot groups on a target. It is therefore desirable to know its statistical properties. Since the exact theoretical distribution has not yet been worked out, this paper examines the accuracy of several approximations which are checked against large sample monte carlo values. We find in particular that for the sample sizes considered the extreme spread can be approximated well by a Chi variate.     

指数寿命产品可靠性增长试验的Bayes分析

针对指数寿命产品的定时、定数截尾试验方案,推广了Mazzuchi-Soyer模型的应用范围。首先引入模型假设,以狄氏分布作为先验分布,综合利用产品研制的历史信息和专家信息,结合产品研制各阶段试验数据,给出了各阶段可靠性的联合后验分布。然后利用Gibbs抽样算法解决后验推断计算问题,得到各阶段产品可靠性的Bayes点估计和区间估计。最后给出产品可靠性增长分析实例,表明了模型的优越性。     

Statistical analysis for masked system life data from Marshall‐Olkin Weibull distribution under progressive hybrid censoring

This paper considers the statistical analysis of masked data in a series system, where the components are assumed to have Marshall‐Olkin Weibull distribution. Based on type‐I progressive hybrid censored and masked data, we derive the maximum likelihood estimates, approximate confidence intervals, and bootstrap confidence intervals of unknown parameters. As the maximum likelihood estimate does not exist for small sample size, Gibbs sampling is used to obtain the Bayesian estimates and Monte Carlo method is employed to construct the credible intervals based on Jefferys prior with partial information. Numerical simulations are performed to compare the performances of the proposed methods and one data set is analyzed.     

Asymptotically sufficient grouping

Under certain conditions, a sample from a multivariate distribution can be grouped in such a way that asymptotically (as the sample size increases) no information is lost by grouping, and the joint distribution of the observed frequencies can be approximated by a multivariate normal distribution. © 1993 John Wiley & Sons, Inc.     

磁性目标跟踪的后验克拉美罗下限分析与计算

为了求解磁性目标跟踪问题的后验克拉美罗下限(PCRB),提出了PCRB-GMSPPF算法。该算法利用高斯混合采样粒子滤波算法对目标状态的真实后验概率密度分布进行抽样,再通过蒙特卡洛积分法迭代求解每个观测时刻的Fisher信息矩阵,进而得出目标状态估计的PCRB;克服了基于PF算法求解PCRB过程中由于粒子退化和贫化问题造成不能从后验概率分布中正确抽样的缺点;在建立磁性目标跟踪的状态模型和观测模型的基础上进行仿真分析,将求解出的PCRB与采用GMSPPF及PF算法进行跟踪的均方根误差做对比,验证所提的PCRB-GMSPPF算法的有效性,结果表明:针对磁性目标跟踪问题,PCRB-GMSPPF算法较PCRB-PF算法具有更好的准确性,并可用于一般的非线性模型跟踪误差下限分析。     

The error in the normal approximation to the multinomial with an increasing number of classes

In an earlier paper, it was shown that under certain conditions, if the number of classes in a multinomial distribution increases as the number of trials increases, the probabilities assigned to arbitrary regions by the multinomial distribution are close to the probabilities assigned by the distribution of slightly rounded-off normal random variables. A different method of studying the approximation of the multinomial distribution by a normal distribution is to use the multivariate Berry-Esseen bound. In this paper, these two methods are compared, particularly with respect to the class of multinomial distributions for which the bounds on the error remain useful.     

Asymptotic joint normality of an increasing number of multivariate order statistics and associated cell frequencies

Take n independent identically distributed (IID) observations from a continuous r-variate population, and choose some order statistics from each of the r variates. These order statistics are used to construct a grid in r-dimensional space. Under certain conditions, it is shown that as n increases we can choose an increasing number of order statistics in such a way that the asymptotic joint distribution of the chosen order statistics and of the frequencies of sample points falling in the cells of the grid can be assumed to be a normal distribution. An application to testing independence of random variables is given.     

利用构造性仿真评估导弹精度

通过对导弹落点散布的构造性仿真获得了落点(均值与方差)的验前分布参数,通过与现场试验数据的相容性检验获得了验前信息的可信度,在考虑验前信息可信度的情况下获得了命中点的均值与方差的验后Bayes估计。算例表明该方法对于仿真信息的应用合理可信,考虑可信度下的Bayes估计具有较好的置信度。     

Bayes sequential strategies for crossing a field containing absorption points

A sequential decision problem is considered in which N particles have to cross a given field. Two alternative crossing paths are available. An unknown number of absorption points J₁ and J₂ are planted at each of the crossing paths. The bivariate prior distribution of (J₁,J₂) is given. If a particle passes close to an absorption point it may survive with probability s, 0 < s < 1. If a particle is absorbed, both the particle and the absorption point are ruined. There is no replacement of ruined absorption points. All absorption points act independently. The particles crciss the field in a consecutive order, and a crossing path can be chosen for each particle. The objective is to maximize the expected number of survivors. The Bayes sequential procedure is characterized. The csmditions under which the Bayes strategy is determined by the maximal posterior survival probabilities are specified.     

引信与武器系统的适配性分析

引信是弹药武器系统的重要子系统,引信只有与其它子系统多方面适配,才能充分发挥武器系统的效能。通过分析引信与武器系统中其它子系统之间在任务与功能、信息的利用与传输、能源、材料与结构等方面的适配关系,提出了设计中引信与战斗部、火控、制导等子系统间的适配关系,并采用适配性方法设计引信。     

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.     

武器系统概率指标的贝叶斯决策评定方法

剖析了武器系统试验工程领域中常用二项分布经典假设检验方法存在的问题,从贝叶斯决策思想和理论出发提出了概率指标评定的新方法,通过实例对比证明了贝叶斯决策评定方法有效解决了二项分布经典假设检验方法中存在的问题。     

基于高斯和粒子滤波的AUV水下地形辅助导航方法

针对自主式水下无人航行器(AUV)长时间潜航时的精确导航定位需求,以多波束测深系统为水下地形测量设备,提出一种基于贝叶斯估计的AUV水下地形匹配导航模型。针对贝叶斯滤波后验概率密度函数的求解问题,用高斯混合密度函数近似状态的后验概率密度函数,提出了基于高斯和粒子滤波的水下地形匹配导航方法。基于多波束测深数据的回放式仿真试验表明,提出的方法可以有效近似地形匹配的贝叶斯滤波模型,具有良好的实用性。     

基于最大后验风险的多层Bayes方法

为了对指数型产品进行可靠性鉴定,首先给出了失效率的多层先验分布,然后从最大后验风险的角度,运用Bayes方法,制定出可靠性鉴定试验方案.按照此鉴定试验方案,缩短了试验时间,从而降低了鉴定试验所需的费用.