小子样不可修武器装备的Bayes可靠性增长分析

现有的可靠性增长模型大多是针对可修系统建立的,而现实中大多存在的是不可修产品,即产品投入可靠性增长试验出现故障后,很难修复如新再次投入试验.针对武器装备小子样、不可修的特点,提出了Bayes可靠性增长分析方法.首先利用多台产品异步增长理论得到各阶段试验数据的似然函数,然后构造了增长模型参数的Gamma-均匀验前分布并给出了模型参数估计的ML-II方法,通过Bayes统计推断对装备研制全过程的可靠性增长规律进行分析,最后通过仿真示例说明了该方法在工程上的应用.     

Weibull分布航天产品可靠性评估的MMLE-Bayes方法

航天产品现场使用数据具有小子样、零失效的特点,要实现其工程化可靠性评估,需要充分利用各种环境下的试验信息和相似型号产品的试验信息及使用信息,因此,提出了一种适用于Weibull分布航天产品可靠性综合评估的MMLE—Bayes方法。首先通过MMLE方法得到额定任务时间可靠度的置信下限估计,再通过构造合理的验前分布实现Bayes可靠性评估。在此过程中,为合理融合各来源的验前信息,提出了环境因子和相似因子的概念及其估计方法。最后通过一种航天产品的可靠性评估实例,说明了MMLE—Bayes—Weibull方法的的实用性和有效性。     

左截断右删失下正态分布参数单变点的bayes估计

针对随机变量的寿命试验数据服从正态分布且在缺失数据模型下的情况,对其参数识别以及估计,并应用到实际生活。在此研究中,首先构建正态分布的似然函数,考虑在左截断右删失数据模型下,使用逆变换法和筛选法处理缺失数据。然后将缺失数据模型下的似然函数转化为完全数据情况下的似然函数,可获得变点的位置及其他参数的满条件分布。最后,采用Gibbs抽样和Metropolis-Hastings算法相结合的MCMC方法获得各参数的Gibbs样本,并将其均值作为各参数的贝叶斯估计。结果显示：在相对误差、MC误差的准则下,各参数的贝叶斯估计精度都较高。     

不完全先验信息条件下的可靠性评估

小子样产品可靠性的Bayes评估中通常需要用到主观经验信息,如可靠度均值或可信区间等,这些信息属于不完全先验信息,利用这些信息通常无法确定可靠性分布函数。基于Bayes理论,以贝塔分布作为先验分布类型,利用最大熵原理将不完全信息转化为完全型先验信息,得到产品可靠性的先验分布,再结合观测数据,利用Bayes公式得到产品可靠性后验分布。从仿真算例可以看出,给出的方法能够有效地处理不完全先验信息,提高产品可靠性评估的效率。     

基于复高斯模型的样本缺失窄带雷达信号重构算法

该文提出一种针对窄带雷达信号存在样本缺失情况下的信号重构算法。由于窄带雷达体制下,目标回波近似服从复高斯分布。在这一前提下,首先建立描述样本缺失观测信号与未知完整信号间关系的概率模型,然后根据贝叶斯准则推导出在给定样本缺失观测信号条件下完整信号的后验分布,最后利用期望最大(Expectation Maximization, EM)算法得到模型中参数的最大似然估计,进而得到完整信号的重构。该方法的优势是只需利用样本缺失观测信号就可以重构出未知的完整信号,除了复高斯分布的假设,不需要其他任何样本信息和先验假设帮助参数学习。基于实测数据的实验结果和与现有算法的比较结果表明该方法能够获得较好的重构性能。     

大型相控阵雷达可靠性评估方法

大型相控阵雷达整机外场可靠性试验可分为联调联试和验证试验两个阶段。针对现有的整机可靠性评估仅利用验证试验阶段较少的试验数据,导致整机可靠性评估结果置信度低的问题,提出一种基于改进序化关系模型的整机可靠性评估方法。该方法通过构建新的联合似然函数对传统序化关系模型进行改进,并融合联调联试数据和验证试验数据来评估整机的可靠性水平。实例表明:该方法能提高整机平均故障间隔时间在同一置信水平下的估计下限,缩短平均故障间隔时间的估计区间。     

一种电子设备贝叶斯可靠性评估的新方法

针对贝叶斯方法应用中后验参数的运算复杂性问题,提出了一种电子设备贝叶斯可靠性评估的新方法.基于工程实践中常见的先验信息建立失效率先验分布,通过随机采样构建设备寿命分布参数的离散联合先验分布,结合截尾试验数据,再通过二次随机采样得到分布参数的离散联合后验分布函数.通过实例给出了运算过程,并与其它贝叶斯运算方法进行了比较.结果表明,此方法在确保精度的同时可以大大简化计算过程,在电子设备可靠性评估中有较高的应用价值.     

电子器件生存概率及置信度的Bayes计算方法

针对工程实践中经常遇到的小子样问题,分别以无信息分布、正态分布、产生正态性能分布作为电子器件生存概率随机变量的验前分布,给出了二项抽样实验验后生存概率密度的具体形式,根据某电子器件电流损伤阈值实验数据,得到特定辐射环境下器件生存概率的Bayes点估计、一定置信度下的双边估计、单边估计。仿真结果表明,产生正态性能验前分布要优于无信息分布和正态验前分布,该方法可以应用到工程实践中。     

基于ML-Ⅱ方法的k/n-系统Bayes可靠性评估

n中取k系统(简称k/n-系统)是工程实践中应用最广泛的系统类型之一.为了在系统现场试验样本量很小的情况下进行可靠性评估,首先利用次序统计量推导了k/n-系统寿命分布的密度函数,并给出了模型参数的第二类极大似然估计(ML-Ⅱ估计);然后给出了k/n-系统Bayes可靠性评估的一般步骤;仿真实例表明了方法的可行性.     

基于EM-SBL迭代的稀疏SIMO信道频域盲均衡算法

针对单输入多输出系统下稀疏信道均衡问题,提出了一种新的基于最大似然准则的频域迭代均衡算法.首先将多天线联合均衡问题建模为非完整观测数据集下频域信号序列的最大似然估计问题,利用期望最大化算法进行近似迭代求解,最终得到各个单频信号加权求和形式的均衡输出表达式.在每次迭代过程中,算法依次完成均衡输出的更新和信道参数联合条件后验分布的更新.考虑到信道固有的稀疏特性,在求解信道参数联合条件后验时,引入具有稀疏促进作用的先验分布对信道系数加以约束,使用稀疏贝叶斯学习迭代求解信道参数联合条件后验.仿真结果表明,本文算法具有较好的收敛特性和稳态性能,在中高信噪比条件下可以获得接近信道已知条件下的稳态系统误符号率性能.     

Empirical Bayes Estimation in the Weibull Distribution

In part I empirical Bayes estimation procedures are introduced and employed to obtain an estimator for the unknown random scale parameter of a two-parameter Weibull distribution with known shape parameter. In part II, procedures are developed for estimating both the random scale and shape parameters. These estimators use a sequence of maximum likelihood estimates from related reliability experiments to form an empirical estimate of the appropriate unknown prior probability density function. Monte Carlo simulation is used to compare the performance of these estimators with the appropriate maximum likelihood estimator. Algorithms are presented for sequentially obtaining the reduced sample sizes required by the estimators while still providing mean squared error accuracy compatible with the use of the maximum likelihood estimators. In some cases whenever the prior pdf is a member of the Pearson family of distributions, as much as a 60% reduction in total test units is obtained. A numerical example is presented to illustrate the procedures.     

Estimation of parameters of life from progressively censored data using Burr-XII model

Based on progressively Type-II censored samples, the maximum likelihood, and Bayes estimators for some lifetime parameters (reliability, and hazard functions), as well as the parameters of the Burr-XII model, are derived. The Bayes estimators are obtained using both the symmetric (Squared Error, SE) loss function, and asymmetric (LINEX, and General Entropy, GE) loss functions. This was done with respect to the conjugate prior for the one shape parameter, and discrete prior for the other parameter of this model. Also the existence, uniqueness, and finiteness of the ML parameter estimates for this type of censoring are discussed. A practical example consisting of data from an accelerated test on insulating fluid reported by Nelson (1982) was used for illustration, and comparison. Finally, some numerical results using simulation study concerning different sample sizes, and progressive censoring schemes were reported.     

Approximate MLEs for the location and scale parameters of theextreme value distribution with censoring

For the extreme value distribution, the maximum likelihood method does not provide explicit estimators for the location and scale parameters. A method of deriving explicit estimators by approximating the likelihood function is provided. The authors derive the asymptotic variances, covariance, and conditional bias of these estimators, and show that they are almost as efficient as the maximum likelihood estimators and just as efficient as the best linear unbiased and the best linear invariant estimators. Two examples illustrate this method of estimation     

Estimation and testing in an imperfect-inspection model

An imperfect inspection model in which failures can only be detected with probability β is considered. The lifetimes of all the components are IID exponential with rate λ. Using the approximate likelihood filtering method, a first order binomial autoregressive model is obtained when 1-β is small. When λ is known, a locally most powerful test is proposed for testing the hypothesis that β=1 against the alternative that β<1. The asymptotic distribution of the test statistic is obtained under the null hypothesis as well as under the alternative. The test statistic is modified to handle the case of unknown λ. Its asymptotic distribution is also given. The bias of the maximum likelihood estimators of β and λ obtained from the approximated likelihood function is studied by simulation     

Accelerated life tests for products of unequal size

This paper considers `estimation of the lifetime distribution' and `optimal design of constant-stress accelerated life test plans' for products of unequal size. The distribution is Weibull with a scale parameter that is a `log-linear function of stress' and a `power function of product size with a size-effect parameter'. Maximum likelihood estimators (MLE) of model parameters are obtained, and their properties are studied. Two stress-level optimal test plans are obtained for products that come in two sizes, and a table useful for finding optimal test plans is given. The sum of asymptotic variances of MLE of a specified quantile of the distributions for products of both sizes is used as the optimality criterion. Optimum plans can be used when the ratio of two sizes is not too large. When the ratio is very large, the preestimate of size effect parameter should be carefully chosen     

Weibull分布下基于MLE的红外发光二极管寿命预测

为了对红外发光二极管(LED)恒定及步进应力加速寿命试验的数据进行统计分析,应用Weibull分布函数描述了其寿命分布,利用极大似然法(MLE)及其迭代流程图估计出形状参数和尺度参数,通过最小二乘法确定了红外LED加速寿命方程,对红外LED寿命是否符合威布尔分布进行了Kolmogorov-Smirnov检验,并利用自行开发的寿命预测软件计算出平均寿命和中位寿命。数值结果表明,红外LED的寿命服从Weibull分布,加速寿命方程符合逆幂定律,所估计出的红外LED的寿命对生产厂商和用户有很强的指导意义。     

Lognormal and Weibull accelerated life test plans under distribution misspecification

In this article, we derive expressions for the asymptotic distribution of maximum likelihood estimators of model parameters in accelerated life tests (ALTs) when the model distribution is misspecified. We investigate results for two popular models, namely, the lognormal and Weibull Arrhenius-type ALT models. We propose test plan criteria based on asymptotic bias (ABias) and asymptotic mean squared error (AMSE) to derive ALT test plans. We derive 4:2:1 allocation plans that minimize either ABias/sup 2/ or AMSE. These criteria provide control over estimation bias and variance when the model distribution is misspecified.     

Bayes estimation of hazard and acceleration in accelerated testing

In accelerated life testing, the time transformation function &thetas;(t) is often unknown, even if that function is assumed to be linear. If &thetas;(t) is known, data in the accelerated condition can be adjusted to provide information about the failure time distribution in the use condition. If &thetas;(t) is unknown, the usual estimation procedures require data from the use condition as well as data from the acceleration condition. In this work it is assumed that the uncertainty about &thetas; can be modeled by a prior distribution, chosen from the truncated Pareto family of distributions, and that the uncertainty in λ, the failure rate, can be modeled by a prior distribution from the gamma family. Under these assumptions, the posterior distributions and their first two moments are provided for both λ and &thetas;. Thus, this complete Bayes approach to accelerated life testing with the assumed model allows the adjustment of data taken in the accelerated condition to provide the user with the important estimates in the use condition. The results are illustrated by examples     

Goodness-of-fit tests based on Kullback-Leibler discriminationinformation

We present a general methodology for developing asymptotically distribution-free goodness-of-fit tests based on the Kullback-Leibler discrimination information. The tests are shown to be omnibus within an extremely large class of nonparametric global alternatives and to have good local power. The proposed test procedure is a nonparametric extension of the classical Neyman-Pearson log-likelihood ratio test and is based on mth-order spacings between order statistics cross-validated by the observed log likelihood. The developed method also generalizes Cox's procedure of testing separate families and covers virtually all parametric families of distributions encountered in statistics. It can also be viewed as a procedure based on sum-log functionals of nonparametric density-quantile estimators cross-validated by the log likelihood. With its good power properties, the method provides an extremely simple and potentially much better alternative to the classical empirical distribution function (EDF)-based test procedures. The important problem of selecting the order of spacings m in practice is also considered and a method based on maximizing the sample entropy constrained by the observed log likelihood is proposed. This data driven method of choosing m is demonstrated by Monte Carlo simulations to be more powerful than deterministic choices of m and thus provides a practically useful tool for implementing our test procedure