定时截尾场合双参数威布尔分布的贝叶斯推断

给出了定时截尾下,双参数威布尔分布中参数及可靠性指标的Bayes估计,并且给出了未来观测值的贝叶斯预测问题.     

威布尔分布的Bayes可靠性分析

本文针对两参数的威布尔分布的元件，采用Ｂａｙｅｓ方法对其可靠性进行分析，文中分别对两种假设情况进行了讨论，第一种情况是形状参数为离散取值，尺度参数为连续取值的情况，第二种情况假设形状参数的先验分布为均匀分布，尺度参数的先验分布为逆伽玛分布，推出了对应的可靠性估计和置信下限估计，并给出了计算算法，最后用实例对算法进行了验证。     

Weibull分布场合无失效数据的可靠性验证试验

对于Weibull分布的无失效数据问题,利用Bayes方法给出了产品寿命服从Weibull分布,形状参数的先验分布为U(0,1),尺度参数为1,假定产品的可靠性指标达到某个给定的值的情况下,无失效数据的可靠性验证试验,并利用相同的分析方法给出形状参数的Bayes估计.     

Multivariate distributions having Weibull properties

Random variables X₁ ,…, X_n are said to have a joint distribution with Weibull minimums after arbitrary scaling if min_i(a_iX_i) has a one dimensional Weibull distribution for arbitrary constants a_i > 0, i = 1,…, n. Some properties of this class are demonstrated, and some examples are given which show the existence of a number of distributions belonging to the class. One of the properties is found to be useful for computing component reliability importance. The class is seen to contain an absolutely continuous Weibull distribution which can be generated from independent uniform and gamma distributions.     

逐步区间删失Weibull分布的Bayesian稳健设计

逐步区间删失是获取高可靠性产品相关信息的一种重要方法.文章研究了产品寿命服从Weibull分布,带有随机移除逐步区间删失寿命试验的最优设计问题.采用极大似然方法获取模型参数的估计及其信息矩阵.利用Bayesian方法处理模型参数未知情况下设计准则对模型参数的依赖问题,获得了模型参数估计的Bayesian稳健设计准则.在考虑试验费用有限制的条件下,给出了获得最优稳健设计非线性混合整数算法.同时对先验选取及约束参数设定的敏感性做了分析.数值结果表明文章提出的方法是有效可行的.     

指数分布下Bayes鉴定试验方案

在确保使用方利益的前提下，从最大后验风险的角度运用贝叶斯方法制定了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。     

Weibull分布恒定应力加速寿命试验的Bayes估计

对定时和定数截尾样本情形CE模型下Weibull分布场合恒定应力加速寿命试验进行了Bayes统计分析,利用Laplace方法给出了该模型的近似Bayes估计.最后通过模拟实例表明该Bayes估计是有效的.     

Bayesian single and double variable sampling plans for the Weibull distribution with censoring

The sampling inspection problem is one of the main research topics in quality control. In this paper, we employ Bayesian decision theory to study single and double variable sampling plans, for the Weibull distribution, with Type II censoring. A general loss function which includes the sampling cost, the time-consuming cost, the salvage value, and the after-sales cost is proposed to determine the Bayes risk and the corresponding optimal sampling plan. Explicit expressions for the Bayes risks for both single and double sampling plans are derived, respectively. Numerical examples are given to illustrate the effectiveness of the proposed method. Comparisons between single and double sampling plans are made, and sensitivity analysis is performed.     

指数-威布尔分布下基于期望总成本最小的寿命试验抽样方案

对于寿命遵从指数-威布尔分布的产品,在生产商提供优质保修服务的前提下,采用生产商在产品抽验过程中与产品接收后所承担的总成本期望最小的准则,制定寿命试验的最优抽样方案.通过实例,证实指数-威布尔分布适宜作为当前产品的寿命分布,并验证了这种抽样方案的合理性.     

一般寿命分布和定时截尾的Bayes变量抽样方案

林（1994）研究了指数分布和定时截尾的变量抽样方案．本文将讨论一般寿命分布和定时截尾的一次抽样方案．在多项式损失函数的假设下,我们讨论了Weibull分布、双参数指数分布和-分布三种情形,并着重讨论Weibull分布的情形．本文还提出了一个可用于近似地确定最优抽样方案的有报算法,并且进行了灵敏度分析,还同林较早的模型（1990,1994）做了比较．     

指数和Weibull串联系统环境因子的统计推断

给出了Weibull串联系统环境因子的定义,且研究了元件寿命服从指数分布和Weibull分布时串联系统环境因子的点估计和区间估计,并利用模拟方法研究了所给点估计的精度和广义置信区间的覆盖率.模拟结果表明所给方法是令人满意的.     

Gumbel分布的简单贝叶斯估计

在实际应用中,两参数Gumbel分布的贝叶斯估计往往需要预先知道Gumbel参数的二维联合先验分布。由于获取先验分布的主观性和统计推断的复杂性,目前有关Gumbel分布贝叶斯估计理论及其性质的讨论还比较少,更不要说获得较为简单的Gumbel分布的贝叶斯估计。本文基于Kaminskiy和Vasiliy提出的简单贝叶斯估计过程,利用可靠度函数估计的区间形式表示先验信息,从而得到两个参数Gumbel分布的简单贝叶斯估计。基于此先验信息,该估计过程构造了Gumbel参数的连续联合先验分布,给出了在给定任意时点的可靠度(或累积密度)及其标准差的后验估计,为可靠性与风险评估中简单快速的使用贝叶斯估计刻画极端事件提供了可能.     

参数模型下的时间序贯检验方案

本文研究参数模型下的序贯检验方案 .而以往的序贯检验方案往往采取非参数模型 .由于参数模型在生产实践中是常见的形式 .所以这个检验方案对于产品的检验具有指导意义 .     

A new approach for parameter estimation of finite Weibull mixture distributions for reliability modeling

The aim of this paper is to model lifetime data for systems that have failure modes by using the finite mixture of Weibull distributions. It involves estimating of the unknown parameters which is an important task in statistics, especially in life testing and reliability analysis. The proposed approach depends on different methods that will be used to develop the estimates such as MLE through the EM algorithm. In addition, Bayesian estimations will be investigated and some other extensions such as Graphic, Non-Linear Median Rank Regression and Monte Carlo simulation methods can be used to model the system under consideration. A numerical application will be used through the proposed approach. This paper also presents a comparison of the fitted probability density functions, reliability functions and hazard functions of the 3-parameter Weibull and Weibull mixture distributions using the proposed approach and other conventional methods which characterize the distribution of failure times for the system components. GOF is used to determine the best distribution for modeling lifetime data, the priority will be for the proposed approach which has more accurate parameter estimates.     

Bayesian stopping rules for multistart global optimization methods

By far the most efficient methods for global optimization are based on starting a local optimization routine from an appropriate subset of uniformly distributed starting points. As the number of local optima is frequently unknown in advance, it is a crucial problem when to stop the sequence of sampling and searching. By viewing a set of observed minima as a sample from a generalized multinomial distribution whose cells correspond to the local optima of the objective function, we obtain the posterior distribution of the number of local optima and of the relative size of their regions of attraction. This information is used to construct sequential Bayesian stopping rules which find the optimal trade off between reliability and computational effort.     

可靠度的E-Bayes估计、性质及应用

对二项分布的可靠度,提出了一种新的参数估计方法——E-Bayes估计法.在不同先验分布下,给出可靠度的E-Bayes估计和多层Bayes估计,并给出可靠度的E-Bayes估计的性质——E-Bayes估计和多层Bayes估计的关系.最后,给出了模拟算例,结果表明本文提出的方法可行且便于应用.     

厚尾金融时间序列的贝叶斯单位根检验

在金融时间序列分析中,单位根检验是一个相当重要的研究问题。对于数据生成过程为自回归的厚尾金融时序数据,古典的ADF单位根检验统计量应用非常困难。本文则在贝叶斯框架下,发展了检验带有未知自由度厚尾t分布的自回归金融时间序列单位根的贝叶斯方法。蒙特卡罗模拟结果显示本文发展的方法能够取得好的检验功效。最后,用万科地产月度历史收益数据来演示了本文发展的方法。     

On the normality a posteriori for exponential distributions,using the Bayesian estimation

Summary The Bayesian estimation problem for the parameter θ of an exponential probability distribution is considered, when it is assumed that θ has a natural conjugate prior density and a loss-function depending on the squared error is used. It is shown that, with probability one, the posterior density of the Bayesian—centered and scaled parameter converges pointwise to the normal probability density. The weak convergence of the posterior distributions to the normal distribution follows directly. Both correct and incorrect models are studied and the asymptotic normality is stated respectively.     

两参数Weibull分布平均寿命的置信下限

王蓉华，徐晓岭．两参数Ｗｅｉｂｕｌ分布平均寿命的置信下限．数理统计与管理，１９９８，１７（２），４３～４５．本文给出了求两参数Ｗｅｉｂｕｌ分布定数截尾下平均寿命置信下限的一种方法     

Weibull分布定时截尾试验数据情形下可靠度的置信限

本文针对Weibull分布定时截尾型试验数据提出了一种计算可靠度置信限的方法。通过采用数据填充的方式将不完全数据虚拟成完全数据,利用完全数据情形下可靠度置信限的计算方法得到删失数据情形下可靠度的置信限。模拟研究表明本文提出的算法具有较好的计算稳定性和可操作性。