Bayesian Estimation and Hierarchical Bayesian Estimation of Zero-failure Data

The zero_failure data research is a new field in the recent years, but it is required urgently in practical projects, so the work has more theory and practical values. In this paper, for zero_failure data (t i,n i) at moment t i , if the prior distribution of the failure probability p i=p{T【t i} is quasi_exponential distribution, the author gives the p i Bayesian estimation and hierarchical Bayesian estimation and the reliability under zero_failure date condition is also obtained.

Hierarchical Bayesian Estimation of the Products Reliability Based on Zero-Failure Data

With the development of science and technology, the products reliability is higher and higher. So for high reliability products, zero\|failure data situation appears often in the time ended reliability tests. In this paper, the hierarchical Bayesian estimation of the products reliability is given under the conditions of the Binomial distribution with zero\|failure data and the prior distribution of the reliability being quasi\|Beta distribution. The authors also give a practical calculating example using the theory.

E-Bayesian Estimation of the Products Reliability when Testing Reveals no Failure

This paper develops a new method, named E-Bayesian estimation method, to estimate the reliability parameters. The E-Bayesian estimation method of the reliability are derived for the zero-failure data from the product with Binomial distribution. Firstly, for the product reliability, the definitions of E-Bayesian estimation were given, and on the base, expressions of the E-Bayesian estimation and hierarchical Bayesian estimation of the products reliability was given. Secondly, discuss properties of the E-Bayesian estimation. Finally, the new method is applied to a real zero-failure data set, and as can be seen, it is both efficient and easy to operate.

Estimation of Reliability Derived from Binomial Distribution in Zero-Failure Data

This paper introduces a new method, E-Bayesian estimation method, to estimate the reliability in zero-failure data. The definition of E-Bayesian estimation of the reliability is given. Based on the definition,the formulas of E-Bayesian estimation and hierarchical Bayesian estimation of the reliability are provided, and property of the E-Bayesian estimation, i.e. relation between E-Bayesian estimation and hierarchical Bayesian estimation, is discussed. Calculations performed on practical problems show that the proposed new method is feasible and easy to operate.

Processing for Zero-Failure Data of the Products

In this paper, an estimation method for reliability parameter in the case of zero-failuare data-synthetic estimation method is given. For zero-failure data of double-parameter exponential distribution, a hierarchical Bayesian estimation of the failure probability is presented. After failure information is introduced, hierarchical Bayesian estimation and synthetic estimation of the failure probability, as well as synthetic estimation of reliability are given. Calculation and analysis are performed regarding practical problems in case that life distribution of an engine obeys double-parameter exponential distribution.

Estimation of Parameter in the Case of Zero-Failure Data

In this paper, for zero-fai1ure data (t,, n1), at moment ti, if the prior distribution of the failure probability p, = P {T<ti } is incomplete Fisher--Z distribution: Fisher-Z (0, λi; a, b), the author gives pi hierarchical Biyesian estimation and the estimation of reliability under zero-failure data condition is obtained also. The author also gives a practical ca1culating example using the theory.

Reliability analysis of DOOF for Weibull distribution

Hierarchical Bayesian method for estimating the failure probability Pi under DOOF by taking the quasi-Beta distribution B(pi-1 , 1,1, b ) as the prior distribution is proposed in this paper. The weighted Least Squares Estimate method was used to obtain the formula for computing reliability distribution parameters and estimating the reliability characteristic values under DOOF. Taking one type of aerospace electrical connectoras an example, the correctness of the above method through statistical analysis of electrical connector acceler-ated life test data was verified.

指数分布无失效数据的多层Bayes分析

韩明等．指数分布无失效数据的多层Ｂａｙｅｓ分析．数理统计与管理，１９９８，１７（４），２４～２７．本文对指数分布无失效数据的失效率，在先验分布为Ｇａｍｍａ分布时，给出了多层Ｂａｙｅｓ估计。最后。

对数正态分布无失效数据的可靠性分析

对于对数正态分布的无失效数据问题 ,利用构造先验分布的减函数法给出失效概率的多层Bayes估计 ,从而求出对数正态分布参数与可靠性指标的估计 。

无失效数据情形船舶E-Bayes可靠性分析

为了解决造价昂贵以及高可靠性产品的可靠性评估问题,基于船舶无失效数据情形,提出了船舶寿命的可靠性评估方法。根据E-Bayes(Expected-Bayesian)理论,设船舶寿命服从指数分布,在失效率的先验分布为Gamma分布,且两个超参数选择三种不同的先验分布情况下,给出船舶失效率和可靠度的三种E-Bayes估计模型;对比分析三种模型,给出EBayes估计的渐进性质。结合集装箱5 600船舶(标箱)寿命无失效数据进行计算,结果表明本文提出的船舶可靠性的E-Bayes估计模型可行、便于工程应用,其中第二种模型当两个超参数同时选取均匀分布时,估计结果更稳健更保守。

失效概率的E-Bayes估计及其性质

该文提出了参数的一种新估计方法——E-Bayes估计法,在无失效数据情形,给出了失效概率的E-Bayes估计的定义,在此基础上给出了失效概率的E-Bayes估计,并给出了失效概率的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,结果表明该文提出的E-Bayes估计法可行且便于应用。

无失效数据的多层Bayes可靠性分析

本文对无失效数据（ti,ni）在时刻ti的失效概率pi＝p｛T＜ti｝的先验分布为不完全Beta分布时，给出了pi的多层Bayes估计，由此可以得到无失效数据可靠度的估计．

无失效数据情形可靠性参数的估计和调整

本文在无失效取样情形下,提出了产品可靠性参数的一种估计和调整的方法———加权多层Bayes估计法.在无失效数据情形下失效率的多层Bayes估计和引进失效信息后失效率的多层Bayes估计的基础上,对可靠性参数进行了估计和调整———给出了失效率和可靠度的加权多层Bayes估计.最后,结合发动机的实际问题进行了计算,结果表明本文提出的方法可行且便于应用.

无失效数据情形失效率的综合估计

对指数分布的无失效数据 ,提出了无失效数据情形失效率的综合估计法 .在失效率的先验分布为截尾 Gamma分布时 ,给出了失效率的多层 Bayes估计 .在引进失效信息后 ,在失效率的先验分布为截尾 Gamma分布时 ,给出了失效率的多层 Bayes估计和综合估计 ,并给出了可靠度的综合估计 。

失效率的E-Bayes估计和多层Bayes估计

提出了一种可靠性参数的估计方法—E-Bayes估计法,对寿命服从指数分布的产品,在无失效数据情形,给出了失效率的E-Bayes估计的定义、E-Bayes估计和多层Bayes估计,并在此基础上给出了E-Bayes估计的性质.最后,结合发动机的实际问题进行了计算,结果表明E-Bayes估计法可行且便于应用.

无失效数据失效率的综合多层Bayes估计

文章对指数分布无失效数据的失效率，在先验分布为Ｇａｍｍａ分布时，在引进失效信息后，给出了多层Ｂａｙｅｓ估计以及综合多层Ｂａｙｅｓ估计，并给出了可靠度的综合估计。最后。

无失效数据的Bayes和多层Bayes分析

本文推广了文献［６］的结果，对指数分布无失效数据的失效率，给出了Ｂａｙｅｓ估计、Ｂａｙｅｓ置信上限以及多层Ｂａｙｅｓ估计，从而可以得到无失效数据可靠度的估计。最后，结合实际问题进行了计算。

二项分布无失效数据可靠度的多层Bayes估计

文章对二次分布无失效数据的可靠度，在先验分布为Ｂｅｔａ分布时，给出了可靠度的多层Ｂａｙｅｓ估计。最后，结合实际问题进行了计算。

指数分布无失效数据的Bayes点估计

通过对双指数分布无失效数据的失效率,在先验分布为Gamma分布时得到失效率的估计。并利用Bayes和多层Bayes估计,从而得到无失效数据可靠度的估计,并结合实际问题进行说明。

正态分布无失效数据的多重Bayes方法

基于正态分布场合的无失效数据(si,τi)(i=1,2,…,l),给出了失效概率pi的多重Bayes估计^pi,进而得到总体参数μ和σ的估计,并结合实际问题加以说明.