可靠性工程中参数的一种估计方法

提出了可靠性工程中参数的一种估计方法——新Bayes估计法，给出了失效概率、失效率的新Bayes估计的定义及其新Bayes估计。最后，结合实际问题的数据，进行了具体计算和分析，结果表明所提出的新Bayes估计法有效、可行，便于工程技术人员在工程中应用。     

成败型产品的Bayes鉴定试验方案研究

利用可靠性增长模型给出了成败型产品鉴定试验的一种Bayes方法，提出了Bayes鉴定试验的最大后验风险准则，利用这种准则制定的鉴定试验方案综合了产品研制过程中的先验信息，在确保产品质量的前提下．与传统的鉴定试验方案相比，将大大节省试验时间。     

无失效数据下失效概率的多层Bayes和E Bayes估计的性质

高可靠性产品的可靠性试验很难获得样品失效的数据,可靠性参数估计涉及无失效数据分析,Bayes方法是处理无失效数据分析的有力方法。多层Bayes参数估计涉及到Beta函数比的积分。利用Gamma函数比不等式,导出Beta函数比不等式及Beta函数比的积分不等式,证明了无失效数据下失效概率的EBayes估计与多层Bayes估计渐近相等,且给出多层Bayes估计值小于EBayes估计值的一个充分条件。     

基于Bayes法的电主轴极小子样可靠性研究

针对长寿命的磨削电主轴极小子样的可靠性评估问题,提出了Bayes结合虚拟增广样本的分析方法。首先,在Bayes法基本流程的指导下,研究了基于Bayes法的磨削电主轴可靠性评估方法。根据定时截尾试验的原则对电主轴进行可靠性试验,应用Bayes法结合磨削电主轴试验样本的可靠性试验数据,综合虚拟增广样本法对其可靠性进行评估,最终获得电主轴的可靠性评估结果。最后,将基于Bayes法与基于伪寿命分布法的磨削电主轴极小子样可靠性评估结果进行比较,以验证基于Bayes法可靠性评估理论的合理性。     

基于Mindlin理论的Winkler地基参数动态Bayes识别

基于Bayes理论,提出了Winkler地基参数的动态识别方法。引入Mindlin理论,并利用考虑横向剪切效应板的基本方程,推导了Winkler地基上Mindlin板的控制微分方程。应用Fourier变换技术,推求了Winkler地基上简支板的Fourier闭式解。首次建立了Winkler地基参数的动态Bayes误差函数,推导了地基参数的动态Bayes均值和方差表达式,提出步长的一维自动寻优方案后,并结合共轭梯度法给出了Winkler地基参数的动态Bayes识别步骤。研究表明:动态Bayes识别方法能有效地动态识别Winkler地基参数;Winkler地基参数的收敛性依赖于地基参数先验信息的准确性和考察点位移实测资料的准确性;动态Bayes方法也可用于其它地基模型地基参数的动态识别。     

分组定时截尾无失效数据的迭代Bayes分析

对分组定时截尾无失效数据,文中提出了失效概率的迭代Bayes估计和迭代多层Bayes估计,给出了迭代估计的两个性质.在某型液压泵寿命服从对数正态分布假定下,给出了液压泵无失效数据情形可靠度的估计,并对不同方法得到的估计结果做了随机模拟,说明了迭代多层Bayes方法的有效性.     

基于Novozhilov理论薄壁弯箱位移参数的动态Bayes估计

基于Novozhilov理论推导了薄壁弯箱结构的有限曲条控制方程,并首次建立了薄壁弯箱位移参数的动态Bayes误差函数,推导了参数的动态Bayes均值和方差表达式,提出步长的一维自动搜索方案后,并结合共轭梯度法推导了薄壁弯箱位移参数的动态Bayes估计公式,同时给出了具体计算步骤。通过算例分析,总结了薄壁弯箱位移参数先验信息准确性判定方法及位移参数动态Bayes估计的其它重要结论。     

单桩承载力可靠度分析中试桩信息的应用

Bayes方法是统计学决策方法的基础之一,通过采样,修改先验的概率分布,从而减少了参数的不确定性。本文针对港工中实际试桩少,难以对单桩承载力作出准确统计的问题,用Bayes方法进行了计算,并考虑了主观不定性对抗力的影响,较好地解决了实际问题。     

竞争失效场合Weibull产品的可靠性分析

在竞争失效场合下,建立了Weibull产品的具有二项移走的逐步Ⅱ型截尾寿命试验模型.针对一般近似算法在小样本情形下精度较低的问题,以Gamma分布综合产品的先验信息,采用Gibbs抽样建立了参数的Bayes估计.利用Bootstrap方法、Bayes后验分布法分别构造了参数的置信区间.最后,利用随机模拟方法对估计结果进行了比较,结果表明在小样本情形下,Bayes比MLEs估计效果更好.     

威布尔分布场合下无失效数据的Bayes分析

通过对分布函数进行变换，使变换后的函数成为凹函数，利用凹函数性质给出了各检测时刻失效概率的Bayes估计，进而得到了产品可靠性指标的估计。最后，通过对实际数据进行计算，验证了方法的稳定性。     

Extracting signal limits from samples with multiple independent backgrounds

We discuss how the Bayes method can be used to extract signal information in counting experiments when the measured quantities are contaminated with background contributions from different channels estimated by Monte Carlo events, taking into account statistical fluctuations of these backgrounds.     

The Bayes procedure in exponential reliability family models using conjugate convex tent prior family

A Bayes procedure for estimating the unknown parameter indexed to some of one parameter exponential family distributions is presented. In such a procedure, we shall use a new conjugate prior family that we shall call a conjugate convex tent family. A member of this family could be constructed by assuming a little information about the unknown parameter. Some of the needed parameters for constructing prior density function are the values r, p and q. Bayes estimators for using a priori symmetrical convex tent density can be obtained as special cases of the present work. Numerical simulation study is introduced by using the Monte Carlo method. In this study we have investigated the influence of the prior parameters r, p and q on the accuracy of the Bayes estimators.     

An additive Chen-Weibull distribution and its applications in reliability modeling

In this article, we introduce a new lifetime distribution with increasing and bathtub-shaped failure rates. Some statistical properties of the proposed distribution are studied. We use the method of maximum likelihood for estimating the model parameters and reliability characteristics and discuss the interval estimates using asymptotic confidence intervals and bootstrap confidence intervals on one hand, and we provide Bayes estimators and highest posterior density intervals for the parameters via Hamiltonian Monte Carlo simulation method on the other hand. We demonstrate the superiority of the proposed distribution by fitting two reliability data sets well-known from references.     

A Bayes approach to reliability prediction utilizing data from accelerated life tests and field failure observations

A Bayes approach is proposed to improve product reliability prediction by integrating failure information from both the field performance data and the accelerated life testing data. It is found that a product's field failure characteristic may not be directly extrapolated from the accelerated life testing results because of the variation of field use condition that cannot be replicated in the lab‐test environment. A calibration factor is introduced to model the effect of uncertainty of field stress on product lifetime. It is useful when the field performance of a new product needs to be inferred from its accelerated life test results and this product will be used in the same environment where the field failure data of older products are available. The proposed Bayes approach provides a proper mechanism of fusing information from various sources. The statistical inference procedure is carried out through the Markov chain Monte Carlo method. An example of an electronic device is provided to illustrate the use of the proposed method. Copyright © 2008 John Wiley & Sons, Ltd.     

A comparison of maximum likelihood,exponential smoothing and Bayes forecasting procedures in inventory modelling

This paper compares four major schemes used for forecasting mean demand to be used as input into an inventory model so that ‘ optimum ’ stockage levels can be obtained. The inventory model is the classical order up to S, infinite horizon model with carry-over from period to period and complete back-ordering. Maximum likelihood, exponential smoothing, standard Bayes and adaptive Bayes schemes are used and results, via Monte Carlo simulation, are obtained on the average costs per period for (1) stationary demand, (2) long-term trend and (3) ‘ shock ’ changes in mean demand.     

Bayesian design of life testing plans under hybrid censoring scheme

This article describes Bayes design of hybrid‐censored life testing plans. A design criterion based on posterior variance of quantile of suitable order is proposed. The Weibull lifetime model with gamma prior distribution on model parameters is considered for illustration. Instead of using Markov chain Monte Carlo technique to compute the posterior quantities of interest, a large sample approximation is considered, which is easy to apply. Some life testing plans are presented. The effect of different prior information on the posterior quantity of interest is studied.     

Time-variant reliability global sensitivity analysis with single-loop Kriging model combined with importance sampling

This paper develops a novel failure probability-based global sensitivity index by introducing the Bayes formula into the moment-independent global sensitivity index to approximate the effect of input random variables or stochastic processes on the time-variant reliability. The proposed global sensitivity index can estimate the effect of uncertain inputs on the time-variant reliability by comparing the difference between the unconditional probability density function of input variables and the conditional probability density function in failure state of input variables. Furthermore, a single-loop active learning Kriging method combined with metamodel-based importance sampling is employed to improve the computational efficiency. The accuracy of the results obtained by Kriging model is verified by the reference results provided by the Monte Carlo simulation. Four examples are investigated to demonstrate the significance of the proposed failure probability-based global sensitivity index and the effectiveness of the computational method.     

基于厚尾时间序列的贝叶斯单位根检验

本文运用贝叶斯因子和可信区间两种方法来研究厚尾时间序列中单位根检验问题．通过Monte Carlo模拟证实了这两种方法的有效性,并对两种方法进行对比和分析．然后,考察了先验信息和自由度对单位根检验结果的影响．最后,将这两种方法运用到检验美国失业率和居民消费物价指数时间序列中,发现这两列序列均存在单位根．     

The reduction of computational time of the Monte Carlo method,applied to radiative heat transfer with variable properties,by using a fixed properties loop

The Monte Carlo method has the excellent feature of easy adaptation to problemens such as radiative heat transfer with variable properties, and problems of system of heat transfer including radiation, with complex geometries. However, this method has a deficiency that it requires a large computational time when the energy equation is non-linear. In this paper, a modified Monte Carlo method, named the DPEF method, is suggested to overcome this deficiency, by adding an iterative loop of fixed properties to the conventional method, without sacrificing the advantageous of the Monte Carlo method. An analytical example of this new method, as applied to a model of radiative heat transfer in a furnace with variable properties, is given. It is found that the computational time is reduced by half of that of the conventional Monte Carlo method, and moreover, the stability in iteration process is found to be improved.     

Bayesian Inference and Life Testing Plan for the Weibull Distribution in Presence of Progressive Censoring

This article deals with the Bayesian inference of unknown parameters of the progressively censored Weibull distribution. It is well known that for a Weibull distribution, while computing the Bayes estimates, the continuous conjugate joint prior distribution of the shape and scale parameters does not exist. In this article it is assumed that the shape parameter has a log-concave prior density function, and for the given shape parameter, the scale parameter has a conjugate prior distribution. As expected, when the shape parameter is unknown, the closed-form expressions of the Bayes estimators cannot be obtained. We use Lindley's approximation to compute the Bayes estimates and the Gibbs sampling procedure to calculate the credible intervals. For given priors, we also provide a methodology to compare two different censoring schemes and thus find the optimal Bayesian censoring scheme. Monte Carlo simulations are performed to observe the behavior of the proposed methods, and a data analysis is onducted for illustrative purposes.