Empirical Bayes Approach to Reliability Estimation for the Exponential Distribution

In the empirical Bayes (EB) approach to a reliability estimation for the exponential distribution, a prior distribution is placed on the family of prior gamma distributions to produce an EB estimator. The EB estimator is asymptotically optimal and admissible. The results of a Monte Carlo study are presented to demonstrate the favorable risk behavior of the EB estimator as a Bayes estimator if the sample size is large.     

An Empirical Bayes Approach to Reliability

A Bayesian reliability estimation technique known as the ``empirical Bayes approach' is developed which uses previous experience nce to get a Bayesian point estimator. The techniques require no knowledge of the form of the unknown prior distribution and are robust to assumptions about its form. Empirical Bayes techniques are applicable to situations in which prior, independent observations of the random variable X from the random couple (?, X) are available where ? is the observed parameter of interest distributed in accordance with the unknown prior distribution. Performance comparisons of the empirical Bayes and other well established techniques are developed by examples for the binomial, exponential, Normal, and Poisson situations which often occur in reliability problems. In all cases the empirical Bayes estimator performed better than the classical estimator in minimizing the average squared error.     

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.     

A Bayesian Approach to Parameter and Reliability Estimation in the Poisson Distribution

For life testing procedures, a Bayesian analysis is developed with respect to a random intensity parameter in the Poisson distribution. Bayes estimators are derived for the Poisson parameter and the reliability function based on uniform and gamma prior distributions of that parameter. A Monte Carlo procedure is implemented to make possible an empirical mean-squared error comparison between Bayes and existing minimum variance unbiased, as well as maximum likelihood, estimators. As expected, the Bayes estimators have mean-squared errors that are appreciably smaller than those of the other two.     

一种基于积分微分方程的泊松噪声去除算法

该文提出一种新的基于积分微分方程的泊松噪声去除算法。首先讨论了经典的总变差(TV)最小模型,在此基础上提出一种新的变分多尺度分层图像表示方法,然后在逆尺度空间上积分尺度图像从而得到了新的积分微分方程。这种新的积分微分方程含有一个单调增加的尺度函数。通过选取适当的尺度函数,该方程可以有效地去除泊松型噪声。数值实验证明了该算法比经典的TV和四阶偏微分方程算法具有更好的去噪效果。     

Empirical Bayes Estimators of Reliability for Lognormal Failure Model

Empirical Bayes (EB) procedures are considered for estimating the reliability R(t;?,?) = gaufc[(ln t -?)/?] for the lognormal failure model. EB estimators are obtained for the 2 cases: i)? is unknown and ? is known, and both ? and ? are unknown. The empirical Cdf of the maximum likelihood estimators of the parameters is used to obtain the EB estimators. ii) A smooth EB estimator of R(t;?,?) is developed when ? is unknown and ? is known. A modification of this estimator is proposed for both ? and ? unknown. In both cases, EB estimators are obtained for complete samples at each testing stage. Monte Carlo simulations are presented to compare the EB estimators and the maximum likelihood (ML) estimators of R(t;?,?). The simulations indicate that the smooth EB estimators have smaller mean squared errors than the other EB estimators or the ML estimators.     

Modified Method-of-Moments in Empirical Bayes Estimation

A unit is put on test for a fixed time and the number of failures is observed. The probability distribution of the number of failures is assumed to be Poisson, and the Poisson failure intensity is assumed to be a stochastic variable with gamma prior distribution. Schafer & Feduccia introduced an empirical procedure for estimating the parameters of the prior based on method of moments. We investigate the s-efficiencies of empirical Bayes estimates of Poisson failure intensity and reliability when the prior is estimated by the Schafer & Feduccia method. Mean square errors (MSEs) are compared for a range of parameters which typifies certain military equipment failure data. The empirical Bayes estimates have high s-efficiencies for sample size more than 40. A modification of the Schafer & Feduccia procedure substantially improves s-efficiencies for small sample sizes.     

Bayes inference for a non-homogeneous Poisson process with powerintensity law [reliability]

Monte Carlo simulation is used to assess the statistical properties of some Bayes procedures in situations where only a few data on a system governed by a NHPP (nonhomogeneous Poisson process) can be collected and where there is little or imprecise prior information available. In particular, in the case of failure truncated data, two Bayes procedures are analyzed. The first uses a uniform prior PDF (probability distribution function) for the power law and a noninformative prior PDF for α, while the other uses a uniform PDF for the power law while assuming an informative PDF for the scale parameter obtained by using a gamma distribution for the prior knowledge of the mean number of failures in a given time interval. For both cases, point and interval estimation of the power law and point estimation of the scale parameter are discussed. Comparisons are given with the corresponding point and interval maximum-likelihood estimates for sample sizes of 5 and 10. The Bayes procedures are computationally much more onerous than the corresponding maximum-likelihood ones, since they in general require a numerical integration. In the case of small sample sizes, however, their use may be justified by the exceptionally favorable statistical properties shown when compared with the classical ones. In particular, their robustness with respect to a wrong assumption on the prior β mean is interesting     

On Bayes Estimation of Reliability for the Birnbaum-Saunders Fatigue Life Model

Estimation of reliability for the Birnbaum-Saunders fatigue life distribution is considered. The scale parameter is also the median lifetime, and assuming that the scale parameter is known, Bayes estimators of the reliability function are obtained for a family of proper conjugate priors as well as for Jeffreys' vague prior for the shape parameter. When both parameters are unknown, a modified Bayes estimator of reliability is proposed using a moment estimator of the scale parameter. In addition to being computationally simpler than the MLE of reliability, Monte Carlo simulations for small samples show that the modified Bayes estimator is better than the MME for all values of the shape parameter and as good as the MLE for small values of the shape parameter in the sense of root mean squared errors.     

Bayes Interval Estimation for the Shape Parameter of the Power Distribution

The power distribution is considered as failure model and uses a square-error loss function. Bayes credibility interval estimators for the shape parameter have been obtained assuming 1) the following priors for the shape parameter: Jeffrey's invariant prior, gamma, and inverted gamma; 2) the following priors for reliability: beta and log gamma function. It is straightforward to obtain estimators for reliability when the estimators for the shape parameter are known.     

半导体器件并联系统可靠性评估的经验Bayes方法

为了提高机载开关电源中半导体器件并联系统可靠性评估的准确性,运用经验 Bayes 法和经典的统计方法,研究了该系统的可靠性评估问题。分别给出了系统可靠性指标的经验 Bayes 估计,极大似然估计。利用 Monte-Carlo方法,对两种估计结果进行了比较,结果表明,经验 Bayes 估计的最大绝对误差为 0.07,它小于极大似然估计的最大绝对误差 0.368。     

An Empirical Procedure for Estimating the Parameters of a Mixed Exponential Life Testing Model

A failure-time distribution made up of two exponential distributions having two distinct failure rates and a specific mixture proportion is considered. The associated experiment is terminated after a predetermined time has elapsed and the numbers of failures in each time interval are recorded. As soon as an item fails it can be attributed to the appropriate subpopulation. An empirical procedure is proposed to estimate the 3 parameters of the model. The maximum likelihood estimators and our estimators are compared using both real and simulated data. The procedure can be extended to a mixed model of three or more exponential distributions, and can be applied to ungrouped and/or uncensored samples.     

Pooling Life-Test Data by Means of the Empirical Bayes Method

The Empirical Bayes approach in reliability is reviewed non-technically by discussing the questions: What is Empirical Bayes; how does it differ from Bayes; when can I use it; how do I use it; and what do I gain by using it? The Empirical Bayes method is applied to the problem of estimating the outage rates for two 115 kV transmission circuits of a regional power company.     

An engineering approach to Bayes estimation for the Weibull distribution

In this paper an engineering approach to Bayes reliability analysis of Weibull failure data collected under a randomly censored sampling is proposed. The posterior distribution of several decision variables, such as the meanlife, the reliability function, the reliable life, and the hazard rate, are derived, when either a prior information on the reliability or a prior information on the hazard rate is available. Point estimates of the selected decision variables are given, by assuming both symmetric and asymmetric loss functions. Finally, numerical examples are presented to illustrate the proposed estimation procedures.     

An empirical Bayes estimator for in-scale adaptive filtering

A scale-adaptive filtering scheme is developed for underspread channels based on a model of the linear time-varying channel operator as a process in scale. Recursions serve the purpose of adding detail to the filter estimate until a suitable measure of fidelity and complexity is met. Resolution of the channel impulse response associated with its coherence time is naturally modeled over the observation time via a Gaussian mixture assignment on wavelet coefficients. Maximum likelihood, approximate maximum a posteriori (MAP) and posterior mean estimators, as well as associated variances, are derived. Doppler spread estimation associated with the coherence time of the filter is synonymous with model order selection and a MAP estimate is presented and compared with Laplace's approximation and the popular AIC. The algorithm is implemented with conjugate-gradient iterations at each scale, and as the coherence time is recursively decreased, the lower scale estimate serves as a starting point for successive reduced-coherence time estimates. The algorithm is applied to a set of simulated sparse multipath Doppler spread channels, demonstrating the superior MSE performance of the posterior mean filter estimator and the superiority of the MAP Doppler spread stopping rule.     

一种基于模态分解的时频分析方法

阐述了基于模态分解的时频分析方法的基本原理及特点。并与其他时频分析方法相比较，说明了该方法用于信号进行时频分析的可行性和优点，最后指出了该方法亟待解决的几个问题。     

一种高效的室分系统问题定位方法

室分系统一直存在难监控、难定位的问题。为了快速、全面地诊断LTE室分小区的问题原因,并为LTE室分小区的优化提供指导和参考,本文提出了一种基于MR电平分布的室分定界方法,并进一步结合多维数据完成问题原因的定位,有效地提升了室分系统的问题识别、定位效率。通过现网的验证,该方法准确率达80%     

基于可能性理论的随机应力加速寿命试验分析方法

在加速寿命试验中,随机应力的影响是普遍存在的,但目前对随机应力条件下的加速寿命试验分析缺乏有效的方法.以可能性理论为基础,将随机应力转化为一个模糊应力,通过确定该模糊应力的可能性分布函数.建立随机应力条件下的寿命分布模型.提出一种通过求取模糊数的上、下可能性均值来减小模型误差的方法,并以阿伦尼斯模型为例,分析了温度随机应力条件下的寿命分布模型,结果证明该方法是有效的.     

基于改进Choi-Williams分布的多分量信号频率识别方法

通过相关域内对短时信号模糊函数的分析,针对短时信号对Choi-Williams分布(CWD)的核函数进行了改进,提出对加窗信号运用改进后的CWD提取信号时频信息的方法。仿真实验表明陔方法对多分量信号具有较强的交叉项抑制能力,在提高了信噪比特性的同时,也减少了计算量。