指数分布步加试验的贝叶斯估计

给出了一种基于Gibbs抽样、CE模型下指数分布场合步进应力加速寿命试验的贝叶斯估计.通过模拟例子表明贝叶斯估计比极大似然估计更加有效.     

Inference for a Simple Step-Stress Model With Type-II Censoring, and Weibull Distributed Lifetimes

The simple step-stress model under Type-II censoring based on Weibull lifetimes, which provides a more flexible model than the exponential model, is considered in this paper. For this model, the maximum likelihood estimates (MLE) of its parameters, as well as the corresponding observed Fisher Information Matrix, are derived. The likelihood equations do not lead to closed-form expressions for the MLE, and they need to be solved by using an iterative procedure, such as the Newton-Raphson method. We also present a simplified estimator, which is easier to compute, and hence is suitable to use as an initial estimate in the iterative process for the determination of the MLE. We then evaluate the bias, and mean square error of these estimates; and provide asymptotic, and bootstrap confidence intervals for the parameters of the Weibull simple step-stress model. Finally, the results are illustrated with some examples.      

Accelerated Life Testing?Step-Stress Models and Data Analyses

This paper presents statistical models and methods for analyzing accelerated life-test data from step-stress tests. Maximum likelihood methods provide estimates of the parameters of such models, the life distribution under constant stress, and other information. While the methods are applied to the Weibull distribution and inverse power law, they apply to many other accelerated life test models. These methods are illustrated with step-stress data on time to breakdown of an electrical insulation.     

Longitudinal Models for Non-Stationary Exponential Data

In many manufacturing studies, longitudinal failure time data comprise repeated exponential responses, and a set of multi-dimensional covariates for a large number of independent components or objects. When the covariates collected along with exponential failure times are time dependent, the responses of an object exhibit non-stationary correlations. We examine the effects of the covariates by taking this non-stationary correlation structure into account. First, we develop Gaussian type non-stationary AR(1), MA(1), and exchangeable correlation structures for the repeated exponential failure times; and then exploit the suitable auto-correlation structure to obtain consistent, efficient estimates for the effects of the covariates by using a generalized quasi-likelihood (GQL) estimating equation approach. The finite sample estimation performance of the GQL approach is examined through a simulation study.      

Universal Models for the Exponential Distribution

This paper considers the problem of constructing information theoretic universal models for data distributed according to the exponential distribution. The universal models examined include the sequential normalized maximum likelihood (SNML) code, conditional normalized maximum likelihood (CNML) code, the minimum message length (MML) code, and the Bayes mixture code (BMC). The CNML code yields a codelength identical to the Bayesian mixture code, and within O(1) of the MML codelength, with suitable data driven priors.     

Inference for a Multivariate Exponential Distribution with a Censored Sample

Maximum likelihood estimators for the parameters of a multivariate exponential Cdf are easily obtained from partial information about a random sample, censored or not. The partial information consists of the minimum from each multivariate observation and the counts of how often each r.v. was equal to the minimum in an observation. The censoring might cause only the smallest r out of n minima to be observed along with the counts. The estimators depend on the total time-on-test statistic familiar in univariate exponential life testing. A likelihood ratio test for s-independence is derived which has s-significance ? = 0 and easily calculated power function.     

Adaptive Exponential Smoothing Models for Reliability Estimation

Four methods are discussed for determining the smoothing parameters in an adaptive exponential smoothing model which is used to assess reliability of a complex system tested in stages. The adaptive model is defined as Ri = ?iri + (1 - ?i)Ri-1, i = 2,...k, where Ri-1 is the assessed reliability at stage (i -1), ri is the ratio of the number of successes to the number of trials at stage i. Among the four procedures given here for determining the smoothing parameters xi two empirical methods and an empirical Bayes procedure are considered in some detail including a numerical example in which these techniques are compared.     

Bayesian Inference for Linear Dynamic Models With Dirichlet Process Mixtures

Using Kalman techniques, it is possible to perform optimal estimation in linear Gaussian state-space models. Here, we address the case where the noise probability density functions are of unknown functional form. A flexible Bayesian nonparametric noise model based on Dirichlet process mixtures is introduced. Efficient Markov chain Monte Carlo and sequential Monte Carlo methods are then developed to perform optimal batch and sequential estimation in such contexts. The algorithms are applied to blind deconvolution and change point detection. Experimental results on synthetic and real data demonstrate the efficiency of this approach in various contexts.     

Optimum Simple Step-Stress Plans for Accelerated Life Testing

This paper presents optimum plans for simple (two stresses) step-stress tests where all units are run to failure. Such plans minimize the asymptotic variance of the maximum likelihood estimator (MLE) of the mean life at a design stress. The life-test model consists of: 1) an exponential life distribution with 2) a mean that is a log-linear function of stress, and 3) a cumulative exposure model for the effect of changing stress. Two types of simple step-stress tests are considered: 1) a time-step test and 2) a failure-step test. A time-step test runs a specified time at the first stress, whereas, a failure-step test runs until a specified proportion of units fail at the first stress. New results include: 1) the optimum time at the first stress for time-step test and 2) the optimum proportion failing at the low stress for a failure-step test, and 3) the asymptotic variance of these optimum tests. Both the optimum time-step and failure-step tests have the same asymptotic variance as the corresponding optimum constant-stress test. Thus step-stress tests yield the same amount of information as constant-stress tests.     

指数型光波导的近似解析法

本文用一级微扰理论，对指数型折射率分布光波导，进行了波方程的解析求解，推得用Ａｉｒｙ函数表示的场解和色散方程。用一级近似计算了传播常数（β／ｋ）ｍ，与Ｃｏｎｗｅｌｌ的精确计算相比较，其结果也是好的。     

基于四阶混合累积量的衰减指数模型估计

定义了衰减指数模型的四阶混合累积量，给出了单样本有限长数据条件下的样本估计，提出了高斯色噪声条件下估计模型参数的两种有效方法。仿真实验结果表明：四阶混合累积量能明显提高KTProny、MP和ESPRIT方法在高斯色噪声条件下的估计性能，且后两种方法的估计性能优于第一种方法。     

Optimum Bivariate Step-Stress Accelerated Life Test for Censored Data

A step-stress accelerated life test for two stress variables is developed. The time to failure follows the Weibull distribution, and the test is subject to termination at a predetermined time, leading to censored failure data. An optimum test plan is developed to determine the test interval for each combination of stress levels. The scale parameter of the Weibull distribution for each combination of stress levels is defined as a log linear function of the stress levels. The optimal criterion is defined to minimize the asymptotic variance of the maximum likelihood estimator of the life for a specified reliability     

一类时滞Hopfield神经网络系统的全局指数稳定

研究一类时滞Hopfield神经网络系统的平衡状态全局指数稳定性.在放宽对激励函数的可微性与单调性要求的前提下,利用矩阵理论构造适当的李雅普诺夫泛函,得到系统全局指数稳定的充分条件.     

Optimal Step-Stress Accelerated Degradation Test Plan for Gamma Degradation Processes

Step-stress accelerated degradation testing (SSADT) is a useful tool for assessing the lifetime distribution of highly reliable products (under a typical-use condition) when the available test items are very few. Recently, an optimal SSADT plan was proposed based on the assumption that the underlying degradation path follows a Wiener process. However, the degradation model of many materials (especially in the case of fatigue data) may be more appropriately modeled by a gamma process which exhibits a monotone increasing pattern. Hence, in practice, designing an efficient SSADT plan for a gamma degradation process is of great interest. In this paper, we first introduce the SSADT model when the degradation path follows a gamma process. Next, under the constraint that the total experimental cost does not exceed a pre-specified budget, the optimal settings such as sample size, measurement frequency, and termination time are obtained by minimizing the approximate variance of the estimated MTTF of the lifetime distribution of the product. Finally, an example is presented to illustrate the proposed method.      

Proper Orthogonal Decomposition in the Generation of Reduced Order Models for Interconnects

In this paper, reduced order models are generated using the technique of proper orthogonal decomposition (POD), also known as Karhunen-LoÈve decomposition (KLD) for the simulations of interconnect problems. Model order reduction is achieved by projecting the state-space of the original problems onto a subspace spanned by a few number of proper orthogonal modes (POMs) extracted by the POD procedure from an ensemble of system responses at a series of selected frequencies. The proper orthogonal values (POVs) corresponding to the POMs indicate the level of the importance of each POM and provide a guidance for the number of POMs to be used in the reduced order models in order to have enough accuracy. Numerical experiment results obtained from the simulations of a two-conductor interconnect and a spiral inductor demonstrate that the reduced order models generated in this way can simulate the original system more effectively and faithfully than those generated with the standard Krylov subspace method with moment matching at a single point.      

Bayesian Inference on Multiscale Models for Poisson Intensity Estimation: Applications to Photon-Limited Image Denoising

We present an improved statistical model for analyzing Poisson processes, with applications to photon-limited imaging. We build on previous work, adopting a multiscale representation of the Poisson process in which the ratios of the underlying Poisson intensities (rates) in adjacent scales are modeled as mixtures of conjugate parametric distributions. Our main contributions include: 1) a rigorous and robust regularized expectation-maximization (EM) algorithm for maximum-likelihood estimation of the rate-ratio density parameters directly from the noisy observed Poisson data (counts); 2) extension of the method to work under a multiscale hidden Markov tree model (HMT) which couples the mixture label assignments in consecutive scales, thus modeling interscale coefficient dependencies in the vicinity of image edges; 3) exploration of a 2-D recursive quad-tree image representation, involving Dirichlet-mixture rate-ratio densities, instead of the conventional separable binary-tree image representation involving beta-mixture rate-ratio densities; and 4) a novel multiscale image representation, which we term Poisson-Haar decomposition, that better models the image edge structure, thus yielding improved performance. Experimental results on standard images with artificially simulated Poisson noise and on real photon-limited images demonstrate the effectiveness of the proposed techniques.      

Doubly-Selective Channel Estimation Using Data-Dependent Superimposed Training and Exponential Basis Models

Channel estimation for single-user frequency- selective time-varying channels is considered using superimposed training. The time-varying channel is assumed to be well- approximated by a complex exponential basis expansion model (CE-BEM). A periodic (non-random) training sequence is arithmetically added (superimposed) at low power to the information sequence at the transmitter before modulation and transmission. In existing first-order statistics-based channel estimators, the information sequence acts as interference resulting in a poor signal-to-noise ratio (SNR). In this paper a data-dependent superimposed training sequence is used to cancel out the effects of the unknown information sequence at the receiver on channel estimation. A performance analysis is presented. We also consider the issue of superimposed training power allocation. Several illustrative computer simulation examples are presented.     

Utilization of Reliability Measurements in Bayesian Inference: Models and Human Performance

A normative 2-stage model for incorporating reliability measurements of data-reporting sources in a Bayesian inference system is presented. An experiment required human subjects to make intuitive inferences about two hypotheses on the basis of sample data which were reported with a given reliability. When compared with the optimal model, subjects exhibited systematic errors in estimating the diagnostic impact of less than perfectly reliable data. Their responses reflected the use of specific nonoptimal heuristic strategies to process the information. A utility function was added to the normative model to illustrate how a best choice might be made from among potential data-gathering experiments whose costs increase with their reliabilities. Recommendations for using computer aids to enhance efficiency in inference systems are made     

基于时间Petri网的工作流系统模型的线性推理

目前工作流理论的研究主要集中在工作流管理模型的结构及正确性分析,很少有人研究与时间有关的工作流模型的性质,特别是模型中的时序关系推理及性能计算问题.本文重点研究了这方面的问题,用时间Petri网表示工作流模型并对基本工作流模型进行时序分析,给出线性时间推理的规则,运用这些规则,可对复杂的工作流模型进行逐步化简,并在线性时间复杂度内解决时间推理问题.     

Analysis of Incomplete, Censored Data in Competing Risks Models With Generalized Exponential Distributions

This paper presents estimates of the parameters included in a competing risks model in the presence of incomplete & censored data. We consider the case when the competing risks have generalized exponential distributions. The maximum likelihood procedure is used to derive point, and asymptotic confidence interval estimations of the unknown parameters. The relative risks due to each cause of failure are investigated. A set of real data is used to test the hypothesis that the causes of failure follow exponential distributions against that they follow generalized exponential distributions