Introduction to Probability Theory and Statistical Inference

A statistical test for equality of the logarithmic means of two lognormal life distributions is presented for the situation where the information on the first distribution is obtained from a regression analysis of accelerated life test data obtained at various temperatures and the information on the second distribution is the time to the first failure in a sample tested at a particular temperature.     

The Change – Point Problem for Angular Data : A Nonparametric Approach

Some directional data collected in a system evaluation of illumination flares are presented. Preliminary analysis suggested a need for procedures to detect, estimate, and test the significance of possible change points in the data. In this article some nonparametric procedures are proposed and applied to the data.     

分布传播及其在不确定度中的应用

论述分布传播,研究了分布传播分析,讨论了不确定度的分布传播,最后用实例说明了它在不确定度中的应用.     

再结晶织构的计算模拟理论及意义

阐述了再结晶织构模拟的研究的意义，介绍了目前流行的再结晶织构及晶粒生长的模拟理论－蒙特卡洛方法以及国内模拟研究的新进展。     

A Neural Network-Based Approach for Statistical Probability Distribution Recognition

The statistical probability distribution of data should be known in advance, so that we can make some statistical inference based on the data and realize what information the data provides. Until now, a nonparametric goodness of fit test has been widely used in probability distribution recognition. However, such a procedure cannot guarantee a precise distribution recognition when only small data samples are available. In addition, the number of the divided groups will influence the results. This study proposes a neural network-based approach for probability distribution recognition. Two types of neural networks, backpropagation and learning vector quantization, are used in classifying normal, exponential, Weibull, Uniform, Chi-square, t, F, and Lognormal distributions. Implementation results demonstrate that the proposed approach outperforms the traditional statistical approach.     

随机综合生产计划模型及其求解研究

制订一个有效、可行的综合生产计划,必须考虑各种随机因素的影响。本文在前人工作的基础上,提出了一种改进的随机综合生产计划模型,并探讨了采用数学分析和蒙特卡罗模拟相结合的模型求解方法。     

蒙特卡罗方法的过程聚类EWMA控制图研究

以加工"过程"为研究对象,从零件成组加工技术出发,阐述了就如何利用EWMA控制图来进行统计聚类并进行过程质量监控等问题,提出通过统计聚类形成"零件族",对同一"零件族"采用统一的EWMA控制图的应用策略;引入聚类零件族的方差比ρ,利用蒙特卡罗模拟方法,对不同样本数量条件下的统计聚类EWMA控制图性能所产生的影响进行了详细的研究,最后给出了统计聚类的基本原则.     

Probability matching priors for linear calibration

Summary In the linear calibration problem, a model is fit to paired observations arising from two measurement techniques, one known to be far more accurate (but also more expensive) than the other. The fitted model is then used with univariate observations from the less accurate technique to impute values from the more accurate one. The Bayesian paradigm emerges as attractive in this context, but the choice of an appropriate noninformative prior distribution has been controversial. In this paper we derive a class of such distributions, and provide sufficient conditions under which they lead to proper posterior densities. These priors, which we refer to asprobability matching priors, are designed to produce posterior credible intervals which are asymptotically identical to their frequentist counterparts. We provide details on the implementation of our procedure using sampling-based methods, and obtain significant simplifications over previous Bayesian approaches in this area. We compare the performance of several members of our prior class in the context of two illustrative examples.     

Time Series Analysis: Theory and Practice 4

Some adaptive tests are proposed (a) for the general two-sample scale problem and (b) for the restricted two-sample scale problem, in which the random variables are known to be right-skewed and also positive valued. These are based on either the ratio of the adaptively trimmed sample variances or adaptive rank tests of scale, whose quantiles are estimated by means of the bootstrap. Simulations show that, for practical sample sizes, these tests tend to perform better than their competitors. The methodology is illustrated by an application to a problem considered by Nair regarding the breakdown times of an insulating fluid under elevated voltage stress.     

Robust design with dynamic characteristics using stochastic sequential quadratic programming

Robust design with dynamic characteristics is an important off-line quality engineering technique for improving product quality over a range of input conditions by reducing variations caused by uncontrolled factors. Since several studies have indicated that there are important limitations to Taguchi's S/N ratio analysis, the solution procedure for dynamic systems deserves further investigation. This paper proposes a stochastic optimization modeling procedure to overcome the difficulty in Taguchi's method to accommodate dynamic characteristics. The main idea underlying the proposed method is to minimize the total variations on quality characteristics while attaining the target performance over a range of input conditions. Due to the nonlinear nature of the stochastic optimization model, two stochastic versions of sequential quadratic programming respectively embedded with a Monte Carlo simulation and numerical approximations are devised to solve the problem. In the robust design of a temperature control circuit often discussed in dynamic problems, the proposed method performs efficiently and effectively. Compared with the Taguchi method, the design solved in this paper has smaller variations, indicating that the proposed method is a promising technique for dynamic-characteristic robust design.     

摩擦摆系统的稳态响应概率分布研究

基于等效线性化方法推得了摩擦摆系统对高斯白噪声激励稳态响应的联合概率密度函数解析解。与蒙特卡洛模拟结果对比表明，该解析解可以较好地预测系统的稳态随机响应。     

Statistical inference and Monte Carlo algorithms

Summary This review article looks at a small part of the picture of the interrelationship between statistical theory and computational algorithms, especially the Gibbs sampler and the Accept-Reject algorithm. We pay particular attention to how the methodologies affect and complement each other. Read before the Spanish Statistical Society at a meeting organized by the University of Granada on Friday, September 27, 1996     

Monte Carlo simulation on the cation diffusion via vacancies in simple spinels

The correlation factors of cations and vacancies for diffusion in simple spinels were calculated by using the Monte Carlo simulation technique. Since the predominant point defects are cationic vacancies at high temperature and especially at high oxygen partial pressures in many spinels, the cations are considered to move primarily via cationic vacancies in this study. Several input parameters including the lattice size, the number of jumps per cation, etc., were optimized to calculate the correlation factors. Then the correlation factors of cations moving via vacancies in simple spinels were calculated in different types of exchange jumps, i.e., diffusion that occurs on tetrahedral or octahedral or both cationic sites. Results were obtained with satisfactory accuracy. The influence of the vacancy concentration on the correlation factors was also analyzed.     

Calculating and addressing uncertainty for risk-based allowable outage times

This article examines the calculation and treatment of uncertainty in risk-based allowable outage times (AOTs) for operational control at nuclear power plants, where an AOT is defined as the time that a component or system is permitted to be out of service. The US Nuclear Regulatory Commission (NRC) has explored the possibility of using a nuclear power plant's probabilistic risk assessment results to determine component or system AOTs. The analysis and results from previous work prepared for the NRC on determining risk-based AOTs are presented. As part of the discussion, the article examines the inherent uncertainty in calculating risk-based AOTs and presents the difficulties in calculating these risk-based AOTs. It is noted that care should be taken when dealing with uncertainty analysis results where a time-interval is the outcome of the analysis. In addition, potential improvements in the mechanism of calculating risk-based AOTs are suggested.     

A new approach to model isobaric heat capacity and density of some nitride-based nanofluids using Monte Carlo method

A serious gap in the field of nanofluids' modeling is disregarding the effect of molecular structure that must be highlighted. For the first time, the Monte Carlo method was utilized to model isobaric heat capacity and density of nanofluids. A creditable data set was selected contains nitride-based nanofluids (aluminum nitride, titanium nitride, and silicon nitride all dispersed in ethylene glycol). Quasi-simplified molecular-input line-entry system (quasi-SMILES) was applied to represent the structure of nanofluids, successfully. This format made possible incorporating molecular structure besides experimental conditions into the modeling process. The developed models were evaluated precisely; it was found that the statistical qualities were good and their performance was superior to the classical equation. Also, results revealed that some molecular features of nanofluids such as double and triple bond affects isobaric heat capacity and density, while the size of nanoparticles did not impressive affect these properties. It is remarkable to point out that the proposed models introduce a new trend to estimate the thermophysical properties of nanofluids. The utilized approach could be useful for a more reliable and accurate prediction of the other nanofluids' properties.