Equipment failure rate updating-Bayesian estimation

The paper presents a Bayes' method for augmenting generic equipment failure data with a prior distribution - predicated on the evidence, e.g., plant data - resulting in a posterior distribution. The depth of the evidence is significant in shaping the characteristics of the posterior distribution. In conditions of insufficient data about the prior distribution or great uncertainty in the generic data sources, we may use "constrained non-informative priors". This representation of the prior preserves the mean value of the failure rate estimate and maintains a broad uncertainty range to accommodate the site-specific event data. Although the methodology and the case study presented in this paper focus on the calculation of a time-based (i.e., failures per unit time) failure rate, based on a Poisson likelihood function and the conjugate gamma distribution, a similar method applies to the calculation of demand failure rates utilizing the binomial likelihood function and its conjugate beta distribution.     

衡水湖地区气溶胶分布特征的航测研究

利用飞机机载粒子测量系统(PMS)对河北省衡水湖自然保护区上空的大气气溶胶粒子进行观测研究。观测结果表明:下垫面、天气条件、逆温等对气溶胶的分布存在较大的影响;衡水湖上空不同高度的气溶胶平均谱分布均呈现出单峰分布;细粒子谱分布在0.28μm左右处出现峰值;多阶Γ函数对气溶胶粒子谱有较好的拟合效果。     

A generalized planck distribution

We introduce a generalization of the standard Planck distribution discussed by Johnson and Kotz (1970, Section 33.6.1). This generalization results in a very flexible family which contains the gamma distribution as a particular case. In this paper we provide a comprehensive treatment of the mathematical properties of the family. We derive expressions for thenth moment, moment generating function, characteristic function, mean deviation about the mean, mean deviation about the median, Rényi entropy, Shannon entropy and the asymptotic distribution of the extreme order statistics. Estimation and simulation issues are also considered.     

随机过程下的生产配送策略对比

通过研究生产线物料配送的具体流程,考虑信息和物料停滞造成的线边工位等待,以及配送中心的执行费用,运用随机过程理论分别建立定量配送、定时配送和即时配送的成本模型,并对3种配送方式的最优策略进行定量分析。通过实例研究,从成本最优的角度和管理实现的角度对比分析3种配送方式,发现定量配送的一般最优性,以及定时配送和即时配送的特殊适用情况,从而为实际运营中,企业选择合适的配送方式提供科学依据。     

Lifetime test evaluation with mathcad®: Automated weibull parameter and plotting point estimate with arbitrary confidence interval and graphics

This application note describes a computer-based method for automated evaluation of Weibull-distributed life-time data. It uses comercially available software, MathCad, to set up equations and graphs. The computer application is a simple and non-expensive way of evaluating and displaying your life-time data taking into consideration both parametric and non-parametric confidence intervals. It is valid for arbitrarily censored data.     

Control charts to monitor rates and proportions

In this paper, we call attention for monitoring proportions and rates when they are not results of Bernoulli experiments. To deal with this problem, usually control charts based on Beta distributions are built as this distribution is a well‐known one. However, in practice, there are other distributions to be considered as Simplex and Unit Gamma distributions. The impact of the speed to signal a shift in the average proportion in terms of out‐of‐control average run length is measured when the control limits determined under a Beta distribution is equivocally used to monitor individual rates from Simplex or Unit Gamma distributions or vice versa.     

On the statistical distribution of primary and secondary dendrite arm spacing in cast metals

Statistical distributions of dendrite arm spacing have not been addressed in the literature. Two histograms for primary dendrite arm spacing in a cast nickel-based superalloy, and four histograms from a chill cast 5182 aluminium alloy ingots for secondary dendrite arm spacing have been analysed. For all datasets, lognormal distribution provided excellent fits to the data. Moreover, the Lifshitz–Slyozov–Wagner distribution was found to have systematic error in the fits to the secondary arm spacing data.     

Reliability demonstration test for a finite population

In many situations, we want to accept or reject a population with small or finite population size. In this paper, we will describe Bayesian and non‐Bayesian approaches for the reliability demonstration test based on the samples from a finite population. The Bayesian method is an approach that combines prior experience with newer test data in the application of statistical tools for reliability quantification. When test time and/or sample quantity is limited, the Bayesian approach should be considered. In this paper, a non‐Bayesian reliability demonstration test is considered for both finite and large population cases. The Bayesian approach with ‘uniform’ prior distributions, Polya prior distributions, and sequential sampling is also presented. Copyright © 2001 John Wiley & Sons, Ltd.     

Maximum likelihood Estimation of Parameters in the Inverse Gaussian Distribution,With Unknown Origin

Maximum likelihood estimation is applied to the three-parameter Inverse Gaussian distribution, which includes an unknown shifted origin parameter. It is well known that for similar distributions in which the origin is unknown, such as the lognormal, gamma, and Weibull distributions, maximum likelihood estimation can break down. In these latter cases, the likelihood function is unbounded and this leads to inconsistent estimators or estimators not asymptotically normal. It is shown that in the case of the Inverse Gaussian distribution this difticulty does not arise. The likelihood remains bounded and maximum likelihood estimation yields a consistent estimator with the usual asymptotic normality properties. A simple iterative method is suggested for the estimation procedure. Numerical examples are given in which the estimates in the Inverse Gaussian model are compared with those of the lognormal and Weibull distributions.     

Programs in R for computing truncated t distributions

Truncated distributions arise naturally in many industrial settings. Owing to the popularity of the normal distribution, programs have been developed for computing quantities of interest of its truncated version such as the truncated mean, truncated variance and the cumulative probability. In this note, we follow up the work for the Student's t distribution because of its recent popularity as a rival to the normal distribution. We provide programs for computing the mean, variance, cumulative probability and two other quantities of interest for any truncated t distribution: whether it is left truncated, right truncated or doubly truncated. The programs are written in R: a freely downloadable statistical software. Copyright © 2006 John Wiley & Sons, Ltd.     

略谈贝叶斯统计学派的假设检验

假设检验问题是统计推断和决策的基本形式之一，其核心是利用样本所提供的信息对总体的某个假设给出判断，接受假设或者拒绝假设。对于该问题经典统计和贝叶斯统计给出不同的检验方法和检验准则。本文浅谈贝叶斯统计在假设检验方面的优势及不足。     

用优化方法求取统计分布参数

统计分布参数的求取是可靠性研究的基础，对于只含有一个或两个参数的统计分布，已有许多方法来求取其参数，但对于具有复杂形式的分布，其多参数求取比较困难。作者提出把求解统计分布参数问题归结为求解非线性优化问题，调用现成的优化程序即可方便地求出具有复杂形式的统计分布的参数。所给出的例题表明，该方法是可行的。     

A reduced sampling approach for reliability verification

Reliability demonstration tests frequently require large sample sizes which are objectionable from both a cost and time standpoint. The approach presented, referred to as bias sampling, offers a means to demonstrate conformance to reliability objectives with reduced test samples and test time. The reduction is achieved by selection and test of samples from the lower-median sub-population of a random sample. The prediction assumes that the entire population of samples was tested. Rationale for the approach is presented along with guidelines for sample selection. Two application examples illustrate how the methodology is being employed at Chrysler Corporation.     

厨房燃烧废气系统污染传播规律研究

以三种评价方法考察设抽油烟机的封闭厨房内燃烧废气系统污染扩散的规律,分析灶具的安装位置、排烟机高度范围及运行档位对废气系统扩散的影响。运用 Data Fit 拟合实验数据,建立废气系统的浓度扩散和?及总?强度分布的数学模型,利用 VC++可视化编程技术,对模拟结果与实际测试结果进行比较。得出 CO2和 CO 浓度、?扩散模拟规律图表;废气扩散热、浓度总?强度变化图表、实测数据图表、模拟与实测比较图表。厨房废气系统扩散有其规律性和方向性,用 VC++编程对厨房液化气燃烧废气系统的总?强度进行数值模拟反映总污染传播的规律性是可行的。     

Statistical distributions for the temperature of hydrogen pore nucleation in solidifying aluminium alloys

The adequacy of the model originally developed by Charbon and Rappaz for nucleation temperatures of grains to the formation of hydrogen pores during the solidification of aluminium alloys has been investigated. By using four datasets from the literature, it has been found that the Gaussian distribution assumed in the original model for nucleation temperature has provided poor fits to all datasets with systematic error. The hypothesis that undercooling follows the lognormal distribution has been tested. In all four cases, the hypotheses that undercooling is lognormal could not be rejected.     

声呐图像背景灰度分布特性分析及模型研究

在图像声呐滤波、分割以及目标识别中,像素灰度分布特性及其模型的选择与建立具有非常重要的作用。针对当前声呐图像背景灰度分布模型研究尚不够深入的现状,分别采用威布尔分布和瑞利分布模型对声呐图像背景区域像素点灰度分布进行了仿真验证。结果表明,威布尔分布较瑞利分布来说能够更好地逼近图像声呐灰度分布曲线,且具有较强的自适应性。但在某些情况下,可采用瑞利分布替代威布尔分布,以提高运算效率。     

汽轮机复合配汽方式对机组经济性的影响及优化

本文针对汽轮机复合配汽方式进行了探讨,分析了节流调节影响经济性的机理,论证了进行喷嘴配汽优化对机组安全性的影响及解决方案,得出结论：复合配汽方式对机组经济性影响较大,应改为喷嘴配汽。     

Turing instability in an economic–demographic dynamical system may lead to pattern formation on a geographical scale

Spatial distribution of the human population is distinctly heterogeneous, e.g. showing significant difference in the population density between urban and rural areas. In the historical perspective, i.e. on the timescale of centuries, the emergence of densely populated areas at their present locations is widely believed to be linked to more favourable environmental and climatic conditions. In this paper, we challenge this point of view. We first identify a few areas at different parts of the world where the environmental conditions (quantified by the temperature, precipitation and elevation) show a relatively small variation in space on the scale of thousands of kilometres. We then examine the population distribution across those areas to show that, in spite of the approximate homogeneity of the environment, it exhibits a significant variation revealing a nearly periodic spatial pattern. Based on this apparent disagreement, we hypothesize that there may exist an inherent mechanism that may lead to pattern formation even in a uniform environment. We consider a mathematical model of the coupled demographic-economic dynamics and show that its spatially uniform, locally stable steady state can give rise to a periodic spatial pattern due to the Turing instability, the spatial scale of the emerging pattern being consistent with observations. Using numerical simulations, we show that, interestingly, the emergence of the Turing patterns may eventually lead to the system collapse.     

Zeta分布及其应用

基于Ｚｅｔａ函数提出一种新的Ｚｅｔａ分布，将Ｚｅｔａ分布分为两种类型（ＺｅｔａⅠ型及ＺｅｔａⅡ型），并指出连续的ＺｅｔａⅠ型分布就是Ｐａｒｅｔｏ分布。最后给出一个实例予以说明。     

The negative binomial-Lindley distribution as a tool for analyzing crash data characterized by a large amount of zeros

The modeling of crash count data is a very important topic in highway safety. As documented in the literature, given the characteristics associated with crash data, transportation safety analysts have proposed a significant number of analysis tools, statistical methods and models for analyzing such data. Among the data issues, we find the one related to crash data which have a large amount of zeros and a long or heavy tail. It has been found that using this kind of dataset could lead to erroneous results or conclusions if the wrong statistical tools or methods are used. Thus, the purpose of this paper is to introduce a new distribution, known as the negative binomial–Lindley (NB-L), which has very recently been introduced for analyzing data characterized by a large number of zeros. The NB–L offers the advantage of being able to handle this kind of datasets, while still maintaining similar characteristics as the traditional negative binomial (NB). In other words, the NB–L is a two-parameter distribution and the long-term mean is never equal to zero. To examine this distribution, simulated and observed data were used. The results show that the NB–L can provide a better statistical fit than the traditional NB for datasets that contain a large amount of zeros.