根据子样本的过程能力指数及其置信区间的估计

自1980年以来,分析过程能力的统计方法有显著的进展,已在实践中得到大量应用.过程能力指数是衡量生产过程中的产品尺寸适合规格限和接近目标值的能力.最普遍使用的能力指数是cp和cpk,这些指数曾被广泛地应用于日本、美国和英国的各工业公司和企业.文中对这些指数提出根据子样本估计标准差、能力指数及其置信区间的简单近似方法.     

流程性材料过程性能的评价方法

过程能力指数已广泛地应用于度量和评价过程性能。使用各种标准能力指数的先决条件是测量数据相互独立，且服从正态分布；然而，对流程性材料生产过程，测量数据往往不满足应用过程能力指数的条件。本文根据确定过程能力指数的基本思想，提出了拓广的过程能力指数Ｃｐｐ，以给出流程性材料过程性能的评价方法，并通过具体事例证实了这种方法的可行性和有效性。     

基于质量损失的过程网络及其关键质量链分析

针对传统的过程能力分析仅以生产线中某一单一的生产工序(过程)为对象这一问题,将影响产品质量的所有生产过程视为一个过程网络,根据Taguchi田口方法,阐述了过程能力指数与质量损失的关系,给出了生产制造过程网络过程能力指数的计算方法.进一步应用PERT/CPM的基本思想,建立了生产制造过程网络关键质量链的规划模型,将质量损失最大的路径视为关键质量链.通过实例分析表明,以上方法改进了传统的统计质量控制和分析方法,能够有效地实现过程网络的质量管理.     

基于差异系数的多元过程能力指数

过程能力指数表示过程能力满足产品质量标准的程度的评价指标，最普遍使用的过程能力指数有Cp、Cpk、Cpm、Cpkm等，它们已在各大工业部门得到了广泛的应用，但是多元质量特性的过程能力指数尚未得到很好的解决。许多学试图以不同的方式、方法计算多元质量特性的过程能力指数，但存在局限性。本以多元正态分布为基础，比较分析了每个质量特征的差异系数，给出了多元过程能力指数的计算公式。最后的一个算例表明，该方法是有效且符合实际的。     

过程能力指数评价过程能力的可靠性影响因素分析

利用过程能力指数评价过程能力,其可靠性程度会受到抽样误差、测量误差以及数据自相关性的影响,分析了观测数据受各种因素影响下过程能力指数估计的统计性质,给出了通过添加纠偏系数获得过程能力指数无偏估计或无偏估计近似值的方法。     

过程能力指数综述

统计过程控制是现代化工业生产中确保产品质量和可靠性的核心方法之一，而过程能力指数则是度量一个工业过程能力的重要指标．本文综述了过程能力指数的研究现状，首先介绍了过程能力指数的概念，然后较详细地介绍了几种主要的过程能力分析方法，并进一步说明了非正态分布的处理．最后给出了结论，并展望了过程能力指数今后的研究和发展方向．     

非正态条件下过程能力指数的仿真研究

研究基于各类计算非正态条件下过程能力指数方法的有效性,采用蒙特卡洛方法,通过建立各方法的仿真模型,模拟仿真并比较各方法的性能优劣.仿真结果显示,Johnson转换法较Box-Cox转换法具有更加广泛的适用范围,并在绝大多数参数取值范围内具有优越性.偏态过程能力指数Cs由于不受数据分布类型的影响,在实际生产中具有较高的应用范围.最后利用研究对焊机关键质量特性进行实证分析,并验证了方法的有效性与可行性.     

注重课堂教学中归纳猜想能力的培养

1 同课异构,两案例对比引发思考 数学思想方法和能力的培养是数学教学的核心内容之一.<新课标>对学生归纳和猜想的能力的要求是:能通过观察、实验、归纳、类比等获得数学猜想,并进一步寻求证据,给出证明或举出范例,能清晰有条理地表达自己的思考过程,做到言之有理,落笔有据.这些要求说明新课标已把思想方法和能力的培养放在了教学的重要地位.     

人口发展过程的预测

本文的目的是建立人口发展过程的预测理论和方法,主要包括人口发展过程的数学模型、各项人口指数的定义及其计算方法,并确定了初始条件、边界条件和各项参数.根据本文预测方法,文中首次全面预测了我国今后一百年内各项人口指数数据,最后还提出了关于平均期望寿命的计算公式.     

关于过程能力指数公式的几点辨析

文献[1-2]认为当过程能力指数为零时,合格率却不为零的情形不符合常理。因而对过程能力指数C_p及C_(pk)公式提出质疑。本文从多个角度辨析这种质疑是不成立的.     

定数截尾时可靠性指标的 Bootstrap 区间估计

在工程可靠性试验数据的统计分析中,关于可靠性指标的置信区间的获得是一个有实际意义的课题.这个问题历史上通常是对特定的分布作大量模拟计算,这种做法不但计算量大,而且随着寿命分布的不同必须另行重复模拟,使用极为不便,特别对某些我们所关心的指标,至今缺少较为理想的求置信区间的办法.例如,某些电子元件的寿命服从     

Confidence intervals for ratio of two Poisson rates using the method of variance estimates recovery

Inference based on ratio of two independent Poisson rates is common in epidemiological studies. We study the performance of a variety of unconditional method of variance estimates recovery (MOVER) methods of combining separate confidence intervals for two single Poisson rates to form a confidence interval for their ratio. We consider confidence intervals derived from (1) the Fieller’s theorem, (2) the logarithmic transformation with the delta method and (3) the substitution method. We evaluate the performance of 13 such types of confidence intervals by comparing their empirical coverage probabilities, empirical confidence widths, ratios of mesial non-coverage probability and total non-coverage probabilities. Our simulation results suggest that the MOVER Rao score confidence intervals based on the Fieller’s theorem and the substitution method are preferable. We provide two applications to construct confidence intervals for the ratio of two Poisson rates in a breast cancer study and in a study that examines coronary heart diseases incidences among post menopausal women treated with or without hormones.     

二项抽样下基于鞍点逼近方法的流行病相对风险置信区间构造

相对风险是流行病学研究中的重要指标之一,它是度量一种暴露因素是否与某病的致病有联系的统计指标.以该指标的数值大小来表明这一暴露因素对某病的发生具有何种影响及影响的大小,体现了暴露与疾病的关联程度.精确地得到相对风险指标的区间估计,对病因推断具有重要意义.但是由于相对风险指标的估计量是两个概率值的估计量的比值,要得到其精确分布一般而言是很困难的,因此已有研究成果大都采用渐近方法估计相对风险的置信区间,这在小样本情况下表现不佳.在二项抽样条件下,对相对风险的点估计、置信区间估计一直被人们所关注.在二项采样下利用鞍点逼近的方法构造相对风险的置信区间,并通过实例与蒙特卡洛模拟,与传统的置信区间构造方法对比,模拟结果显示其优点,尤其是在小样本量条件下估计效果比较好.     

Resampling based inference for a distribution function using censored ranked set samples

This article deals with constructing confidence intervals/bands for a distribution function based on censored ranked set samples. Toward this end, a resampling plan is suggested and its validity is investigated. Monte Carlo simulations are used to compare performances of the bootstrap confidence intervals with their asymptotic analogs, and their modifications by jackknife. An environmental data set is finally analyzed.     

On the tail index of a heavy tailed distribution

This paper proposes some new estimators for the tail index of a heavy tailed distribution when only a few largest values are observed within blocks. These estimators are proved to be asymptotically normal under suitable conditions, and their Edgeworth expansions are obtained. Empirical likelihood method is also employed to construct confidence intervals for the tail index. The comparison for the confidence intervals based on the normal approximation and the empirical likelihood method is made in terms of coverage probability and length of the confidence intervals. The simulation study shows that the empirical likelihood method outperforms the normal approximation method.     

Estimation of the statistical error of the direct simulation Monte Carlo method

The statistical error of the direct simulation Monte Carlo method for numerical solution of the rarefied gas dynamics problems is investigated. Based on the central limit theorem for Markov processes, asymptotic confidence intervals for the errors connected with the number of time steps are obtained for estimates of the three main macroparameters of the flow (density, velocity, and temperature). For the quantities involved in the expressions for the confidence intervals, practical recommendations are given concerning their numerical evaluation simultaneously with the calculation of the flow macroparameters. The proposed approaches to constructing the confidence intervals are illustrated using the classical problem of heat transfer between two infinite parallel plates as an example.     

Panel模型中的精确检验和置信区间

利用广义p-值和广义置信区间的概念,研究了Panel模型中未知参数的检验和置信区间问题.对于回归系数,分别考虑了单个情形和多个线性无关情形下的检验和置信区间问题,得到了精确检验和置信区间.对于方差分量,研究了其任意线性组合的检验和置信区间问题,建立了精确检验和置信区间.基于广义p-值和广义置信区间,获取精确检验和置信区间的方法具有计算方便、易应用于小样本问题的特点.最后,分别从理论和数值上研究了这些精确检验和置信区间的统计性质.     

Individual confidence intervals for solutions to expected value formulations of stochastic variational inequalities

Stochastic variational inequalities (SVIs) provide a means for modeling various optimization and equilibrium problems where data are subject to uncertainty. Often the SVI cannot be solved directly and requires a numerical approximation. This paper considers the use of a sample average approximation and proposes three methods for computing confidence intervals for components of the true solution. The first two methods use an “indirect approach” that requires initially computing asymptotically exact confidence intervals for the solution to the normal map formulation of the SVI. The third method directly constructs confidence intervals for the true SVI solution; intervals produced with this method meet a minimum specified level of confidence in the same situations for which the first two methods are applicable. We justify the three methods theoretically with weak convergence results, discuss how to implement these methods, and test their performance using three numerical examples.     

Confidence Intervals for Quantiles and Tolerance Intervals Based on Ordered Ranked Set Samples

Confidence intervals for quantiles and tolerance intervals based on ordered ranked set samples (ORSS) are discussed in this paper. For this purpose, we first derive the cdf of ORSS and the joint pdf of any two ORSS. In addition, we obtain the pdf and cdf of the difference of two ORSS, viz. , 1 ≤ r < s ≤ N. Then, confidence intervals for quantiles based on ORSS are derived and their properties are discussed. We compare with approximate confidence intervals for quantiles given by Chen (Journal of Statistical Planning and Inference, 83, 125–135; 2000), and show that these approximate confidence intervals are not very accurate. However, when the number of cycles in the RSS increases, these approximate confidence intervals become accurate even for small sample sizes. We also compare with intervals based on usual order statistics and find that the confidence interval based on ORSS becomes considerably narrower than the one based on usual order statistics when n becomes large. By using the cdf of, we then obtain tolerance intervals, discuss their properties, and present some tables for two-sided tolerance intervals.