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.     

不同标准差估计方法下的过程能力指数的置信区间的比较研究

采用样本标准差$s$、$s/c_4$、$\ol{R}/d_2$以及MVA分析后的$\wh{\sigma}_{\text{TOTAL}}$分别估计总体标准差,介绍了相应的$\wh{C}_p$和$\wh{C}_{pk}$以及$C_p$的置信区间,分析了每种标准差估计方法的特点, 结合案例进行比较研究.     

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．     

多个子样本下过程能力指数估计量的比较研究

过程能力指数(C_p)估计的关键是对总体标准差的估计。在多个子样本情形下,采用4个无偏估计量■,■_s,■_R,■_p分别估计总体标准差σ,证明了直接以此为基础的过程能力指数的估计量都是有偏的,且都有高估C_p的倾向;之后构造了C_p的4个无偏估计量;探讨了其中3个无偏估计量的估计效率;最后结合案例计算了C_p的不同估计值。     

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。     

过程能力指数与不合格品率的关系模型

传统的质量管理观认为,过高或过低的过程能力指数都不利于企业经济效益的提高。本文基于传统的质量管理观,研究过程能力指数与产品不合格品率之间的关系,建立了过程有无漂移时的过程能力指数与产品不合格品率之间的关系模型。     

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.     

置信区间的随机加权估计

用随机加权法建立了分位点ｑ的置信区间，又用后向临界点导出了更实用的置信区间。导出的置信区间是非参数的且和原置信区间长度相同。     

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。     

参数区间估计时置信区间的优选法

利用拉格朗日函数求条件极值的方法可解释参数区间估计时置信区间的选取方法及其若干应用.     

非正态情形下过程能力指数的近似置信限

文章讨论了当过程不满足正态性假设的情形下过程能力指数的近似置信限,并以Weibull分布为例给出了指数C′_(pm)的近似置信区间的具体形式和假设检验的检验统计量。最后给出了模拟验证。     

一类基于非对称偏差的过程能力指数

以基本尺寸为基准,研究非对称偏差下总体质量特性值的分布及过程离散程度,在给出一类非对称分布的基础上,研究基于非对称偏差的过程能力指数,并将其推广到角度质量控制问题。     

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.     

Confidence Intervals and Accuracy Estimation for Heavy-Tailed Generalized Pareto Distributions

The generalized Pareto distribution (GPD) is a two-parameter family of distributions which can be used to model exceedances over a threshold. We compare the empirical coverage of some standard bootstrap and likelihood-based confidence intervals for the parameters and upper p-quantiles of the GPD. Simulation results indicate that none of the bootstrap methods give satisfactory intervals for small sample sizes. By applying a general method of D. N. Lawley, correction factors for likelihood ratio statistics of parameters and quantiles of the GPD have been calculated. Simulations show that for small sample sizes accuracy of confidence intervals can be improved by incorporating the computed correction factors to the likelihood-based confidence intervals. While the modified likelihood method has better empirical coverage probability, the mean length of produced intervals are not longer than corresponding bootstrap confidence intervals. This article also investigates the performance of some bootstrap methods for estimation of accuracy measures of maximum likelihood estimators of parameters and quantiles of the GPD.     

Likelihood Based Confidence Intervals for the Tail Index

For the estimation of the tail index of a heavy tailed distribution, one of the well-known estimators is the Hill estimator (Hill, 1975). One obvious way to construct a confidence interval for the tail index is via the normal approximation of the Hill estimator. In this paper we apply both the empirical likelihood method and the parametric likelihood method to obtaining confidence intervals for the tail index. Our limited simulation study indicates that the normal approximation method is worse than the other two methods in terms of coverage probability, and the empirical likelihood method and the parametric likelihood method are comparable.     

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.     

Comparison of Parametric and Bootstrap Approaches to Obtaining Confidence Intervals for Logspline Density Estimation

In earlier articles, we developed an automated methodology for using cubic splines with tail linear constraints to model the logarithm of a univariate density function. This methodology was subsequently modified so that the knots were determined by stepwise addition-deletion and the remaining coefficients were determined by maximum likelihood estimation. An alternative approach, referred to as the free knot spline procedure, is to use the maximum likelihood method to estimate the knot locations as well as the remaining coefficients. This article compares various approaches to constructing confidence intervals for logspline density estimates, for both the stepwise procedure and the free knot procedure. It is concluded that a variation of the bootstrap, in which only a limited number of bootstrap simulations are used to estimate standard errors that are combined with standard normal quantiles, seems to perform the best, especially when coverages and computing time are both taken into account.     

多因素交互作用及可信区间的估计

有一类研究是观测某个结局事件发生的时间,分析时需要考虑影响该结局事件发生的因素.由于因素之间往往存在交互作用,因而一个因素对结局事件发生的时间的影响量受到另一个因素的修饰.因此分析因素之间是否存在交互作用,对正确认识各因素对结局事件的发生的作用是十分重要的.对以时间为观测指标的多元分析中因素之间交互作用的分析方法作探讨,推导出了估计交互作用及95%可信区间的计算公式.并应用于肿瘤患者生存时间的影响因素之间的交互作用分析.