基于正态分布的逐批抽样检验贝叶斯控制图控制限研究

在生产条件受控的状态下,先验分布与后验分布应服从同一分布,在假设该分布为正态分布的前提下,根据贝叶斯理论推导出均值、极差和标准差的迭代计算公式,并依此计算控制图的控制限,使有效的先验批检验信息得到充分运用,弥补传统控制图在小批量生产环境下样本信息不足的缺点。研究发现,基于贝叶斯原理的统计控制图控制限随着检验批次的逐渐增加,更接近控制界限的实际值,比传统控制图的控制效果更加可靠、有效。     

样本数较少时的极值控制图

「１」中研究了样本数较少时中位值和极差控制图。本文研究样本数较少时极值控制图的制定方法，给出与极值有关的统计量的分布，建立极值图的控制限，极值图不需计算，有关集中和分散的信息在一个图上给出，且可画上规格限，在实践中应用方便，本文制定的极值控制可应用于小批量生产的生产过程。     

多品种小批量生产情形下的工序质量控制图

在现代制造业中 ,企业经常出现多品种小批量的生产方式 ,且对不同品种的产品 ,其生产工序的质量特性值的分布一般是不同的 ,针对这种情况 ,本文建立了相应的 X -R控制图和 X -S控制图 ,并给出了实证分析     

基于粒子滤波的改进型单值控制图

针对高度复杂小批量生产环境下的统计过程控制问题,提出基于粒子滤波的改进型单值控制图。通过状态空间模型描述过程运行特征,并运用粒子滤波技术估计过程的运行状态,以状态粒子群的均值为对象,运用平均移动极差控制图对正态分布过程的漂移进行监控。研究结果表明,该方法是小批量生产过程质量控制的有效工具。     

有偏总体的EWMA均值控制图

基于总体分布有偏并假定总体分布未知情况下均值-极差控制图的控制限的研究结果,将其推广到EWMA均值控制图,给出总体分布有偏并假定总体分布未知情况下EWMA均值控制图的控制界限,并以质量特性值服从对数正态分布为例,给出EWMA均值控制图的控制效果的模拟分析.     

基于尺度赋权方差的有偏总体EWMA均值控制图

基于尺度赋权方差法给出总体分布有偏并假定总体分布未知情况下休哈特均值控制图的控制限.基于此研究结果,将其推广到EWMA均值控制图,给出总体分布有偏并假定总体分布未知情况下EWMA均值控制图的控制界限,并以质量特性值服从对数正态分布为例,给出EWMA均值控制图的控制效果的模拟分析.     

有偏总体的极差控制图

根据加权标准差方法建立有偏总体的极差控制图,它基于有偏总体来计算对应于正态分布的控制图常数,根据样本数据的偏度来计算上下控制限,对于总体是对称分布,该控制图退化为标准的休哈特控制图.最后,用蒙特卡洛方法给出了改进的控制图常数.     

小批量生产的贝叶斯质量控制模型

本应用贝叶斯统计推断方法，研究了基于正态共轭先验分布和正态——逆伽玛共轭先验分布的小批量生产下的质量控制模型问题，根据不同控制对象的预报分布密度函数，分别构造了方差已知时的贝叶斯均值控制图和方差未知时的贝叶斯均值——标准差控制图，并与经典质量控制模型进行了比较。     

联合监测过程位置参数和尺度参数的非参数Shewhart控制图

用于检测生产服务过程的传统控制图多数都假定过程的分布是已知的。这些控制困经常是在正态分布的假设下构建的,然而在服务质量实时监控中数据往往是非正态的。在这种情况下,基于正态分布假设的控制图的结果是不可靠的。为了解决这个问题,通常考虑非参数方法,因为在过程分布未知情况下,非参数控制图比参数图更加稳健有效。本文提出一个新的基于Van der Waerden和Klotz检验的Lepage型非参数Shewhart控制图(称为LPN图)用于同时检测未知连续过程分布的位置参数和尺度参数。文中给出了LPN图在不同参数下的控制限。依据运行长度分布的均值,方差和分位数,分析了LPN图在过程受控和失控时的性能,并与其他一些现有的非参数控制图进行比较。基于蒙特卡洛的模拟结果表明,LPN图对非正态分布具有很好的稳健性,并且在不同的过程分布下对检测位置参数和尺度参数,尤其对检测尺度参数的漂移都具有很好的性能。最后通过监控出租车服务质量说明LPN图在实际中的应用。     

混合正态分布下基于斜线截断的稳健似然比累积和控制图北大核心CSCD

累积和控制图主要用于对正态分布过程中均值的中小漂移的检测,但是对厚尾分布过程监测并不稳定.MacEachern等(2007)提出了用于监测厚尾分布过程的稳健似然比累积和(RLCUSUM)控制图.文章主要研究RLCUSUM控制图的性质,包括可控平均运行长度关于控制限的性质和过程失控时不同真实均值对平均运行长度的影响等,并提出了对于对数似然比函数进行斜线截断的方式,同时分析总结了不同污染程度的混合正态分布下各种截断方式得到的RLCUSUM控制图的适用情况.     

一种多指标质量动态控制图及其应用

研究了将多指标在一个图上标示的多指标控制图。提出了三种质量控制限并作了比较。控制上限(UCL)取Hotelling的T2统计量的α/2上侧分位数。预控上限(UPCL)取Hotelling的T2统计量的λα/2上侧分位数。当第k个观测点的T2k值超过UPCL时,则接下去的抽样区间将缩短,以便及早发现失控状态。对超出控制限的情况下如何确定哪一个质量指标发生异常的问题,提出了一种可靠的分析方法。用这种方法解决了某卷烟厂的烟丝生产过程中的多指标质量控制和管理问题。     

The total median in statistical quality control

In industry, most of the process observations are assumed to come from a normal population, but usually we merely want to control the process mean value. It is thus sensible to find control statistics, which are ‘robust’ to monitor the process mean, giving the expected rate of false alarms whenever that mean is close to the target value, although not under a normal regime. Simulation studies for a few symmetric and asymmetric distributions allow us to suggest the total median as a robust median estimator. We shall here analyse such a robustness, as well as the robustness of the total median chart comparatively to the sample mean chart, whenever we want to control the mean value of a symmetric underlying parent. Some indication is also provided on the comparative out‐of‐control behaviour of the two charts. Copyright © 2004 John Wiley & Sons, Ltd.     

Economic design of an attribute control chart for monitoring mean life based on multiple deferred state sampling

In this paper, we design an attribute np control chart using multiple deferred state (MDS) sampling under Weibull distribution based on time truncated life test. This chart is constructed for monitoring the variation of mean life of the product in a manufacturing process. The optimal parameters of MDS sampling and the control limit coefficients are determined so that the in‐control average run length (ARL) is as close as to the target ARL. The optimal parameters of MDS sampling are sample size and number of successive subgroups required for declaring the current state of process. Out‐of‐control ARL is considered as a measure of the performance of proposed chart and reported with determined optimal parameters for various shift constants. The out‐of‐control ARL of the proposed chart obtained under various distributions is compared with each other. The performance of proposed control chart is compared with the performance of the existing control chart designed under single sampling. In addition, the economic design of proposed chart using variable sampling interval scheme is discussed, and sensitivity analysis on expected costs is also investigated.     

Control charts based on randomized quantile residuals

In practice, quality characteristics do not always follow a normal distribution, and quality control processes sometimes generate non‐normal response outcomes, including continuous non‐normal data and discrete count data. Thus, achieving better results in such situations requires a new control chart derived from various types of response variables. This study proposes a procedure for monitoring response variables that uses control charts based on randomized quantile residuals obtained from a fitted regression model. Simulation studies demonstrate the performance of the proposed control charts under various situations. We illustrate the procedure using two real‐data examples, based on normal and negative binomial regression models, respectively. The simulation and real‐data results support our proposed procedure.     

基于惩罚似然比的高维空间相关过程EWMA质量监控模型

变量选择控制图是高维统计过程监控的重要方法。针对传统变量选择控制图较少考虑高维过程空间相关性而造成监控效率低的问题,提出一种基于Fused-LASSO的高维空间相关过程监控模型。首先,利用Fused LASSO算法对似然比检验进行改进;然后,推导出基于惩罚似然比的监控统计量;最后,通过仿真模拟和真实案例分析所提监控模型的性能。仿真实验和真实案例均表明:在高维空间相关过程中,当相邻监控变量同时发生异常时,利用所提监控方法能够准确识别潜在异常变量,取得较好的监控效果。     

一个监控方差的与分布无关的变点模型

文献中绝大部分与分布无关的控制图用于监控过程位置参数,如均值或中位数,而非过程方差.该文开发了一个新的与分布无关的控制图,通过整合一个两样本非参数检验和有效的变点模型.所提出的控制图容易计算,方便应用,并且对于探测过程方差的漂移非常有效.因为它避免了在监控之前的一个很长时间的收集数据的阶段,并且它不需要潜在的过程分布的知识,因此,所提出的控制图在开始阶段或者短程运行情况下特别有用.     

Multivariate Bayesian process control for a finite production run

Most industrial products and processes are characterized by several, typically correlated measurable variables, which jointly describe the product or process quality. Various control charts such as Hotelling’s T², EWMA and CUSUM charts have been developed for multivariate quality control, where the values of the chart parameters, namely the sample size, sampling interval and the control limits are determined to satisfy given economic and/or statistical requirements. It is well known that this traditional non-Bayesian approach to a control chart design is not optimal, but very few results regarding the form of the optimal Bayesian control policy have appeared in the literature, all limited to a univariate chart design. In this paper, we consider a multivariate Bayesian process mean control problem for a finite production run under the assumption that the observations are values of independent, normally distributed vectors of random variables. The problem is formulated in the POMDP (partially observable Markov decision process) framework and the objective is to determine a control policy minimizing the total expected cost. It is proved that under standard operating and cost assumptions the control limit policy is optimal. Cost comparisons with the benchmark chi-squared chart and the MEWMA chart show that the Bayesian chart is highly cost effective, the savings are larger for smaller values of the critical Mahalanobis distance between the in-control and out-of-control process mean.     

两指标双F统计过程控制图

当产品质量指标服从二元正态分时,可用T2控制图与Λ控制图联合判断产品生产的过程是否处于受控状态。本文利用T2统计量与F统计量、Λ统计量与F统计量之间的关系,得到了两指标情形下两类基于F分布统计量的统计过程控制图,简称双F统计过程控制图,并给出了控制图应用实例。     

Cumulative conformance count chart with variable sampling intervals and control limits

The cumulative conformance count (CCC) chart has been used for monitoring processes with very low fraction of nonconforming items. Typically, the items produced from the process were examined using 100% inspection for generating the CCC chart. However, this would be costly when taking the inspection cost and time into consideration and thus limit its application. Instead of inspecting the items one by one, this study takes sample from them, and regards the time between two successive samples as the sampling interval. In order to increase the sensitivity of the CCC chart to process change, the sampling interval and control limits are allowed to vary in this study. The average time to signal process change of the modified CCC chart (called the variable sampling interval and control limit (VSI/VCL) CCC chart) is derived by the Markov chain approach and taken as the performance measure to evaluate its statistical efficiency. With some minor changes, this chart can be reduced to the VSI CCC chart, the VCL CCC chart, and the standard CCC chart. In addition, comparisons among them are made and discussed. Copyright © 2010 John Wiley & Sons, Ltd.