一种可用于检测过程尺度参数的非参数控制图

传统的控制图多数是在已知过程分布的假设下构建的,这种控制图被称为参数控制图。然而,在实际应用中,大多数过程因为其数据的复杂性导致他们的精确分布往往难以确定。当预先指定的参数分布无效时,参数控制图的结果将不再可靠。为了解决这个问题,通常考虑非参数控制图,因为非参数控制图比参数控制图更加稳健。近年来对非参数控制图的研究越来越多,但大多数现有的控制图主要是用于检测位置参数的变化。本文提出一个新的非参数Shewhart控制图(称为LOG图),可用来检测未知连续过程分布的尺度参数。文中依据运行长度分布的均值,方差和分位数,分析了LOG图在过程受控和失控时的性能表现,并与其他非参数控制图进行比较。模拟结果表明,LOG图在不同过程分布下对检测尺度参数的漂移都具有很好的性能。最后用一个实例来说明LOG图在实际中的应用。     

联合检测过程位置参数和尺度参数的非参数Cusum控制图

用于检测生产过程的多数传统控制图都假定过程的受控分布是已知的,并假定数据服从正态分布。然而在很多情况下,由于没有足够的数据来估计过程的分布,这种假定就变得不现实,而非参数控制图却不需要任何关于分布的特殊形式的假定。另外,多数的已有控制图都是使用两个单独的均值与方差控制图来同时检测生产过程.本文中,我们提出一个新的基于Cramer-von-Mises(CvM)检验的非参数累积和控制图(称为CvM图)来同时检测过程位置参数和尺度参数。文中给出了基于不同受控平均运行长度(ARL)下的CvM图的控制限,通过步长的均值、方差及分位数来研究控制图的性能表现。最后用一个实例来说明CvM图的实际应用。     

联合监控位置和尺度参数控制图综述

近二十年来,在各种应用的驱动下,联合监控过程位置参数和尺度参数的变化越来越受到研究工作者们的重视。在此背景下,大量的研究工作被学者们提出。本文将系统梳理和回顾这二十年的联合监控过程位置参数和尺度参数控制图的研究进展。为此,我们首先回顾受控分布为正态分布且受控参数已知情况下的联合监控均值和方差的控制图方案,并对这些控制图给出我们的评价观点。然后,我们讨论正态分布下,受控分布参数未知时的联合监控方案。进而,我们从稳健性的角度回顾当受控分布完全未知时的非参数或者分布自由的联合监控方案。最后,我们针对一些复杂数据过程,譬如,多元过程,相关过程,存在测量误差的过程,给出这方面联合监控的简要综述,并在这些复杂过程的基础上,给出未来的可能研究方向。     

带马尔可夫均值估计量的非参数自适应CUSUM控制图

本文提供了一个带马尔可夫均值估计量的非参数自适应CUSUM控制图用于监测位置参数的持续性漂移。它可以通过马尔可夫均值估计量预测未知的漂移大小,自适应的调整控制图参数,来对不同大小的未知漂移进行一个很好的监控。这是一个自启动非参数控制图,可以用于监控开始阶段,并且不需要依赖于任何样本的分布.通过数据模拟研究显示出这个控制图不仅在各种不同分布下具有很好的稳健性,并且对各种大小的漂移都很有效。     

一类基于次序秩的带可变抽样区间的非参数动态控制图

文章提供了一类用于检测位置参数持续性漂移的非参数动态控制图.此类控制图基于次序秩统计量带有可变的抽样区间,提高了控制图的监控效率.此外,它们是一类自启动的非参数控制图,不需要预先知道样本的分布,可用于监控的初始阶段.通过数据模拟显示此类控制图不仅在各种不同分布下具有很好的稳健性,并且对各种大小的漂移都有很好的监控效率.     

基于拟合优度检验的非参数EWMA控制图

文章提出了一种基于拟合优度检验的非参数控制图,以实现对连续型数据的监控.所提出的方法不仅适用于单值观测的情况,也可用于分组样本.不同于传统的控制图要求数据服从正态分布,文章的方法不限制数据的分布,可用于正态以及非正态的任意分布;并且能够监控数据分布的变化,例如分布中的位置参数、尺度参数、以及形状参数等.仿真结果表明,文章提出的控制图计算迅速、使用方便,在各种分布下都表现稳健,对分布变化的监控非常有效.     

检测尺度参数的非参数控制图

本文基于Ansari-Bradley检验提出两种在过程分布未知时检测过程尺度参数的非参数控制图,即混合指数加权移动平均与累积加和(mixed exponentially weighted moving averagecumulative sum,EWMA-CUSUM)控制图与混合累积加和与指数加权移动平均(mixed cumulative sum-exponential weighted moving average,CUSUM-EWMA)控制图.通过比较平均运行链长等多个指标来衡量控制图的性能表现,并考虑了阶段Ⅰ及阶段Ⅱ样本容量对阶段Ⅱ检测性能的影响.最后用实例来说明本文提出的控制图的实际应用.     

阶段Ⅱ联合检测过程位置和尺度的非参数EWMA控制图（英文）

本文提出了一个基于Cucconi检验的非参数指数加权移动平均(EWMA)控制图(简称为EC图)来同时检测过程位置参数和尺度参数.依据步长分布的均值、方差及分位数,给出了EC图与其他一些现有的非参数EWMA控制图的模拟比较.基于蒙特卡洛的模拟结果表明,EC图具有很好的性能.详细分析了阶段I中参考样本大小对EC图受控性能的影响.最后用一个实例来说明EC图的实际应用。     

基于次序秩的非参数EWMA联合控制图

本文提供了一个基于次序秩的非参数EWMA联合控制图(DNE)用于监测位置参数的持续性漂移.这是一个自启动控制图,不用累积大量可控样本数据,可以用于监控开始阶段。同时,我们不需要预先知道样本的分布,也不需要预先调整任何参数.通过数据模拟研究显示出这个控制图不仅在各种不同分布下具有很好的稳健性,并且对各种大小的漂移都很有效。文章最后通过工业上一个真实例子表明,这个控制图在实际应用中有着非常好的表现。     

过程参数未知时的连续检验问题

对连续检验问题,Page(Page,1954）提出的累积和控制图（CUSUM）已被证明在检测小的漂移时效果很好,然而,当受控过程的参数未知时,CUSUM的应用受到限制,Quensenberyy（1991）提出用变换的方法将观测值中的未知参数消去,在原假设“过程保持一致”成立的条件下,变换得到的Q统计量为独立同分布的标准正态变量,这里有二个问题：问题之一是,如果过程中有一漂移发生,变换得到的Q统计量的分布就很复杂,漂移对Q统计量的均值的影响是非时间齐次的,随着过程的推移,漂移对Q的均值的影响越来越小,因此,基于Q统计量的检验问题与一般的连续检验问题是不同的,好的检验方法应将这种不同反映出来,因此,基一种基于Q的新的累积和检验统计量,模拟结果显示,这种统计量的效果是不错的,问题之二是,当过程方差未知时,Q统计量的值的计算很难,它需要计算t分布的分布函数和正态分布函数的逆函数,这在实际使用中几乎是做不到的,本文提出一种近似方法,它不需计算复杂的分布函数,而是给出近拟服从标准正态分布的统计量为作为检验统计量,模拟研究的结果显示,这种近似的效果很好,它的各项指标与精确方法的相应指标非常接近。     

A Distribution-Free Phase II EWMA Control Chart for Joint Monitoring of Location and Scale

A single distribution-free (nonparametric) Phase II exponentially weighted moving average (EWMA) chart based on the Cucconi statistic, referred to as the EWMA-Cucconi (EC) chart, is considered here for simultaneously monitoring shifts in the unknown location and scale parameters of a univariate continuous process. A comparison with some other existing nonparametric EWMA charts is presented in terms of the average, the standard deviation and some percentiles of the run length distribution. Numerical results based on Monte Carlo analysis show that the EC chart provides quite a satisfactory performance. The effect of the Phase I (reference) sample size on the IC performance of the EC chart is studied in detail. The application of the EC chart is illustrated by two real data examples.     

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??A single distribution-free (nonparametric) Phase II exponentially weighted moving average (EWMA) chart based on the Cucconi statistic, referred to as the EWMA-Cucconi (EC) chart, is considered here for simultaneously monitoring shifts in the unknown location and scale parameters of a univariate continuous process. A comparison with some other existing nonparametric EWMA charts is presented in terms of the average, the standard deviation and some percentiles of the run length distribution. Numerical results based on Monte Carlo analysis show that the EC chart provides quite a satisfactory performance. The effect of the Phase I (reference) sample size on the IC performance of the EC chart is studied in detail. The application of the EC chart is illustrated by two real data examples.     

Distribution-free monitoring of univariate processes

We consider statistical process control (SPC) of univariate processes when observed data are not normally distributed. Most existing SPC procedures are based on the normality assumption. In the literature, it has been demonstrated that their performance is unreliable in cases when they are used for monitoring non-normal processes. To overcome this limitation, we propose two SPC control charts for applications when the process data are not normal, and compare them with the traditional CUSUM chart and two recent distribution-free control charts. Some empirical guidelines are provided for practitioners to choose a proper control chart for a specific application with non-normal data.     

An evaluation of the multivariate dispersion charts with estimated parameters under non‐normality

Various charts such as |S|, W, and G are used for monitoring process dispersion. Most of these charts are based on the normality assumption, while exact distribution of the control statistic is unknown, and thus limiting distribution of control statistic is employed which is applicable for large sample sizes. In practice, the normality assumption of distribution might be violated, while it is not always possible to collect large sample size. Furthermore, to use control charts in practice, the in‐control state usually has to be estimated. Such estimation has a negative effect on the performance of control chart. Non‐parametric bootstrap control charts can be considered as an alternative when the distribution is unknown or a collection of large sample size is not possible or the process parameters are estimated from a Phase I data set. In this paper, non‐parametric bootstrap multivariate control charts |S|, W, and G are introduced, and their performances are compared against Shewhart‐type control charts. The proposed method is based on bootstrapping the data used for estimating the in‐control state. Simulation results show satisfactory performance for the bootstrap control charts. Ultimately, the proposed control charts are applied to a real case study.     

A note on interval estimation of the standard deviation of a gamma population with applications to statistical quality control

Traditional process control charts for a measurement standard deviation are based on the assumption of normality, which may not always be valid. Assuming that measurements follow a gamma distribution, we have obtained an approximate distribution of the sample variance, scaled appropriately. This approximate distribution, which happens to be another gamma model, is used to derive an interval estimate of the population standard deviation. Further, the above approximate gamma model for the sample variance can be used to develop a process control chart as demonstrated by a simulated data set.     

Nonparametric Multivariate CUSUM Chart and EWMA Chart Based on Simplicial Data Depth

Simplicial data depth is a useful tool for describing how central a vector is in a multivariate distribution. If the average simplicial depth of a subgroup of observations from a multivariate distribution is too small, it may indicate that a shift in its location or/both scale occurs. In this paper, we propose two new types of nonparametric control charts which are one-sided CUSUM and EWMA control schemes based on simplicial data depth. We also compute the Average Run Length of the CUSUM chart and the EWMA chart by Markov chain method. Recommendations on how to choose the optimal reference value and the smoothing parameter are also given. Comparisons between these two proposed control schemes and the multivariate EWMA are presented.     

A new control chart in contaminated data of t‐Student distribution for individual observations

Control charts are the most popular tool for monitoring production quality. In traditional control charts, it is usually supposed that the observations follow a multivariate normal distribution. Nevertheless, there are many practical applications where the normality assumption is not fulfilled. Furthermore, the performance of these charts in the presence of measurement errors (outliers) in the historical data has been improved using robust control charts when the observations follow a normal distribution. In this paper, we develop a new control chart for t‐Student data based on the trimmed T² control chart () through the adaptation of the elements of this chart to the case of this distribution. Simulation studies show that a control chart performs better than T² in t‐Student samples for individual observations. Copyright © 2012 John Wiley & Sons, Ltd.     

自相关过程的改进型EWMA控制图

常规指数加权移动平均(EWMA)控制图的假设前提是观测数据相互独立,但在实际生产过程中,数据相关违背假设条件。本文首先讨论了序列自相关对常规EWMA控制图的影响,结果表明其检测效能降低。因此,重新估计了平稳过程的σz并在此基础上建立了改进型EWMA控制图。然后运用平均链长比较了改进型EWMA控制图与休哈特图和残差控制图,模拟研究说明当过程非强相关且过程均值发生中小偏移条件下。改进型EWMA控制图的检测效果要优于其他两种控制图。最后,通过一个实例验证了该方法的有效性。     

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.