平稳自相关过程的EWMA控制图

讨论了对平稳自相关过程中出现的较小波动进行监控的一种方法.采用自回归移动平均(ARMA)模型对平稳自相关过程进行适当的拟合,通过计算残差的方法消除过程中的自相关要素,并在此基础上提出对于均值和方差出现的较小波动进行监控的指数加权移动平均(EWMA)控制图的构造.通过与其它几种方法的比较来说明该方法在监控平稳自相关过程时有更好的效率.     

基于控制图的GPS异常监测数据检验方法研究

为了有效地判别GPS异常监测数据,建立了GPS监测序列异常检验的数学模型,提出利用统计过程控制中的控制图对监测序列进行异常检验和预警的新方法;针对GPS监测数据不服从正态分布的问题,提出利用累积分布函数的核密度估计将其转换为Q统计量,并以此为基础构建基于Q统计量的控制图用于GPS异常波动数据的检验;该文文末利用仿真数据对比分析了休哈特控制图与累积和控制图对不同异常偏移值的检验效果,结果表明两种控制图各有利弊、相互补充,休哈特控制图对于3倍以上标准差的异常偏移能够给出有效的预警,但缺乏小偏移检测的能力,累积和控制图能够精确检测出最小达0.5倍标准差的连续小偏移,但是随着偏移值的增大其误警率会有所增加。     

休哈特控制图在分光光度计检定装置期间核查中的应用

文中阐述了休哈特控制图在分光光度计检定装置期间核查中的应用。以标准中性滤光片为例,对测量数据进行定量分析,进而判定标准中性滤光片性能的稳定性。实践证明,此方法切实可行,且能实时有效地反映分光光度计检定装置的受控状态。     

信噪比在分析残差控制图检测能力中的应用

应用信噪比与平均运行长度2种方法,分析了自相关过程由时间序列模型AR(1)描述时,残差控制图对过程均值变化的检测能力.结果表明,信噪比是控制图的检测能力的一个良好指标,在合理参数0.1≤λ≤1-φ范围内,残差EWMA控制图对过程均值小偏移较灵敏,对过程均值大偏移的检测能力略差于残差Shewhart控制图.     

对休哈特控制图中平均值控制界限的商讨

采用休哈特控制图的方法可以对测量过程是否处于统计控制状态进行控制.但是,对于平均值控制界限的确定则认为不妥,根本原因是,平均值控制界限依据重复性条件下所得数据的标准偏差来设置,用它来控制复现性条件下子组的平均值的波动性,由于条件不同,因此,前者不能来控制后者.依据计量保证方案(MAP)提出的控制界限的确定,是用在复现性条件下各子组的平均值的组间标准差来设置控制界限,也就是用组内平均值的分散性来控制组内平均值.通过对二等电阻、直流电压和电能表标准装置同一组试验数据进行上述两种控制图的制作比较,以及对确定控制界限的理论分析,证明了休哈特控制图平均值控制界限的确定不妥.     

基于APL的偏态控制图优化设计

以平均产品长度(APL)为评价控制图性能的标准,研究了偏态控制图的优化设计问题.针对一般控制图无法有效解决偏态总体的不对称性的情况,采用赋权方差法来构造非对称的偏态控制图,并获得其最优设计模型;最后给出了模型的灵敏度分析及算例.     

基于多点报警准则的高质量过程缺陷率控制图

为了提高用于高质量过程监控的累积计点值控制图的监控效率,提出了一类采用多点报警准则的高质量过程缺陷率控制图设计,并给出了计算这类改进型控制图的平均运行长度的马尔科夫链方法。为了验证该设计方法的改进效果,分析比较了采用多点报警规则的3种累积计点值控制图（报警规则为连续两点出界、连续三点中有两点出界、连续三点出界）与报警规则不改变的（报警规则为有一个点出界）累积计点值控制图的监控效率。比较结果表明：在受控状态下平均运行长度都为370的情况下,多点报警的累积计点值控制图的失控状态下的平均运行长度分别较报警规则不变的控制图的平均运行长度减小了约44%、40%、63%,控制图发现缺陷率增大的效率明显改善。得出结论：这种多点报警的累积计点值控制图发现缺陷率增大的速度提高40%~60%。     

控制图在砝码检定/校准过程控制中的应用

一、引言 休哈特控制图即通常说的测量过程控制图,是一种有控制界限的图,用于对已经完成的测量过程或测量阶段进行分析,以评估测量过程是否稳定并处于受控状态。     

休哈特控制图在眼镜片顶焦度标准装置期间核查中的应用

本文阐述了休哈特控制图在眼镜片顶焦度标准装置期间核查中的应用。对测量数据进行定量分析,进而判定眼镜片顶焦度标准装置性能的稳定性。实践证明,此方法切实可行,能实时有效地反映该标准装置的受控状态。     

A New Hybrid Exponentially Weighted Moving Average Control Chart for Monitoring Process Mean: Discussion

A new hybrid exponentially weighted moving average (HEWMA) control chart has been proposed in the literature for efficiently monitoring the process mean. In that paper, the computed variance of the HEWMA statistic was, unfortunately, not correct! In this discussion, the correct variance of the HEWMA statistic is given, and the run length characteristics of the HEWMA control chart are studied and explored. It is noticed that not only the superiority of the HEWMA control chart remains over the existing (considered before) charts but also the new results based on the corrected control limits are more profound and reflective. Copyright © 2016 John Wiley & Sons, Ltd.     

Robustness properties of multivariate EWMA control charts

In this paper, the robustness of the multivariate exponentially weighted moving average (MEWMA) control chart to non‐normal data is examined. Two non‐normal distributions of interest are the multivariate distribution and the multivariate gamma distribution. Recommendations for constructing MEWMA control charts when the normality assumption may be violated are provided. Copyright © 2002 John Wiley & Sons, Ltd.     

A New Exponentially Weighted Moving Average Control Chart for Monitoring the Process Mean

Exponentially weighted moving average (EWMA) quality control schemes have been recognized as a potentially powerful process monitoring tool because of their superior speed in detecting small to moderate shifts in the underlying process parameters. In quality control literature, there exist several EWMA charts that are based on simple random sampling (SRS) and ranked set sampling (RSS) schemes. Recently, a mixed RSS (MxRSS) scheme has been introduced, which encompasses both SRS and RSS schemes, and is a cost‐effective alternative to the RSS scheme. In this paper, we propose new EWMA control charts for efficiently monitoring the process mean based on MxRSS and imperfect MxRSS (IMxRSS) schemes, named EWMA–MxRSS and EWMA–IMxRSS charts, respectively. Extensive Monte Carlo simulations are used to estimate the run length characteristics of the proposed EWMA charts. The run length performances of the suggested EWMA charts are compared with the classical EWMA chart based on SRS (EWMA–SRS). It turns out that both EWMA–MxRSS and EWMA–IMxRSS charts perform uniformly better than the EWMA–SRS chart when detecting all different shifts in the process mean. An application to a real data set is provided as an illustration of the design and implementation of the proposed EWMA chart. Copyright © 2014 John Wiley & Sons, Ltd.     

A New Hybrid Exponentially Weighted Moving Average Control Chart for Monitoring Process Mean

Cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) control charts are commonly used for monitoring the process mean. In this paper, a new hybrid EWMA (HEWMA) control chart is proposed by mixing two EWMA control charts. An interesting feature of the proposed control chart is that the traditional Shewhart and EWMA control charts are its special cases. Average run lengths are used to evaluate the performances of each of the control charts. It is worth mentioning that the proposed HEWMA control chart detects smaller shifts substantially quicker than the classical CUSUM, classical EWMA and mixed EWMA–CUSUM control charts. Copyright © 2012 John Wiley & Sons, Ltd.     

Effect of estimation under nonnormality on the phase II performance of linear profile monitoring approaches

The number of studies about control charts proposed to monitor profiles, where the quality of a process/product is expressed as function of response and explanatory variable(s), has been increasing in recent years. However, most authors assume that the in‐control parameter values are known in phase II analysis and the error terms are normally distributed. These assumptions are rarely satisfied in practice. In this study, the performance of EWMA‐R, EWMA‐3, and EWMA‐3(d²) methods for monitoring simple linear profiles is examined via simulation where the in‐control parameters are estimated and innovations have a Student's t distribution or gamma distribution. Instead of the average run length (ARL) and the standard deviation of run length, we used average and standard deviation of the ARL as performance measures in order to capture the sampling variation among different practitioners. It is seen that the estimation effect becomes more severe when the number of phase I profiles used in estimation decreases, as expected, and as the distribution deviates from normality to a greater extent. Besides, although the average ARL values get closer to the desired values as the amount of phase I data increases, their standard deviations remain far away from the acceptable level indicating a high practitioner‐to‐practitioner variability.     

A new adaptive CUSUM control chart for detecting the multivariate process mean

We propose a new multivariate CUSUM control chart, which is based on self adaption of its reference value according to the information from current process readings, to quickly detect the multivariate process mean shifts. By specifying the minimum magnitude of the process mean shift in terms of its non‐centrality parameter, our proposed control chart can achieve an overall performance for detecting a particular range of shifts. This adaptive feature of our method is based on two EWMA operators to estimate the current process mean level and make the detection at each step be approximately optimal. Moreover, we compare our chart with the conventional multivariate CUSUM chart. The advantages of our control chart detection for range shifts over the existing charts are greatly improved. The Markovian chain method, through which the average run length can be computed, is also presented. Copyright © 2010 John Wiley & Sons, Ltd.     

A New Maximum Exponentially Weighted Moving Average Control Chart for Monitoring Process Mean and Dispersion

Maximum exponentially weighted moving average (MaxEWMA) control charts have attracted substantial interest because of their ability to simultaneously detect increases and decreases in both the process mean and the process variability. In this paper, we propose new MaxEWMA control charts based on ordered double ranked set sampling (ODRSS) and ordered imperfect double ranked set sampling (OIDRSS) schemes, named MaxEWMA‐ODRSS and MaxEWMA‐OIDRSS control charts, respectively. The proposed MaxEWMA control charts are based on the best linear unbiased estimators obtained under ODRSS and OIDRSS schemes. Extensive Monte Carlo simulations are used to estimate the average run length and standard deviation of the run length of the proposed MaxEWMA control charts. The run length performances and the diagnostic abilities of the proposed MaxEWMA control charts are compared with that of their counterparts based on simple random sampling (SRS), ordered ranked set sampling (ORSS) and ordered imperfect ranked set sampling schemes (OIRSS) schemes, that is, MaxEWMA‐SRS, maximum generally weighted moving average (MaxGWMA‐SRS), MaxEWMA‐ORSS and MaxEWMA‐OIRSS control charts. It turns out that the proposed MaxEWMA‐ODRSS and MaxEWMA‐OIDRSS control charts perform uniformly better than the MaxEWMA‐SRS, MaxGWMA‐SRS, MaxEWMA‐ORSS and MaxEWMA‐OIRSS control charts in simultaneous detection of shifts in the process mean and variability. An application to real data is also provided to illustrate the implementations of the proposed and existing MaxEWMA control charts. Copyright © 2014 John Wiley & Sons, Ltd.     

A New Bivariate Control Chart to Monitor the Multivariate Process Mean and Variance Simultaneously

In this article a new control chart which enables a simultaneous monitoring of both the process mean and process variance of a multivariate data will be proposed. A thorough discussion in identifying whether the process mean or variability shifts is also given. Simulation studies will be performed to study the performance of the new chart by means of its average run length (ARL) profiles. Numerous examples are also given to show how the new chart is put to work in real situations.     

Practitioner advice: ERLDAT–A web-based tool to design and analyze EWMA control charts

The performance of a control chart is completely characterized by its run length distribution. Quality practitioners usually do not have access to the run length distribution but rely on the average run length (ARL) to design and evaluate the performance of an exponentially weighted moving average (EWMA) control chart. This article presents a web-based tool that provides users easy access to the Phase 2 (online or monitoring phase) run length distribution for a two-sided EWMA control chart with known parameters. The web-based tool calculates the run length distribution, percentiles of the run length distribution, as well as the mean (ARL) and variance (VRL) of the run length distribution. Additional functionality of the web-based tool includes plotting the run length distribution functions, building tables of the quantiles of the run length distribution, finding the smoothing parameter (λ) for an EWMA control chart for fixed control limit that satisfies ARL, VRL or percentile performance, and finding the control chart limit (k) for an EWMA control chart that satisfies ARL, VRL, or percentile performance. This tool and these techniques enable quality practitioners to better design and evaluate EWMA control charts.