Adaptive Control Charts for Attributes

We develop a general model for adaptive c , np , u and p control charts in which one, two or three design parameters (sample size, sampling interval and control limit width) switch between two values, according to the most recent process information. For a given in-control average sampling rate and a given false alarm rate, the adaptive chart detects changes in the process much faster than a chart with fixed parameters. Moreover, this study also offers general guidance on how to choose an effective design.     

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.     

Variation Charts for Multivariate Processes

Hotelling's T² is customarily used as the control chart for multivariate SPC analysis. This chart responds to changes in both the mean values and the covariance matrix of the responses. In this article, we propose the use of a chart that concentrates on changes in the covariance matrix. The use of this covariance chart in concert with the T² chart enables the user to better determine whether T² points out of control are due to changes in mean values or due to changes in the covariance matrix. Using this chart in conjunction with T² thus furnishes a suite of tools similar to the x-bar and standard deviation charts for univariate processes.     

与控制点方法论相结合的V-mask累积和控制图

V-mask累积和控制图虽然能够有效地监控过程中发生的微小偏移,但是因为它需要存储大量统计量且计算时间较长,所以在计算机中实施起来比较困难.为了解决这一问题,介绍了将控制点方法论应用于V-mask累积和控制图这一方法,并通过实例来进一步说明.结果表明,与控制点方法论结合的控制图减少了存储量,缩短了计算时间,而且将在顾客满意度控制中得到广泛应用.     

基于控制图的模糊资料判别研究

与一般处理如合格或不合格等布尔型数据的质量控制图不同,针对不适合采用布尔逻辑的产品质量数据,应用模糊逻辑构建质量控制图,以加权平均法来解模糊化,权重采用模糊中位数作为不同语言类别的表示值.通过实例分析,这种方法可以比较满意地进行工序控制工作.     

Two Modified Semicircle Control Charts for Detecting Process Improvement

A semicircle control chart can be used in detecting both increases and decreases in the mean and/or variance. In this paper, we propose two modified semicircle charts for detecting a reduction in the process variance, a.k.a. process improvement. Each of these modified semicircle charts, namely, SC1 and SC2 has two limits, defined by the inner and outer semicircles. A process improvement is detected by the SC1 scheme if a point is plotted inside the smallest semicircle, or if two successive points are plotted between the inner and outer semicircles and by the SC2 scheme if a point plots inside the smallest semicircle or if two of three successive points plot between the inner and outer semicircles. It will be shown that the two modified semicircle charts have superior average run length (ARL) performances to the basic semicircle chart in the detection of process improvement. The ARL study is conducted by means of a simulation.     

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.     

New Corrections for Old Control Charts

When using standard control charts, typically several parameters need to be estimated. For the usual sample sizes, this is known to affect the performance of the chart. Here we present simple corrections to solve this problem. As a basis, we use existing factors which are widely used for the traditional charts. The advantage of the new proposals is that a clear link is made to the actual performance characteristics of the chart.     

Comparisons of Some Exponentially Weighted Moving Average Control Charts for Monitoring the Process Mean and Variance

An exponentially weighted moving average (EWMA) control chart for monitoring the process mean μ may be slow to detect large shifts in μ when the EWMA tuning parameter λ is small. An additional problem, sometimes called the inertia problem, is that the EWMA statistic may be in a disadvantageous position on the wrong side of the target when a shift in μ occurs, which may significantly delay detection of a shift in μ. Options for improving the performance of the EWMA chart include using the EWMA chart in combination with a Shewhart chart or in combination with an EWMA chart based on squared deviations from target. The EWMA chart based on squared deviations from target is designed to detect increases in the process standard deviation σ, but it is also very effective for detecting large shifts inμ. Capizzi and Masarotto recently proposed the option of an adaptive EWMA control chart in which λ is a function of the data. With the adaptive feature, the EWMA chart behaves like a standard EWMA chart when the current observation is close to the previous EWMA statistic, and like a Shewhart chart otherwise. Here we extend the use of the adaptive feature to EWMA charts based on squared deviations from target, and also consider an alternate way of defining the adaptive feature. We discuss performance measures that we believe are appropriate for assessing the effects of inertia, and compare the performance of various charts and combinations of charts. Standard practice is to simultaneously monitor both μ and σ, so we consider control chart performance when the objective is to detect small or large changes in μ or increases in σ. We find that combinations of EWMA control charts that include a chart based on squared deviations from target give good overall performance whether or not these charts have the adaptive feature.     

Two Charts: Not One

Difficulties can occur in the operation of traditional control charts. A principal reason for this is that the data coming from a typical operating process do not vary about a fixed mean. It is shown how by using a nonstationary model a continuously updated local mean level is provided. This can be used to produce (a) a bounded adjustment chart that tells you when to adjust the process to achieve maximum economy and (b) a Shewhart monitoring chart seeking assignable causes of trouble applied to the deviations from the local mean. Estimation of the mean and “standard deviation” are not required.     

Individuals Charts and Additional Tests for Changes in Spread

A number of authors have indicated that it is not a good idea to use the moving range chart (MR‐chart) with an individuals chart to detect shifts in the spread. However, the combination of these charts is still used in practice and even presented as ‘best practice’ in some cases. In addition, some more recent articles present arguments that justify the use of the additional MR‐chart in specific situations. In this paper we investigate these arguments and add to the literature by providing two more reasons not to use the MR‐chart. First, the merit of using an MR‐chart has never been evaluated before in the context of runs rules. Earlier papers investigated the change in performance as a result of adding a MR‐chart to a bare individuals chart. We show that relative to existing well‐known runs rules, there is no advantage in using a close alternative to the MR‐chart. Secondly, we investigate the suggestion of some of the proponents of the MR‐chart that its weak performance is due to a bad design. We show that this is not the case. We evaluate the average run length performance of the combination of an individuals chart and a MR‐chart under the most favorable circumstances for several out‐of‐control situations by optimizing the design of the two charts for each situation. Our results show that even this ‘best‐case’ performance of the combination is hardly better than that of the individuals chart alone. Copyright © 2005 John Wiley & Sons, Ltd.     

Computing the Percentage Points of the Run-Length Distributions of Multivariate CUSUM Control Charts

Multivariate CUSUM control charts are often used instead of the standard Hotelling's control charts in many practical problems when detection of small shifts in the process mean is important. However, design of multivariate CUSUM control charts are usually based on the average run length (ARL). In this work, we will compute the percentage points of the run-length distributions of two multivariate CUSUM control charts. It will be shown that interpretations based on ARL can be misleading since the in-control run-length distribution of a multivariate CUSUM is highly skewed. On the other hand, the percentage points of the run-length distribution provide additional information such as the median run length, early false out-of-control signals, and the skewness of the run-length distribution for a particular scheme. These extra information might provide quality control engineers further knowledge of a particular multivariate CUSUM control chart scheme.     

Adapting EWMA Control Charts for Batch-Correlated Data

Batch production is common in the chemical and process industries. This article demonstrates how EWMA charts should be modified to account for substantial batch-to-batch variation. A batch-correlation model is considered, and methods of estimation and hypothesis testing for the batch-correlation coefficient are developed. This discussion is most appealing for production processes in which items are processed in batches but are related within batch.     

Comparison of Multivariate Control Charts for Process Dispersion

In this article we compare four multivariate control charts for process dispersion in the retrospective analysis of a historical data set. Among the schemes compared, a new control chart based on a robust estimation of the variance-covariance matrix proved to be very effective in detecting changes in the process dispersion matrix.     

联合监控均值和方差的累积和控制图优化设计

为了提高监测均值和方差微小偏移的敏感度,围绕生产过程质量控制,建立同时监控均值和方差的累积和控制图.模型考虑均值和方差的变化,针对生产过程中的微小偏差,提出了一个新的累积和控制图,并给出了基于马尔可夫链理论的新控制图的平均链长计算方法.编程求解后对比文献中各控制图的平均链长数据以及更换变量数值改进控制图,通过计算变动比率得出新控制图的检测力度在不同偏移力度下都明显优于其他控制图方法.     

VSI Q控制图应用研究

VSI Q控制图可以解决经典休哈特控制图在样本数据缺乏的情况下不能应用的问题,并且可以加快检出速度.具体方法是将样本数据转换成服从标准正态分布的统计数据,再利用可变抽样区间技术确定抽样间隔时间.应用研究证明,VSI Q控制图在缺乏样本数据时也能用于监控生产过程,快速检测出异常.     

Incorporating Runs Rules into Hotelling's χ2 Control Charts

This paper illustrates a simple and effective method of incorporating runs rules into Hotelling χ² control charts. A Markov chain will be used to obtain a desired in-control average run length (ARL). Comparisons between the basic multivariate χ² control chart and the multivariate χ² control chart, which incorporates the various runs rules, are based on their respective ARL performances. All multivariate χ² control charts that incorporate the various runs rules have shown better ARL performance compared to the basic multivariate χ² control chart for small shifts in distance λ from the in-control mean vector μ₀ to the out-of-control mean vector μ_s. An example of the application, based on the proposed method, is also given.