Multivariate variability monitoring using EWMA control charts based on squared deviation of observations from target

Recent research works have shown that control statistics based on squared deviation of observations from target have the ability to monitor variability in both univariate and multivariate processes. In the current research, the properties of the control statistic S _t that has been proposed by Huwang et al. (J. Quality Technology 2007; 39 :258–278) are first reviewed and three new S _t‐based multivariate schemes are then presented. Extensive simulation experiments are performed to compare the performances of the proposed schemes with those of the multivariate exponentially weighted mean squared deviation (MEWMS) and the L₁‐norm distance of the MEWMS deviation from its expected value (MEWMSL₁) charts. The results show that one of the proposed schemes outperforms the others in detecting shifts in correlation coefficients and another has the best general performance among the compared charts in detecting shifts in which at least one of the variances changes. Copyright © 2011 John Wiley & Sons, Ltd.     

Detecting multiple special causes from multivariate data with applications to fault detection in manufacturing

Several articles in the recent literature propose linear models of product quality for both single station and multistation manufacturing processes. We show how these models may be used in conjunction with statistical methods to design a procedure for multivariate Statistical Process Control (SPC) that outperforms direct application of multivariate SPC. We show how to design the procedure and evaluate its performance in shift detection for models with and without singularities. The use of the procedure is illustrated using two examples from automobile body assembly.     

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 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.     

Design Strategies for the Multivariate Exponentially Weighted Moving Average Control Chart

The multivariate exponentially weighted moving average (MEWMA) control chart has received significant attention from researchers and practitioners because of its desirable properties. There are several different approaches to the design of MEWMA control charts: statistical design; economic–statistical design; and robust design. In this paper a review and comparison of these design strategies is provided.Copyright © 2004 John Wiley & Sons, Ltd.     

Detecting outbreaks in temporally dependent networks

Dynamic networks require effective methods of monitoring and surveillance in order to respond promptly to unusual disturbances. In many applications, it is of interest to identify anomalous behavior within a dynamic interacting system. Such anomalous interactions are reflected by structural changes in the network representation of the system. In this paper, a dynamic random graph model is proposed that takes into account the past activities of the individuals in the social network and also represents temporal dependency of the network. The model parameters are appearance and disappearance probabilities of an edge which are estimated using a maximum likelihood approach. A generalization of a single path‐dependent likelihood ratio test is employed to detect changes in the parameters of the proposed model. Through monitoring the estimated parameters, one can effectively detect structural changes in a temporal‐dependent network. The proposed model is employed to describe the behavior of a real network, and its parameters are monitored via dependent likelihood ratio test and multivariate exponentially weighted moving average control chart. Results indicate that the proposed dynamic random graph model is a reliable mean to modeling and detecting changes in temporally dependent networks.     

监控不合格品率的MEWMA-p控制图设计

传统Shewhart-p控制图只对单一属性的不合格品率进行监控,在过程发生偏移时有一定的滞后性。为提高不合格品率控制图的精度,提出一种多元指数加权移动平均不合格品率(multivariate exponentially weighted moving average p, MEWMA-p)控制图。该控制图将多个属性的不合格品率应用于多元指数加权移动平均控制图,可同时对多个属性进行监控,并且对于小范围的偏移更加敏感。对比分析同等偏移程度下指数加权移动平均不合格品率(exponentially weighted moving average p, EWMA-p)控制图与MEWMA-p控制图的平均运行长度(average run length,ARL)结果,并通过模拟仿真说明该方法的有效性。     

The Max EWMAMS control chart for joint monitoring of process mean and variance with individual observations

A traditional approach to monitor both the location and the scale parameters of a quality characteristic is to use two separate control charts. These schemes have some difficulties in concurrent tracking and interpretation. To overcome these difficulties, some researchers have proposed schemes consisting of only one chart. However, none of these schemes is designed to work with individual observations. In this research, an exponentially weighted moving average (EWMA)‐based control chart that plots only one statistic at a time is proposed to simultaneously monitor the mean and variability with individual observations. The performance of the proposed scheme is compared with one of the two other existing combination charts by simulation. The results show that in general the proposed chart has a significantly better performance than the other combination charts. Copyright © 2010 John Wiley & Sons, Ltd.     

A nonparametric triple exponentially weighted moving average sign control chart

Nonparametric control charts are used in process monitoring when there is insufficient information about the form of the underlying distribution. In this article, we propose a triple exponentially weighted moving average (TEWMA) control chart based on the sign statistic for monitoring the location parameter of an unknown continuous distribution. The run-length characteristics of the proposed chart are evaluated performing Monte Carlo simulations. We also compare its statistical performance with existing nonparametric sign charts, such as the cumulative sum (CUSUM), exponentially weighted moving average (EWMA), generally weighted moving average (GWMA), and double exponentially weighted moving average (DEWMA) sign charts as well as the parametric TEWMA-$\overline{X}$ chart. The results show that the TEWMA sign chart is superior to its competitors, especially for small shifts. Moreover, two examples are given to demonstrate the application of the new scheme.     

Improved design of robust exponentially weighted moving average control charts for autocorrelated processes

Residual‐based control charts for autocorrelated processes are known to be sensitive to time series modeling errors, which can seriously inflate the false alarm rate. This paper presents a design approach for a residual‐based exponentially weighted moving average (EWMA) chart that mitigates this problem by modifying the control limits based on the level of model uncertainty. Using a Bayesian analysis, we derive the approximate expected variance of the EWMA statistic, where the expectation is with respect to the posterior distribution of the unknown model parameters. The result is a relatively clean expression for the expected variance as a function of the estimated parameters and their covariance matrix. We use control limits proportional to the square root of the expected variance. We compare our approach to two other approaches for designing robust residual‐based EWMA charts and argue that our approach generally results in a more appropriate widening of the control limits. Copyright © 2010 John Wiley & Sons, Ltd.     

Nonparametric triple exponentially weighted moving average signed-rank control chart for monitoring shifts in the process location

Nonparametric (or distribution-free) control charts are used for monitoring processes where there is a lack of knowledge about the underlying distribution. In this article, a triple exponentially weighted moving average control chart based on the signed-rank statistic (referred as TEWMA-SR chart) is proposed for monitoring shifts in the location parameter of an unknown, but continuous and symmetric, distribution. The run-length characteristics of the proposed chart are evaluated performing Monte Carlo simulations. A comparison study with other existing nonparametric control charts based on the signed-rank statistic, the TEWMA sign chart, and the parametric TEWMA-$\overline{X}$ chart indicates that the proposed chart is more effective in detecting small shifts, while it is comparable with the other charts for moderate and large shifts. Finally, two illustrative examples are provided to demonstrate the application of the proposed chart.     

Error Detection and Pattern Prediction Through Phase II Process Monitoring

The continuous monitoring of the machine is beneficial in improving its process reliability through reflected power function distribution. It is substantial for identifying and removing errors at the early stages of production that ultimately benefit the firms in cost-saving and quality improvement. The current study introduces control charts that help the manufacturing concerns to keep the production process in control. It presents an exponentially weighted moving average and extended exponentially weighted moving average and then compared their performance. The percentiles estimator and the modified maximum likelihood estimator are used to constructing the control charts. The findings suggest that an extended exponentially weighted moving average control chart based on the percentiles estimator performs better than exponentially weighted moving average control charts based on the percentiles estimator and modified maximum likelihood estimator. Further, these results will help the firms in the early detection of errors that enhance the process reliability of the telecommunications and financing industry.     

Simultaneous Use of Runs Rules and Auxiliary Information With Exponentially Weighted Moving Average Control Charts

Quality has become a key determinant of success in all aspects of industry. Exponentially weighted moving average control chart is an important tool of statistical process control used to monitor and improve quality of industrial processes. To enhance the performance of control charts, there are many strategies including the choice of an efficient plotting statistic, the choice of an efficient sampling design, the application of runs rules, and the use auxiliary information among many others. In this study, we propose nine different signaling schemes to enhance the performance of an exponentially weighted moving average control chart for location parameter, which is based on the exploitation of auxiliary information. Performance evaluation of the proposed schemes is carried out in terms of average run length. Comparisons of proposals are made with the classical as well as the auxiliary based exponentially weighted moving average and cumulative sum charts, which indicate that the proposed schemes perform better than the comparative counterparts under discussion. Copyright © 2016 John Wiley & Sons, Ltd.     

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.     

An exponentially weighted moving average chart based on likelihood‐ratio test for monitoring Weibull mean and variance with subgroups

Monitoring changes in the Weibull mean and variance simultaneously is of interest in quality control. The mean and variance of a Weibull process are determined by its shape and scale parameters. Most studies are focused on monitoring the Weibull scale parameter with fixed shape parameter or the Weibull shape parameter with fixed scale parameter. In this paper, we propose an exponentially weighted moving average chart based on the likelihood‐ratio test and an inverse error function called ELR chart to monitor changes in the Weibull mean and variance simultaneously. The simulation approach is used to derive the average run length. We compare our proposed chart with other existing control charts for 3 cases, including scale parameter changes with fixed shape parameter, shape parameter changes with fixed scale parameter, and both parameters changes. The results show that the ELR chart outperforms the other control charts in terms of average run length in most cases. Two numerical examples are used to illustrate the applications of the proposed control chart.     

Autocorrelated SPC for Non‐Normal Situations

The importance of statistical process control (SPC) techniques in quality improvement is well recognized in industry. However, most conventional SPC techniques have been developed under the assumption of independent, identically and normally distributed observations. With advances in sensing and data capturing technologies, large volumes of data are being routinely collected from individual units in manufacturing industries. These data are often autocorrelated and skewed. Conventional SPC techniques can lead to false alarms or other types of poor performance monitoring of such data. There is a great need for process control techniques for variation reduction in these environments. Much recent research has focused on the development of appropriate SPC techniques for autocorrelated data, but few studies have considered the impact of non‐normality on these techniques. This paper investigates the effect of skewness on conventional autocorrelated SPC techniques, and provides an effective approach based on a scaled weighted variance approach to improve SPC performance in such an environment. Copyright © 2005 John Wiley & Sons, Ltd.     

Model Inadequacy and Residuals Control Charts for Autocorrelated Processes

As a result of time series parameter estimation based on previous data, the probability content of residuals control charts may vary when standard control limits are used. In this paper, we consider the AR(1) process with the autoregressive parameter being estimated from a sample of observations. The performance of the exponentially weighted moving average (EWMA) control chart for residuals is investigated. Modified control limits that account for the uncertainty in the parameter estimate are provided. Comparisons through simulation signify the importance of the modified control limits. Copyright © 2004 John Wiley & Sons, Ltd.