A new multivariate EWMA scheme for monitoring covariance matrices

Shen, Xiaobei; Tsung, Fugee; Zou, Changliang

doi:10.1080/00207543.2013.842019

Cited by 38 publications

(40 citation statements)

References 20 publications

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“…Considering this feature, the MaxNorm control chart integrates the sum of the squared deviations with the maximum absolute deviation, 9 which are calculated, respectively, as Considering this feature, the MaxNorm control chart integrates the sum of the squared deviations with the maximum absolute deviation, 9 which are calculated, respectively, as…”

Section: Maxnorm Control Chartmentioning

confidence: 99%

“…9 Once the simulated ARL 0 value reaches 200±1, the simulation is terminated, and the corresponding UCL value is adopted. Unfortunately, the distributions or the moments of the charting statistics for these control charts are difficult to be specified explicitly, so the associated UCLs may not be calculated accordingly.…”

Section: Settings Of Control Chartsmentioning

confidence: 99%

“…To resolve this issue, the augmented sample covariance matrix may be used, which combines the sample data from Phase II stage with those collected in Phase I stage. [6][7][8][9] Besides, the penalized likelihood method has been applied to obtain a positive definite estimator via regularization on the structure of the target covariance matrix. [6][7][8][9] Besides, the penalized likelihood method has been applied to obtain a positive definite estimator via regularization on the structure of the target covariance matrix.…”

Section: Introductionmentioning

confidence: 99%

“…For these control charts, a positive definite estimator of the covariance matrix is obtained using the EWMA scheme. 9 In all the aforementioned distance-based control charts, various norm-based distance measures are used to devise the charting statistics. More specifically, considering only the diagonal elements in the covariance matrix, the MEWMSL 1 and MEWMSL 2 charts are proposed using, respectively, the sum of the absolute deviations and the sum of the squared deviations.…”

Section: Introductionmentioning

confidence: 99%

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A simulation comparison of some distance‐based EWMA control charts for monitoring the covariance matrix with individual observations

Ning

2019

Quality & Reliability Eng

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It is common in modern manufacturing to simultaneously monitor more than one process quality characteristic. In such a multivariate scenario, the monitoring of the covariance matrix, along with the mean vector, plays an important role in assessing whether a process stays in control or not. However, monitoring the covariance matrix is technically more difficult, especially when there is only one observation available in each subgroup, disabling the usual sample covariance matrix as an effective estimator. To monitor the covariance matrix with individual observations in Phase II stage, several exponentially weighted moving average (EWMA) control charts have been constructed based on the distance between the estimated process covariance matrix and its target value.In this paper, two new control charts are devised using the sum of the square roots of the absolute deviations and its combination with the sum of squared deviations. These distance-based control charts are compared via the simulation experiments on different simulated out-of-control covariance matrices with respect to the number of quality characteristics being monitored, the shift pattern, and the shift magnitude. The simulation results identify the control charts that perform relatively robust and show that these various control charts may have their respective merits on different out-of-control scenarios.

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Section: Maxnorm Control Chartmentioning

confidence: 99%

Section: Settings Of Control Chartsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A simulation comparison of some distance‐based EWMA control charts for monitoring the covariance matrix with individual observations

Ning

2019

Quality & Reliability Eng

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“…In the health care industry, the foetal state may be determined using a technique called cardiotocography, which measures multiple features such as the number of accelerations per second and the number of foetal movements per second. Any significant deviation of the covariance matrix of those features from the normal state indicates that the foetus may have a health problem …”

Section: Introductionmentioning

confidence: 99%

A control scheme for monitoring process covariance matrices with more variables than observations

Tsung

2018

Quality & Reliability Eng

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In this paper, we propose a new control chart that integrates a powerful high‐dimensional covariance matrix test with the exponentially weighted moving average procedure for monitoring high‐dimensional variability with individual observations. Design and implementation of the proposed chart are provided, including search algorithm and a table for the control limits, diagnostic aids after the signal, effect of misspecifying the in‐control distribution, and a bootstrap procedure. Monte Carlo simulation results show that the new chart, with its powerful inherited properties, provides satisfactory performance in various cases, especially for covariance shifts that involve diagonal components. The application of the proposed method is illustrated with a real data example from a white wine production process.

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A distribution‐free control chart for monitoring high‐dimensional processes based on interpoint distances

Shu

Fan

2018

Naval Research Logistics

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Funding informationFundo para o Desenvolvimento das Ciências e da Tecnologia, FDCT/053/2015/A2. University of Macau Research Committee, MYRG2016-00012-FBA.With rapid advances in sensing technology and data acquisition systems, high-dimensional data appear in many settings. The high dimensionality presents a new challenge to the traditional tools in multivariate statistical process control, due to the "curse of dimensionality." Various tests for mean vectors in high dimensional situations have been discussed recently; however, they have been rarely adapted to process monitoring. This paper develops a distribution-free control chart based on interpoint distances for monitoring mean vectors in high-dimensional settings. Other than the Euclidean distance, the family of Minkowski distance is used for discussion, which is a generalization of the former and other distances. The proposed approach is very general as it represents a class of distribution-free control charts based on distances. Numerical results show that the proposed control chart is efficient in detecting mean shifts in both symmetric and heavy-tailed distributions. KEYWORDS control chart, Minkowski distance, multivariate statistical process control 1 Naval Res Logistics 2018;65:317-330 wileyonlinelibrary.com/journal/nav

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A new multivariate EWMA scheme for monitoring covariance matrices

Cited by 38 publications

References 20 publications

A simulation comparison of some distance‐based EWMA control charts for monitoring the covariance matrix with individual observations

A simulation comparison of some distance‐based EWMA control charts for monitoring the covariance matrix with individual observations

A control scheme for monitoring process covariance matrices with more variables than observations

A distribution‐free control chart for monitoring high‐dimensional processes based on interpoint distances

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