Statistical monitoring of the covariance matrix in multivariate processes: A literature review

Ebadi, Mohsen; Chenouri, Shojaeddin; Lin, Dennis K.J.; Steiner, Stefan H.

doi:10.1080/00224065.2021.1889419

Cited by 26 publications

(16 citation statements)

References 117 publications

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“…Alt and Smith 4 proposed three control charts, two of which are multivariate dispersion charts that are based on the determinant of the sample covariance matrix and the square root of the determinant as the summary statistics, while the third chart is based on the likelihood ratio test. For more information on multivariate dispersion charts based on grouped observations, see the review articles by Zwetsloot and Woodall, 5 Ebadi et al, 6 Yeh et al 7 and Bersimis et al 8 In some industrial applications, the data used for quality characterization are stored as individual measurements. Therefore, various designed techniques have been adopted in the multivariate dispersion charts to monitor the variability of individual observations.…”

Section: Introductionmentioning

confidence: 99%

A new multivariate CUSUM chart for monitoring of covariance matrix with individual observations under estimated parameter

Ajadi

Wong

Mahmood

et al. 2021

Quality & Reliability Eng

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Multivariate charts for process dispersion detect changes in the variancecovariance matrix of a process. Most of the existing multivariate charts for monitoring the dispersion of individual observations were designed based on exponentially weighted moving average (EWMA) charting schemes. However, an alternative to the EWMA scheme is the cumulative sum (CUSUM) control chart, which has proven to be better in some cases. In the last decades, few studies have been conducted on methods based on multivariate CUSUM (MCUSUM) schemes to monitor the covariance matrix of individual observations. Consequently, we propose a new MCUSUM dispersion chart. Besides, most of the existing methods have been developed by assuming that the process parameters are known and that the process distribution is normal; these assumptions are not always true in practice. Hence, we compare the performance of the proposed chart and its counterparts based on the estimation effects under normal and nonnormal distributions. The results show that the proposed chart outperforms the other charts in terms of minor shifts in the process. Similarly, the proposed chart is the most robust to the normality assumption among the compared charts. The average value of the conditional average run length was used as the performance measure. Finally, the proposed method was also implemented with a simulated dataset to support the stated proposal findings.

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Section: Introductionmentioning

confidence: 99%

A new multivariate CUSUM chart for monitoring of covariance matrix with individual observations under estimated parameter

Ajadi

Wong

Mahmood

et al. 2021

Quality & Reliability Eng

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“…For example, Huwang et al 1 . noted that several correlated quality characteristics affect the quality of a polished wafer in chemical planarization processes in semiconductor industry settings, and Maboudou‐Tchao and Agboto 2 described an example in which it was essential to simultaneously monitor the critical signs of a patient, such as systolic blood pressure, heart rate, and body temperature in an intensive care unit (ICU) in a health industry situation (see Ebadi 3 ), and Susanty et al 4 . explained that the drinking water quality is always influenced by some related dominant variables.…”

Section: Introductionmentioning

confidence: 99%

“…explained that the drinking water quality is always influenced by some related dominant variables. Stoumbos et al., 5 Yeh, et al., 6 Bersimis et al., 7 Montgomery, 8 Chen and Zhou, 9 Huwang et al., 10 Ebadi 3 and Yang et al 11 . emphasized that multivariate control charts are one of the most important topics of SPC.…”

Section: Introductionmentioning

confidence: 99%

“…For example, Huwang et al 1 noted that several correlated quality characteristics affect the quality of a polished wafer in chemical planarization processes in semiconductor industry settings, and Maboudou-Tchao and Agboto 2 described an example in which it was essential to simultaneously monitor the critical signs of a patient, such as systolic blood pressure, heart rate, and body temperature in an intensive care unit (ICU) in a health industry situation (see Ebadi 3 ), and Susanty et al 4 explained that the drinking water quality is always influenced by some related dominant variables. Stoumbos et al, 5 Yeh, et al, 6 Bersimis et al, 7 Montgomery, 8 Chen and Zhou, 9 Huwang et al, 10 Ebadi 3 and Yang et al 11 emphasized that multivariate control charts are one of the most important topics of SPC. So far, many multivariate process control charts have developed, such as mean vector control charts, covariance matrix control charts, and shape matrix control charts.…”

Section: Introductionmentioning

confidence: 99%

“…For example, Alt 15 and Alt and Smith 16 constructed a multivariate control chart based on the likelihood ratio test statistic. For details and excellent reviews on multivariate covariance matrix charts, see Wierda, 17 Lowry and Montgomery, 14 Mason et al, 18 Yeh et al, 6 Bersimis et al, 7 Montgomery 8 and Ebadi et al 3 Ajadi et al 19 gave an overview of process dispersion control charts but only for samples of size one.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A new phase II EWMA dispersion control chart

Yang

Arnold

Liu

et al. 2021

Quality & Reliability Eng

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Statistical process control (SPC) methods are useful for improving or maintaining a manufacturing or service process in a stable and satisfactory state. Nowadays, in many industrial applications, it is necessary to simultaneously monitor more than two related quality variables of a process. Multivariate control charts are thus becoming an important research area. Using separate control charts to monitor related quality variables independently is very unreasonable and misleading. The problem of monitoring multivariate statistical process (MSPC) for several related quality variables is of current interest. So far in the literature, a few papers have discussed monitoring process dispersion for cases in which the process has a multivariate normal or non‐normal distribution. A new EWMA dispersion control chart is proposed to monitor the process covariance matrix. Moreover, the proposed new EWMA dispersion control chart is independent of the out‐of‐control process mean vector. It overcomes the problem in many existing covariance matrix control charts of assuming that there are no shifts in the process mean vector which, depending on the existence of shifts in mean, can lead to an increased false alarm rate. The derivation of the new EWMA dispersion control chart is illustrated and its out‐of‐control detection performance investigated. The proposed new EWMA dispersion control chart performs better than the existing control charts for detecting out‐of‐control process variances whether the covariances change or not. An example involving semi‐conductor data is adopted to demonstrate the application of the proposed new EWMA dispersion control chart.

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On monitoring high‐dimensional processes with individual observations

Ebadi,

Chenouri,

Steiner

2024

Naval Research Logistics

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Modern data collecting methods and computation tools have made it possible to monitor high‐dimensional processes. In this article, we investigate phase II monitoring of high‐dimensional processes when the available number of samples collected in phase I is limited in comparison to the number of variables. A new charting statistic for high‐dimensional multivariate processes based on the diagonal elements of the underlying covariance matrix is introduced and we propose a unified procedure for phases I and II by employing a self‐starting control chart. To remedy the effect of outliers, we adopt a robust procedure for parameter estimation in phase I and introduce the appropriate consistent estimators. The statistical performance of the proposed method is evaluated in phase II using the average run length (ARL) criterion in the absence and presence of outliers. Results show that the proposed control chart scheme effectively detects various kinds of shifts in the process mean vector. Finally, we illustrate the applicability of our proposed method via a manufacturing application.

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Statistical monitoring of the covariance matrix in multivariate processes: A literature review

Cited by 26 publications

References 117 publications

A new multivariate CUSUM chart for monitoring of covariance matrix with individual observations under estimated parameter

A new multivariate CUSUM chart for monitoring of covariance matrix with individual observations under estimated parameter

A new phase II EWMA dispersion control chart

On monitoring high‐dimensional processes with individual observations

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