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

Li, Zhonghua; Tsung, Fugee

doi:10.1002/qre.2403

Cited by 11 publications

(3 citation statements)

References 60 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Khoo and Quah proposed a chart that is based on the successive difference between pairs of multivariate observations. Li and Tsung proposed the multivariate dispersion chart to monitor high dimensional variability with individual observations. In addition, other methods were introduced by Yeh et al, Hawkins and Maboudou‐tchao, Mason et al, Djauhari, Hwang, Fan et al, Huwang et al, and Memar and Niaki .…”

Section: Compared Methods For Monitoring Multivariate Dispersionmentioning

confidence: 99%

Should observations be grouped for effective monitoring of multivariate process variability?

Ajadi

Zwetsloot

2020

Quality & Reliability Eng

View full text Add to dashboard Cite

A multivariate dispersion control chart monitors changes in the process variability of multiple correlated quality characteristics. In this article, we investigate and compare the performance of charts designed to monitor variability on the basis of individual and grouped multivariate observations. We compare one of the most well‐known methods for monitoring individual observations—a multivariate exponentially weighted mean squared deviation (MEWMS) chart—with various charts based on grouped observations. In addition, we compare charts based on monitoring with overlapping and nonoverlapping subgroups. We recommend using charts based on overlapping subgroups when monitoring with subgroup data. The effect of subgroup size is also investigated. Steady‐state average time to signal is used as the performance measure. We show that monitoring methods based on individual observations are the quickest in detecting sustained shifts in the process variability. We use a simulation study to obtain our results and illustrated these with a case study.

show abstract

Section: Compared Methods For Monitoring Multivariate Dispersionmentioning

confidence: 99%

Should observations be grouped for effective monitoring of multivariate process variability?

Ajadi

Zwetsloot

2020

Quality & Reliability Eng

View full text Add to dashboard Cite

show abstract

“…They called the proposed MEWMV chart, the variability change with a large p (MVP) chart. Li and Tsung [2019] showed that the MVP chart is less affected by the high dimensionality than the charts proposed by Yeh et al [2012], Li et al [2013] and Shen et al [2014] and more effective if the process shifts cause changes in variance components.…”

Section: Monitoring Covariance Matrix Alone When N < Pmentioning

confidence: 99%

“…In another attempt to remove the effect of tuning parameter, Li and Tsung [2019] used the two-sample test statistic of Ledoit and Wolf [2004] for high-dimensional covariance matrices (n ≪ p). Their proposed control chart integrated the powerful two sample test of Ledoit and Wolf [2004] with EWMA procedure for multivariate process with individual observation.…”

Section: Monitoring Covariance Matrix Alone When N < Pmentioning

confidence: 99%

Statistical Monitoring of the Covariance Matrix in Multivariate Processes: A Literature Review

Ebadi¹,

Chenouri²,

Lin³

et al. 2020

Preprint

View full text Add to dashboard Cite

Monitoring several correlated quality characteristics of a process is common in modern manufacturing and service processes. For this purpose, control charts have been developed to detect assignable causes before producing nonconforming products. Although a lot of attention has been paid to monitoring the multivariate process mean, not many control charts are available for monitoring the covariance matrix. This paper presents a comprehensive overview of the literature on control charts for monitoring covariance matrix in multivariate statistical process monitoring (MSPM) framework. It classifies the research that have previously appeared in the literature. We highlight the challenging areas for research and provide some directions for future research.

show abstract

Monitoring the covariance matrix of bivariate processes with the DVMAX control charts

Machado

Quinino

et al. 2021

Appl Stoch Models Bus & Ind

View full text Add to dashboard Cite

Two versions of Phase II attribute+variable (DVMAX) control charts are investigated for monitoring the covariance matrix Σ of bivariate processes. Monitoring always starts with an attribute chart employing the Max D control chart and, depending on the outcome, a variable control chart named VMAX chart is run at a second stage to check for process stability. In the first version, denoted as the DVMAX 1 chart, two independent samples are used at the two stages of the same inspection; with the second version, denoted as the DVMAX 2 chart, the same sample is used at both the first and second stage of the same inspection. This approach, based on the implementation of two types of charts, can be designed to be more advantageous than a single variable control chart in terms of detection speed of a shift in the covariance matrix. In general, we conclude that the DVMAX 1 control charts not only shows the best statistical performance but also presents a lower average sampling cost.A numerical example illustrates the implementation of the proposed control charts.

show abstract

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

Cited by 11 publications

References 60 publications

Should observations be grouped for effective monitoring of multivariate process variability?

Should observations be grouped for effective monitoring of multivariate process variability?

Statistical Monitoring of the Covariance Matrix in Multivariate Processes: A Literature Review

Monitoring the covariance matrix of bivariate processes with the DVMAX control charts

Contact Info

Product

Resources

About