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

Monitoring the covariance matrix of bivariate processes with the DVMAX control charts Two versions of Phase II attribute+variable (DVMAX) control charts are investigated for monitoring the covariance matrix ∑ 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 DVMAX1 chart, two independent samples are used at the two stages of the same inspection; with the second version, denoted as the DVMAX2 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 DVMAX1 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Stochastic Models in Business and Industry Wiley

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

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Publisher
Wiley
Copyright
© 2021 John Wiley & Sons, Ltd.
ISSN
1524-1904
eISSN
1526-4025
DOI
10.1002/asmb.2651
Publisher site
See Article on Publisher Site

Abstract

Two versions of Phase II attribute+variable (DVMAX) control charts are investigated for monitoring the covariance matrix ∑ 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 DVMAX1 chart, two independent samples are used at the two stages of the same inspection; with the second version, denoted as the DVMAX2 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 DVMAX1 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.

Journal

Applied Stochastic Models in Business and IndustryWiley

Published: Oct 10, 2021

Keywords: average run length; Max D chart; simulation; truncated normal distribution; VMAX chart

References