The S chart with variable charting statistic to control bi and trivariate processes

Costa, Antônio Fernando Branco; Neto, Antonio Faria

doi:10.1016/j.cie.2017.09.001

Cited by 11 publications

(4 citation statements)

References 28 publications

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“…Recently, Costa & Faria (2017) proposed the S chart with variable charting statistic (VCS) to control the covariance matrix as an alternative to the use of the bivariate S chart and the trivariate VMAX chart. The idea of the S chart with variable charting statistic is working with only one characteristic per time.…”

Section: Introductionmentioning

confidence: 99%

Monitoring bivariate processes with synthetic control charts based on sample ranges

2023

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The RMAX chart was proposed to control the covariance matrix of two quality characteristics. The monitoring statistic of the RMAX chart is the maximum of two standardized sample ranges from bivariate observations of two quality characteristics. In this article, we investigate the performance of two synthetic RMAX charts. The first synthetic chart signals when a second point, not far from the first one, falls beyond the warning limit. The second synthetic chart additionally signals when a sample point falls beyond the control limit. The performance of the synthetic RMAX charts are compared with the performance of the standard RMAX chart and the generalized variance S chart. The proposed charts are the best option to detect moderate or even small changes in the covariance matrix. To detect large changes in the covariance matrix, additional run rules are not necessary.

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Section: Introductionmentioning

confidence: 99%

Monitoring bivariate processes with synthetic control charts based on sample ranges

2023

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“…(2015) added a VSI feature to the multivariate synthetic shewart type S control chart. Costa and Neto (2017) proposed the S chart with variable charting statistic (called VCS S chart) which is a Shewhart-type chart specially designed to control the covariance matrix of bi-and tri-variate processes. Though they found their method superior to the trivariate case, the only advantage of their method compared to the bi-variate generalized variance method was that it was easier to compute.…”

Section: Introductionmentioning

confidence: 99%

A new adaptive control chart for the simultaneous monitoring of the mean and variability of multivariate normal processes

Sabahno

Amiri

Castagliola

2021

Computers & Industrial Engineering

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This paper considers adaptive schemes for the simultaneous monitoring of the mean and variability of a multivariate normal quality characteristic. At first, we extend an already existing bivariate nonadaptive simultaneous control chart to a multivariate one. Then, we develop several adaptive schemes, which will cover both previously bivariate and newly multivariate charts. After having designed adaptive schemes for the multivariate chart, eight performance measures are computed based on the run length, time to signal, number of observations to signal and number of switches to signal and evaluated using a new Markov chain model. With the developed performance measures, non-adaptive and adaptive schemes under different mean, variability, simultaneous shift sizes, and different number of quality characteristics are compared. Our scheme is also compared to one of the best methods available in the literature. A numerical example is also provided in order to demonstrate how the adaptive scheme can be implemented in practice.

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“…[2009b], Quinino et al [2012], Costa and Neto [2017], Gadre and Kakade [2018], and Machado et al [2018] proposed some variants of the VMAX and improved it in bivariate and trivariate cases. In addition to the aforementioned bivariate charts, Cheng and Cheng [2011] proposed an artificial neural network based approach which showed better performance than traditional generalized variance chart in detecting variance shifts of a bivariate process.…”

Section: Introductionmentioning

confidence: 99%

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

Ebadi¹,

Chenouri²,

Lin³

et al. 2020

Preprint

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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.

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The S chart with variable charting statistic to control bi and trivariate processes

Cited by 11 publications

References 28 publications

Monitoring bivariate processes with synthetic control charts based on sample ranges

Monitoring bivariate processes with synthetic control charts based on sample ranges

A new adaptive control chart for the simultaneous monitoring of the mean and variability of multivariate normal processes

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

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