A review of multivariate control charts

Lowry, Cynthia A.; Montgomery, Douglas C.

doi:10.1080/07408179508936797

Cited by 583 publications

(301 citation statements)

References 23 publications

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“…For some additional discussion of Shewhart charts for monitoring Σ, see Alt (1984), Lowry and Montgomery (1995), and Barnett (1996a, 1996b).…”

Section: Multivariate Shewhart Control Chartsmentioning

confidence: 99%

“…Jackson (1959), and Ghare and Torgersen (1968) presented multivariate Shewhart control charts based on Hotelling's T 2 statistic. Other multivariate Shewhart control charts are discussed by Alt (1984), Wierda (1994), and Lowry and Montgomery (1995). Exponentially weighted moving average (EWMA) charts are much more effective than Shewhart-type charts for detecting small and moderate shifts in process parameters.…”

Section: Introductionmentioning

confidence: 99%

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Multivariate Shewhart control charts for monitoring the variance-covariance matrix

Jeong¹,

Cho

2012

Journal of the Korean Data and Information Science Society

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Multivariate Shewhart control charts are considered for the simultaneous monitoring the variance-covariance matrix when the joint distribution of process variables is multivariate normal. The performances of the multivariate Shewhart control charts based on control statistic proposed by Hotelling (1947) are evaluated in term of average run length (ARL) for 2 or 4 correlated variables, 2 or 4 samples at each sampling point. The performance is investigated in three cases, that is, the variances, covariances, and variances and covariances are changed respectively.

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“…For some additional discussion of Shewhart charts for monitoring Σ, see Alt (1984), Lowry and Montgomery (1995), and Barnett (1996a, 1996b).…”

Section: Multivariate Shewhart Control Chartsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Multivariate Shewhart control charts for monitoring the variance-covariance matrix

Jeong¹,

Cho

2012

Journal of the Korean Data and Information Science Society

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“…In this paper, we have outlined the computation for ' of MMSE-control processes, which is shown in the appendix. The T 2 chart (5) is a directionally invariant chart since it has equal sensitivity for shifts with the same magnitudes and is not influenced by shift directions (Lowry and Montgomery 1995). However, the dynamic shift feature of a feedback-controlled process, which is believed to convey informative signals about process failures, is not considered by this scheme.…”

Section: Review Of Spc Schemes For Feedback-controlled Processesmentioning

confidence: 99%

Monitoring feedback-controlled processes using adaptiveT²schemes

Wang

Tsung

2007

International Journal of Production Research

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The integration of engineering process control (EPC) and statistical process control (SPC) has drawn wide attention because of its capability to minimize long-term process variation and improve product quality. However, dynamic shift patterns are usually observed when feedback-control loops exist, which consequently lead to poor charting performance. In this paper, the dynamic patterns in mean shifts of proportional integral (PI) controlled and minimum mean square error (MMSE) controlled processes are formulated and analysed.In conjunction with a model-free forecasting algorithm, an adaptive T 2 charting procedure is applied to improve detection power. This adaptive procedure is constructed upon the uniformly most powerful (UMP) unbiased test with the consideration of time-varying patterns. Monte Carlo simulations have shown that the proposed strategy possesses significantly improved detection sensitivity over intended shift ranges.

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“…Most multivariate control charts are generalizations of the univariate counterparts (Mohmoud and Maravelakis, 2013), such as the multivariate Shewhart control chart, the multivariate exponentially weighted moving average (MEWMA) control chart proposed by Lowry et al (1992), and the multivariate cumulative sum (MCUSUM) control chart (Bersimis et al, 2005(Bersimis et al, , 2007. Many practitioners have addressed the problem of correlated data in MSPC (Lowry and Montgomery, 1995), and multivariate control charts with the lack of related joint distribution.…”

Section: Introductionmentioning

confidence: 99%

Copula modelling for multivariate statistical process control: a review

Busababodhin

Amphanthong

2016

CSAM

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Modern processes often monitor more than one quality characteristic that are referred to as multivariate statistical process control (MSPC) procedures. The MSPC is the most rapidly developing sector of statistical process control and increases interest in the simultaneous inspection of several related quality characteristics. Most multivariate detection procedures based on a multi-normality assumptions are independent, but there are many processes that assume non-normality and correlation. Many multivariate control charts have a lack of related joint distribution. Copulas are tool to construct multivariate modelling and formalizing the dependence structure between random variables and applied in several fields. From copula literature review, there are a few copula to apply in MSPC that have multivariate control charts, and represent a successful tool to identify an out-of-control process. This paper presents various types of copulas modelling for the multivariate control chart. The performance measures of the control chart are the average run length (ARL) and the average number of observations to signal (ANOS). Furthermore, a Monte Carlo simulation is shown when the observations were from an exponential distribution.

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A review of multivariate control charts

Cited by 583 publications

References 23 publications

Multivariate Shewhart control charts for monitoring the variance-covariance matrix

Multivariate Shewhart control charts for monitoring the variance-covariance matrix

Monitoring feedback-controlled processes using adaptiveT²schemes

Copula modelling for multivariate statistical process control: a review

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A review of multivariate control charts

Cited by 583 publications

References 23 publications

Multivariate Shewhart control charts for monitoring the variance-covariance matrix

Multivariate Shewhart control charts for monitoring the variance-covariance matrix

Monitoring feedback-controlled processes using adaptiveT2schemes

Copula modelling for multivariate statistical process control: a review

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Monitoring feedback-controlled processes using adaptiveT²schemes