Application of copulas to multivariate control charts

Verdier, Ghislain

doi:10.1016/j.jspi.2013.05.005

Cited by 27 publications

(17 citation statements)

References 15 publications

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“…In order to establish Shewhart control charts [9,10] for 2 , , the centerline, upper control limit, and lower control limit of each control chart are shown in…”

Section: The Equation Derivation Of Centerline the Upper Control Limmentioning

confidence: 99%

Research on Fault Diagnosis of Flexible Material R2R Manufacturing System Based on Quality Control Chart and SoV

Deng

Zhou

Xiali³

et al. 2018

Mathematical Problems in Engineering

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The Stream of Variation (SoV) model and control chart are combined to study the fault diagnosis method of flexible materials R2R manufacturing system. Based on the analysis of the correlation between the fault source and product quality in the manufacturing process and also the statistical distribution rule of the processing quality characteristic vector and the fault source , SoV model under controlled or uncontrolled states and the mathematical model of the probability distribution of the statistic 2 , of the quality characteristic variable are deduced. And the calculation equation of the centerline, the upper limit, and the lower limit of the control chart are deduced. The experimental results show that, under controlled or uncontrolled condition, when the program runs to 500 steps, the Average Run Length (ARL) of the performance parameters tends to be stable; and when program reaches 1000 steps, the actual ARL value is almost the same as the theoretical value. The fault diagnosis experiment shows that, under the condition when the fault source is strongly correlated or the fault source correlation coefficient is the same, using the control chart established in this paper can simply and quickly determine the fault location in the system.

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“…In order to establish Shewhart control charts [9,10] for 2 , , the centerline, upper control limit, and lower control limit of each control chart are shown in…”

Section: The Equation Derivation Of Centerline the Upper Control Limmentioning

confidence: 99%

Research on Fault Diagnosis of Flexible Material R2R Manufacturing System Based on Quality Control Chart and SoV

Deng

Zhou

Xiali³

et al. 2018

Mathematical Problems in Engineering

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show abstract

“…Alternative approaches have been proposed based on parametric or non-parametric methods. The control chart obtained is not subject to the curse of dimension for non-parametric approaches and remains relatively flexible thanks to a wide choice of copula families (Verdier, 2013). However, they still must consider the problem of deciding if an observation X test has been generated from a reference distribution F. If the objective is to detect a change in dynamic system (from an unknown time t c , the system is out of control and all the new observation are generated from a new distribution G), the control chart which proposed can be called without memory like the Hotelling T 2 rule or the data depth rule.…”

Section: Application Of Copula To Multivariate Control Chartmentioning

confidence: 99%

“…Copulas create a link between multivariate joint distributions and univariate marginal distributions; they have been widely studied and applied in areas concerned with the problem of dependence relations. Many researchers have developed the copula for use with control charts (Dokouhaki and Noorossana, 2013;Fatahi et al, 2011Fatahi et al, , 2012Hryniewicz, 2012;Hryniewicz and Szediw, 2010;Kuvattana et al, 2016;Verdier, 2013). Time is used to represent some attibutes or variable measures in the manufacturing processes.…”

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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“…All of these methods, however, require some assumptions on the marginal distributions or the joint copula density. Verdier (2013) proposed using a copula function to construct monitoring charts based on the estimated density levels of the observations and showed that the classical Hotelling T 2 rule can produce many false alarms for non-Gaussian data. In this paper, we show that the charts constructed using density levels may not detect changes in the shape of the multivariate distribution of the monitored process variables.…”

Section: Introductionmentioning

confidence: 99%

Copula-based monitoring schemes for non-Gaussian multivariate processes

Krupskii

Harrou

Hering

et al. 2019

Journal of Quality Technology

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Multivariate statistical monitoring charts are efficient tools for assessing the quality of a process by identifying abnormalities. Most commonly used multivariate monitoring charts, such as the Hotelling T 2 rule, however, assume the availability of uncorrelated Gaussian observations. Unfortunately, very often, real data do not satisfy these assumptions, and thus limit the usefulness of these techniques in practice. Furthermore, in many real applications, changes can occur in the shape of the multivariate distribution of the process while its mean or variance remains the same. Conventional process monitoring charts, such as the T 2 chart, fail to detect such changes in the distribution. In this paper, we develop new copula-based multivariate monitoring techniques for possibly autocorrelated, non-Gaussian data that can detect changes in the shape of a multivariate distribution that are usually overlooked by conventional monitoring charts. Using synthetic data, we demonstrate the effectiveness of the developed charts over a conventional monitoring chart. Results indicate that the proposed charts are very promising because copula-based charts are, in practice, designed to monitor the entire distribution of a process instead of the individual components. The developed monitoring charts are validated through practical application on data from a decentralized wastewater treatment plant in Golden, CO, USA.

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Application of copulas to multivariate control charts

Cited by 27 publications

References 15 publications

Research on Fault Diagnosis of Flexible Material R2R Manufacturing System Based on Quality Control Chart and SoV

Research on Fault Diagnosis of Flexible Material R2R Manufacturing System Based on Quality Control Chart and SoV

Copula modelling for multivariate statistical process control: a review

Copula-based monitoring schemes for non-Gaussian multivariate processes

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