• Communications for Statistical Applications and Methods
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• v.23 no.6
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• pp.497-515
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• 2016

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.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.25 no.2
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• pp.1-10
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• 2002

Process capability indices are widely used in industries and quality assurance system. In past years, process capability analysis have been used to characterize process performance on the basis of univariate quality characteristics. However, in actual manufacturing industrial, statistical process control (SPC) often entails characterizing or assessing processes or products based on more than one engineering specification or quality characteristic. Therefore, the analysis have to be required a multivariate statistical technique. This paper introduces to multivariate capability indices and then selects a multivariate process capability index incorporated both the process variation and the process deviation from target among these indices under the multivariate normal distribution. We propose a new multivariate capability index $MC_{pm}^+$ using quality loss function instead of the process variation and this index is compared with the proposed indices when quality characteristics are independent and dependent of each other.

• Communications for Statistical Applications and Methods
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• v.4 no.3
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• pp.715-723
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• 1997

Multivariate control statistics to simultaneously monitor both means and variances for several quality variables under multivariate normal process are proposed. Performances of the proposed multivariate charts are evaluated in terms of average run length(ARL). Multivariate Shewhart chart is also proposed to compare the performances of multivariate exponentially weighted moving average(EWMA) charts. A numerical comparison shows that multivariate EWMA charts are more efficient than multivariate Shewhart chart for small and moderate shifts and multivariate EWMA scheme based on accumulate-combine approach is more efficient than corresponding multivariate EWMA chart based on combine-accumulate approach.

• Journal of Korean Society for Quality Management
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• v.40 no.3
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• pp.337-346
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• 2012

Purpose: A Control chart is one of the important statistical process control tools that can improve processes by reducing variability and defects. Methods: In the present study, we propose the local $T^2$ multivariate control chart that can efficiently detect abnormal observations by considering the local pattern of the in-control observations. Results: A simulation study has been conducted to examine the property of the proposed control chart and compare it with existing multivariate control charts. Conclusion: The results demonstrate the usefulness and effectiveness of the proposed control chart.

• The Korean Journal of Applied Statistics
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• v.31 no.1
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• pp.1-11
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• 2018

Multivariate process control has become important in various applied fields. For instance, there are many situations in which the simultaneous monitoring of multivariate quality characteristics is necessary for the manufacturing industry. Despite its importance, its practical usage is not as convenient because it is difficult to identify the source of the out-of-control signal in a multivariate control chart. In this paper, we will introduce how to detect the source of the out-of-control by using confidence intervals for new observations, and will discuss the identification and interpretation of the out-of-control variable through simulation studies.

• Communications for Statistical Applications and Methods
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• v.12 no.2
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• pp.265-273
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• 2005

In this paper, we proposed multivariate EWMA control charts for both combine-accumulate and accumulate-combine approaches to monitor dispersion matrix of multiple quality variables. Numerical performance of the proposed charts are evaluated in terms of average run length(ARL). The performances show that small smoothing constants with accumulate-combine approach is preferred for detecting small shifts of the production process.

• Journal of the Korean Data and Information Science Society
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• v.27 no.2
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• pp.523-530
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• 2016

Most classical control charts assume that processes are serially independent, and autocorrelation among variables makes them unreliable. To address this issue, a variety of statistical approaches has been employed to estimate the serial structure of the process. In this paper, we propose a multioutput least squares support vector regression and apply it to construct a residual multivariate cumulative sum control chart for detecting changes in the process mean vector. Numerical studies demonstrate that the proposed multioutput least squares support vector regression based control chart provides more satisfying results in detecting small shifts in the process mean vector.

• Smart Structures and Systems
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• v.14 no.3
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• pp.377-395
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• 2014

Vibration-based fault detection and condition monitoring of rotating machinery, using statistical process control (SPC) combined with statistical pattern recognition methodology, has been widely investigated by many researchers. In particular, the discrete wavelet transform (DWT) is considered as a powerful tool for feature extraction in detecting fault on rotating machinery. Although DWT significantly reduces the dimensionality of the data, the number of retained wavelet features can still be significantly large. Then, the use of standard multivariate SPC techniques is not advised, because the sample covariance matrix is likely to be singular, so that the common multivariate statistics cannot be calculated. Even though many feature-based SPC methods have been introduced to tackle this deficiency, most methods require a parametric distributional assumption that restricts their feasibility to specific problems of process control, and thus limit their application. This study proposes a nonparametric multivariate control chart method, based on multiscale wavelet scalogram (MWS) features, that overcomes the limitation posed by the parametric assumption in existing SPC methods. The presented approach takes advantage of multi-resolution analysis using DWT, and obtains MWS features with significantly low dimensionality. We calculate Hotelling's $T^2$-type monitoring statistic using MWS, which has enough damage-discrimination ability. A bootstrap approach is used to determine the upper control limit of the monitoring statistic, without any distributional assumption. Numerical simulations demonstrate the performance of the proposed control charting method, under various damage-level scenarios for a bearing system.

• Journal of the Korean Data and Information Science Society
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• v.26 no.4
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• pp.1027-1034
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• 2015

A control chart is very useful in monitoring various production process. There are many situations in which the simultaneous control of two or more related quality variables is necessary. When the joint distribution of the process variables is multivariate normal, multivariate Shewhart control charts using the function of the maximum likelihood estimator for monitoring the dispersion matrix are considered for the simultaneous monitoring of the dispersion matrix. The performances of the multivariate Shewhart control charts based on the proposed control statistic are evaluated in term of average run length (ARL). The performance is investigated in three cases, where the variances, covariances, and variances and covariances are changed respectively. The numerical results show that the performances of the proposed multivariate Shewhart control charts are not better than the control charts using the trace of the covariance matrix in the Jeong and Cho (2012) in terms of the ARLs.

• The Korean Journal of Applied Statistics
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• v.31 no.6
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• pp.811-823
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• 2018

Multivariate control chart based on Hotelling's $T^2$ statistic is a powerful tool in statistical process control for identifying an out-of-control process. It is used to monitor multiple process characteristics simultaneously. Detection of the out-of-control signal with the $T^2$ chart indicates mean vector shifts. However, these multivariate signals make it difficult to interpret the cause of the out-of-control signal. In this paper, we review methods of signal interpretation based on the Mason, Young, and Tracy (MYT) decomposition of the $T^2$ statistic. We also provide an example on how to implement it using R software and demonstrate simulation studies for comparing the performance of these methods.