• Industrial Engineering and Management Systems
• /
• 제11권4호
• /
• pp.385-389
• /
• 2012

With the development of computer storage and the rapidly growing ability to process large amounts of data, the multivariate control charts have received an increasing attention. The existing univariate and multivariate control charts are a single hypothesis testing approach to process mean or variance by using a single statistic plot. This paper proposes a multiple hypothesis approach to developing a new multivariate control scheme. Plotted Hotelling's $T^2$ statistics are used for computing the corresponding p-values and the procedure for controlling the false discovery rate in multiple hypothesis testing is applied to the proposed control scheme. Some numerical simulations were carried out to compare the performance of the proposed control scheme with the ordinary multivariate Shewhart chart in terms of the average run length. The results show that the proposed control scheme outperforms the existing multivariate Shewhart chart for all mean shifts.

• Communications for Statistical Applications and Methods
• /
• 제27권4호
• /
• pp.397-412
• /
• 2020

In this paper, a notion of data depth is used to propose nonparametric multivariate two sample tests for difference between scale parameters. Data depth can be used to measure the centrality or outlying-ness of the multivariate data point relative to data cloud. A difference in the scale parameters indicates the difference in the depth values of a multivariate data point. By observing this fact on a depth vs depth plot (DD-plot), we propose nonparametric multivariate two sample tests for scale parameters of multivariate distributions. The p-values of these proposed tests are obtained by using Fisher's permutation approach. The power performance of these proposed tests has been reported for few symmetric and skewed multivariate distributions with the existing tests. Illustration with real-life data is also provided.

• Journal of the Korean Data and Information Science Society
• /
• 제4권
• /
• pp.31-44
• /
• 1993

Multivariate exponentially weighted moving average (EWMA) control charts for monitoring the variance-covariance matrix are investigated. A variable sampling interval (VSI) feature is considered in these charts. Multivariate EWMA control charts for monitoring the variance-covariance matrix are compared on the basis of their average time to signal (ATS) performances. The numerical results show that multivariate VSI EWMA control charts are more efficient than corrsponding multivariate fixed sampling interval (FSI) EWMA control charts.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제3권1호
• /
• pp.81-98
• /
• 1999

In spite of the well developed theory and the practical use of the univariate B-spline, the theory of multivariate B-spline is very new and waits its practical use. We compare in this article the multivariate B-spline approximation with the polynomial approximation for the surface fitting. The graphical and numerical comparisons show that the multivariate B-spline approximation gives much better fitting than the polynomial one, especially for the surfaces which vary very rapidly.

• 품질경영학회지
• /
• 제22권1호
• /
• pp.66-81
• /
• 1994

Several sample statistics to simultaneously monitor both means and variances for multivariate quality characteristics under multivariate normal process are proposed. Performances of multivariate Shewhart schemes and cumulative sum(CUSUM) schemes are evaluated for matched fixed sampling interval(FSI) and variable sampling interval(VSI) feature. Numerical results show that multivariate CUSUM charts are more efficient than Shewhart charts for small or moderate shifts and VSI feature is more efficient than FSI feature.

• Journal of applied mathematics & informatics
• /
• 제27권5_6호
• /
• pp.1429-1433
• /
• 2009

The likelihood distance for the joint distribution of two multivariate normal distributions with common covariance matrix is explicitly derived. It is useful for identifying outliers which do not follow the joint multivariate normal distribution with common covariance matrix. The likelihood distance derived here is a good ground for the use of a generalized Wilks statistic in influence analysis of two multivariate normal data.

• Communications for Statistical Applications and Methods
• /
• 제2권2호
• /
• pp.330-335
• /
• 1995

The rebustness of one sample Chi-square test for multivariate normal mean vector is investigated when the multivariate normal population is mixed with another multivariate normal population with differing in the mean vector. Explicit expressions for the level of significance and power of the test are derived. Some numerical results indicate that the Chi-square test procedure is quite robust against slight mixtures of multivariate normal populations differing in location parameters.

• Journal of the Korean Data and Information Science Society
• /
• 제16권2호
• /
• pp.467-476
• /
• 2005

Multivariate control charts for monitoring mean vector of several related quality variables with combine-accumulate approach and accumulate-combine apprach were investigated. Shewhart chart is also proposed to compare the performances of CUSUM and EWMA charts. Numerical comparisons show that CUSUM and EWMA charts are more efficient than Shewhart chart for small or moderate shifts, and multivariate charts based on accumulate- combine approach is more efficient than corresponding multivariate charts based on combine-accumulate approach.

• Journal of the Korean Statistical Society
• /
• 제19권1호
• /
• pp.71-79
• /
• 1990

In the linear model which consider both the multivariate parallel-line bioassay and the multivariate linear calibration, this paper presents a Bayesian procedure which is an extension of Hunter and Lamboy (1981) and has several advantages compared with the non Bayesian techniques. Based on the methods of this article we discuss the effect of multivariate calibration and give a numerical example.

• Communications for Statistical Applications and Methods
• /
• 제23권6호
• /
• pp.497-515
• /
• 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.