• The Korean Journal of Applied Statistics
• /
• v.13 no.2
• /
• pp.343-352
• /
• 2000

In this study. the author proposes a nonhierarchical clustering method. called the "Double K-Means Clustering", which performs clustering of multivariate observations with the following algorithm: Step I: Carry out the ordinary K-means clmitering and obtain k temporary clusters with sizes $n_1$,... , $n_k$, centroids $c_$1,..., $c_k$ and pooled covariance matrix S. $\bullet$ Step II-I: Allocate the observation x, to the cluster F if it satisfies ..... where N is the total number of observations, for -i = 1, . ,N. $\bullet$ Step II-2: Update cluster sizes $n_1$,... , $n_k$, centroids $c_$1,..., $c_k$ and pooled covariance matrix S. $\bullet$ Step II-3: Repeat Steps II-I and II-2 until the change becomes negligible. The double K-means clustering is nearly "optimal" under the mixture of k multivariate normal distributions with the common covariance matrix. Also, it is nearly affine invariant, with the data-analytic implication that variable standardizations are not that required. The method is numerically demonstrated on Fisher's iris data.

• Communications for Statistical Applications and Methods
• /
• v.6 no.2
• /
• pp.413-422
• /
• 1999

Multivariate EWMA control charts to simultaneously monitor correlation coefficients of correlated quality characteristics under multivariate normal process are proposed. Performances of the proposed charts are measured in terms of average run length(ARL). Numerical results show that smalle values for smoothing constant with accumulate-combine approach are preferred for detecting smalle shifts.

• Proceedings of the Safety Management and Science Conference
• /
• 2005.11a
• /
• pp.300-310
• /
• 2005

Mahalanobis Taguchi System (MTS) is developed by Genishi Taguchi as a part of his quality engineering methodology. The basic idea of Taguchi's quality engineering is looking for the way of effectiveness of analyzing multivariate system. In the MTS, with the standardized variables of healthy normal data, Mahalanobis Distance(MD) calculated and that can be discriminate between normal and abnormal objects. If this discrimination process is successful, next step is optimization which is try to reduce number of attributes by neglecting less effective attributes to MD. Orthogonal Array (OA) and Signal to Noise ratio (S/N) are used to evaluate the amount contribution of each attribute to the MD. Wisconsin Breast Cancer study, from machining learning repository at University of California at Irvine, used for examining the discriminant ability of MTS.

• Journal of the Korean Statistical Society
• /
• v.25 no.2
• /
• pp.255-263
• /
• 1996

Let $(X_{1j}, X_{2j}, … , X_{nj}, Y_j/)$j = 1, 2, … , n, be a sample of size n on an (m + l)-dimensional vector $(X_1, X_2, … , X_m, Y)$, m .geq. 1. If $Y_{(r)}$ denote the rth order statistic from Y, then the $X_{[r:n]}$ paired with $Y_(r)$ is termed the concomitant vector of the order statistics. The general distributions of concomitant of order statistics will be found. The mean, variance and covariance of$X_{[r:n]}$ Will be studied. Then we will apply the results to the multivariate normal variate case.e.

• Communications for Statistical Applications and Methods
• /
• v.18 no.2
• /
• pp.189-199
• /
• 2011

In this paper, we develop the noninformative priors for the common intraclass correlation coefficient when independent samples drawn from multivariate normal populations. We derive the first and second order matching priors. We reveal that the second order matching prior dose not match alternative coverage probabilities up to the second order and is not a HPD matching prior. It turns out that among all of the reference priors, one-at-a-time reference prior satisfies a second order matching criterion. Our simulation study indicates that one-at-a-time reference prior performs better than the other reference priors in terms of matching the target coverage probabilities in a frequentist sense.

• Journal of Integrative Natural Science
• /
• v.15 no.1
• /
• pp.1-8
• /
• 2022

In a multivariate normal production process N_p(µ,Σ), a chart combining three EWMA charts with accumulate-combine method for µ, variance components of Σ, and off-diagonal elements of Σ, into a EWMA (exponentially weighted moving average) chart is considered, which is called a combined EWMA chart. Through simulation work, the proposed combined EWMA chart's numerical performance and properties are examined. The simulation results show that the proposed combined EWMA chart, which is simultaneously monitoring all the process parameters of multivariate normal production process, works effectively in the perspective of means, variances and correlation coefficients. In addition, the combined EWMA chart is extended to VSI chart.

• Structural Engineering and Mechanics
• /
• v.88 no.6
• /
• pp.569-581
• /
• 2023

This paper introduces a system to detect and diagnose anomalies in pumped storage hydropower plants. We collect data from various types of sensors, including those monitoring temperature, vibration, and power. The data are classified according to the operation modes (pump and turbine operation modes) and normalized to remove the influence of the external environment. To detect anomalies and diagnose their types, we adopt a multivariate normal distribution analysis by learning the distribution of the normal data. The feasibility of the proposed system is evaluated using actual monitoring data of a pumped storage hydropower plant. The proposed system can be used to implement condition monitoring systems for other plants through modifications.

• Korean Journal of Mathematics
• /
• v.23 no.1
• /
• pp.1-10
• /
• 2015

This paper concerns the rate of convergence in the multidimensional normal approximation of functional of Gaussian fields. The aim of the present work is to derive explicit upper bounds of the Kolmogorov distance for the rate of convergence instead of Wasserstein distance studied by Nourdin et al. [Ann. Inst. H. Poincar$\acute{e}$(B) Probab.Statist. 46(1) (2010) 45-98].

• Communications for Statistical Applications and Methods
• /
• v.16 no.1
• /
• pp.143-155
• /
• 2009

Best subset selection procedure based on mutual information (MI) between a set of explanatory variables and a dependent class variable is suggested. Derivation of multivariate MI is based on normal mixtures. Several types of normal mixtures are proposed. Also a best subset selection algorithm is proposed. Four real data sets are employed to demonstrate the efficiency of the proposals.

• Journal of Intelligence and Information Systems
• /
• v.9 no.1
• /
• pp.53-69
• /
• 2003

Many process variables in modem manufacturing processes have influence on quality of products with complicated relationships. Therefore, it is necessary to control multiple quality variables in order to monitor abnormal signals in the processes. This study proposes an integrated procedure of self-organizing map (SOM) neural network and case-based reasoning (CBR) for multivariate process control. SOM generates patterns of quality variables. The patterns are compared with the reference patterns in order to decide whether their states are normal or abnormal using the goodness-of-fitness test. For validation, it generates artificial datasets consisting of six patterns, normal and abnormal patterns. Experimental results show that the abnormal patterns can be detected effectively. This study also shows that the CBR procedure enables to keep Type 2 error at very low level and reduce Type 1 error gradually, and then the proposed method can be a solution fur multivariate process control.