• Journal of the Korean Data and Information Science Society
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• 제10권1호
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• pp.223-232
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• 1999

Multivariate quality control charts with combine-accumulate approach and accumulate-combine apprach for monitoring both means and variances under multivariate normal process are investigated. Numerical performances of the charts show that multivariate EWMA chart with accumulate-combine approach can be recommended for all kinds of shift in means and variances.

• Communications for Statistical Applications and Methods
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• 제4권3호
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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 the Korean Data and Information Science Society
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• 제28권2호
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• pp.421-433
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• 2017

The CTE (conditional tail expectation) is a useful risk management measure for a diversified investment portfolio that can be generally estimated by using a transformed univariate distribution. Hong et al. (2016) proposed a multivariate CTE based on multivariate quantile vectors, and explored its characteristics for multivariate normal distributions. Since most real financial data is not distributed symmetrically, it is problematic to apply the CTE to normal distributions. In order to obtain a multivariate CTE for various kinds of joint distributions, distribution fitting methods using copula functions are proposed in this work. Among the many copula functions, the Clayton, Frank, and Gumbel functions are considered, and the multivariate CTEs are obtained by using their generator functions and parameters. These CTEs are compared with CTEs obtained using other distribution functions. The characteristics of the multivariate CTEs are discussed, as are the properties of the distribution functions and their corresponding accuracy. Finally, conclusions are derived and presented with illustrative examples.

• 산업경영시스템학회지
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• 제25권2호
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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.

• 산업경영시스템학회지
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• 제42권2호
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• pp.18-27
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• 2019

The process control methods based on the statistical analysis apply the analysis method or mathematical model under the assumption that the process characteristic is normally distributed. However, the distribution of data collected by the automatic measurement system in real time is often not followed by normal distribution. As the statistical analysis tools, the process capability index (PCI) has been used a lot as a measure of process capability analysis in the production site. However, PCI has been usually used without checking the normality test for the process data. Even though the normality assumption is violated, if the analysis method under the assumption of the normal distribution is performed, this will be an incorrect result and take a wrong action. When the normality assumption is violated, we can transform the non-normal data into the normal data by using an appropriate normal transformation method. There are various methods of the normal transformation. In this paper, we consider the Box-Cox transformation among them. Hence, the purpose of the study is to expand the analysis method for the multivariate process capability index using Box-Cox transformation. This study proposes the multivariate process capability index to be able to use according to both methodologies whether data is normally distributed or not. Through the computational examples, we compare and discuss the multivariate process capability index between before and after Box-Cox transformation when the process data is not normally distributed.

• 한국통계학회:학술대회논문집
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• 한국통계학회 2002년도 춘계 학술발표회 논문집
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• pp.73-78
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• 2002

In this paper we develop a method for constructing a Bayesian HPD (highest probability density) interval of a ratio of two multivariate normal generalized variances. The method gives a way of comparing two multivariate populations in terms of their dispersion or spread, because the generalized variance is a scalar measure of the overall multivariate scatter. Fully parametric frequentist approaches for the interval is intractable and thus a Bayesian HPD(highest probability densith) interval is pursued using a variant of weighted Monte Carlo (WMC) sampling based approach introduced by Chen and Shao(1999). Necessary theory involved in the method and computation is provided.

• Communications for Statistical Applications and Methods
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• 제24권6호
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• pp.641-649
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• 2017

Multivariate confidence regions were defined using a chi-square distribution function under a normal assumption and were represented with ellipse and ellipsoid types of bivariate and trivariate normal distribution functions. In this work, an alternative confidence region using the multivariate quantile vectors is proposed to define the normal distribution as well as any other distributions. These lower and upper bounds could be obtained using quantile vectors, and then the appropriate region between two bounds is referred to as the quantile confidence region. It notes that the upper and lower bounds of the bivariate and trivariate quantile confidence regions are represented as a curve and surface shapes, respectively. The quantile confidence region is obtained for various types of distribution functions that are both symmetric and asymmetric distribution functions. Then, its coverage rate is also calculated and compared. Therefore, we conclude that the quantile confidence region will be useful for the analysis of multivariate data, since it is found to have better coverage rates, even for asymmetric distributions.

• Communications for Statistical Applications and Methods
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• 제5권3호
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• pp.591-597
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• 1998

We prove (at least empirically) that some forms of the scaled residuals calculated from i.i.d. multivariate normal random vectors are ancillary. We further show that, if the scaled residuals are ancillary, then they have the same distribution whatever form of rotation is rosed to remove sample correlations.

• Journal of the Korean Statistical Society
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• 제30권4호
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• pp.613-635
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• 2001

This paper proposes a skewed multivariate probit model for analyzing a correlated binary response data with covariates. The proposed model is formulated by introducing an asymmetric link based upon a skewed multivariate normal distribution. The model connected to the asymmetric multivariate link, allows for flexible modeling of the correlation structure among binary responses and straightforward interpretation of the parameters. However, complex likelihood function of the model prevents us from fitting and analyzing the model analytically. Simulation-based Bayesian inference methodologies are provided to overcome the problem. We examine the suggested methods through two data sets in order to demonstrate their performances.

• 품질경영학회지
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• 제22권1호
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• pp.66-81
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• 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.