Earticle

최근 상업용 통계 패키지의 발달에 힘입어 다변인 통계분석에 기초한 연구들이 양산되고 있다. 다변인 분석은 단변인 통계에 비해 복잡한 연구문제를 탐색할 수 있는 장점이 있지만, 통계분석의 복잡성으로 인하여 절차상 오류들이 더러 발견된다. 더욱이, 다변인 통계분석의 수학적 기초가 복잡하여 그 원리를 이해하기 어렵고, 분석방법 및 결과 해석이 난해할 수 있으며, 다양한 분석법들이 상반된 결과를 낳아서 결과해석이 곤란해질 수 있다. 따라서 본 연구에서는 다변인분석 적용상의 가능한 오류와 주의점들을 기술하여 이러한 오용을 줄일 수 있는 방안을 제시하고자 하였다.

Due to the recent developments in commercial statistical packages, vast amount of research articles based on multivariate statistics have been published. While the multivariate statistics have advantages over the univariate statistics in dealing with more complicated research hypothesis, abuses and misuses in it's application have been frequently noticed in many researches, due to the underlying complexities. Specifically, it is difficult to understand the basic principle due to the mathematical complexities underlying in it, henceforth making the interpretation of the analysis result be difficult. Even worse, different choice of the analysis methods sometimes result in contradicting results, making the interpretation implausible. This study tried to examine the cases of misuses in the application of multivariate statistics, and to identify the problems. Finally, several precautions for reducing the incidents was proposed.

Because of the nonlinear characteristics of monitoring system in military barracks, the traditional KPCA method either have low sensitivity or unable to detect the fault quickly and accurately. In order to make use of higher-order statistics to get more useful information and meet the requirements of real-time fault diagnosis and sensitivity, a new method of fault detection and diagnosis is proposed based on multivariate statistical kernel principal component analysis (MSKPCA), which combines statistic pattern analysis framework (SPA) and kernel principal component analysis (KPCA). First, the transformation of multivariate statistics and kernel function are conducted in which technology of moving time window is used. Then, PCA is executed to analysis the kernel function obtained from the first step. Moreover, the statistics of T^2 and SPE and the control limits of them are calculated. Finally, simulations on a typical nonlinear numerical example show that the proposed MSKPCA method is more effective than PCA and KPCA in terms of fault detection and diagnosis.

Multivariate statistical procedures were used to analyse data on the chemical composition and in vitro digestibility of four varienties of rice straw after treatment with 4% NaOH solution, 4% urea solution or distilled water (control) for 48 hours. For each treatment, stepwise discriminant analysis identified the variables which maximized differences between varieties and the eigenvectors from principal component analysis quantified the contribution of these criterion variables to varietal differences. The overall response of varieties to chemical treatment was demonstrated qualitatively, by cluster analysis, and quantitatively, from the magnitude of the principal component scores. The analysis revealed that the urea and control treatments elicited the same response whereas NaOH had the greatest effect on the poorest straw variety. Similar analyses conducted on the botanical fractions of the varieties showed that the relative response of the inflorescence, stem, leaf blade and leaf sheath fractions was not altered by chemical treatment.

In the case of system like MES, various sensors collect the data in real time and save it as a big data to monitor the process. However, if there is big data mining in distributed computing system, whole processing process can be improved. In this paper, system to analyze the cause of operation deviation was built using the big data which has been collected from deasphalting process at the two different plants. By applying multivariate statistical analysis to the big data which has been collected through MES(Manufacturing Execution System), main cause of operation deviation was analyzed. We present the example of analyzing the operation deviation of deasphalting process using the big data which collected from MES by using multivariate statistics analysis method. As a result of regression analysis of the forward stepwise method, regression equation has been found which can explain 52% increase of performance compare to existing model. Through this suggested method, the existing petrochemical process can be replaced which is manual analysis method and has the risk of being subjective according to the tester. The new method can provide the objective analysis method based on numbers and statistic.

In multivariate regression analysis there exist many influence measures on the regression estimates. However it seems to be few of influence diagnostics on test statistics in hypothesis testing. Case-deletion approach is fundamental for investigating influence of observations on estimates or statistics. Tang and Fung (1997) derived single case-deletion of the Wilks' ratio, Lawley-Hotelling trace, Pillai's trace for testing a general linear hypothesis of the regression coefficients in multivariate regression. In this paper we derived more extended form of those measures to deal with joint influence among observations. A numerical example is given to illustrate the effect of joint influence on the test statistics.

본 연구는 금강 수계 주요 지류인 미호천수계를 대상으로 수계의 공간적 특성을 조사하고, 수질분석과 통계분석을 이용하여 수질에 영향을 주는 주요인을 파악하였다. 조사 대상은 미호천 수계의 본류에서 수질측정망을 운영 중인 7개 지점으로 선정하였고, 2012년부터 2017년까지 6년간 측정망 수온 등 16개 항목, 기상자료 등을 사용하여 다변량 통계분석을 실시하였다. 수질 분석 결과, 유기물질 지표인 BOD와 COD의 6년간 평균 농도는 환경부 수질 및 수생태계 생활환경기준(하천)과 비교하여 III등급(보통)으로 나타났다. 지점별 비교 결과 질소계열과 인계열의 농도는 상류 지점에서 가장 높게 나타났으며, 이후 감소하는 경향을 보이다 수리적, 지형적 영향으로 다시 증가하는 것으로 나타났다. 공간 및 수질 특성을 고려한 계층적 군집분석 결과, 총 3개의 군집으로 평가되었으며, 수계에 유입되는 오염원의 영향이 큰 것으로 나타났다. 각 군집과 본류 전체를 대상으로 실시한 주성분 및 요인분석 결과, 각각 3~4개의 주성분이 추출되었다. 요인분석 결과 제1요인은 본류와 Cluster1,3에서 질소계열 요인과 계절적 요인, Cluster2에서 질소계열 요인과 수온으로 나타나 미호천 수계의 수질에 가장 큰 영향을 미치는 인자는 질소계열의 농도인 것으로 나타났다.

In The study, is to investigate the spatial characteristics of the Miho stream, which is the main tributary of the Geum River system, and to identify the main factors influencing the water quality using water quality analysis and multivariate analysis. The survey subjects were selected as 7 main sites in the Miho stream water system, From 2012 to 2017, 16 items including weather temperature and weather data were used for multivariate analysis. As a result of the water quality analysis, the average concentration of BOD and COD for 6 years was 3grade (normal) compared with the water quality environmental standard (river) of conditions. The concentrations of nitrogen and phosphorus were highest at th upstream site, then decreased and then increased again by the hydrogeological and geomorphological effect. Cluster analysis of spatial and water quality characteristics, it was evaluated as three clusters and the pollution sources is the greatest impact. As a result of principal component analysis and factor analysis on each cluster and mainstream, three to four major components were extracted. Main stream and the Cluster 1, Cluster 3 first principal factor included nitrogen and seasonal factors,first factor of Cluster 2 included nitrogen and water temperature. Nitrogen is the principal factor which affects water quality in Miho stream.