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임용빈,Lim, Yong-Bin 한국통계학회 2008 응용통계연구 Vol.21 No.4
공업실험에서는 주효과의 검정력을 높일 목적으로 교호작용효과에 대한 예비검정의 결과가 유의하지 않은 경우에, 이 효과를 오차항으로 풀링한 후에 주효과의 유의성을 검정하는 때때로 풀링 (Sometimes pooling)의 분석 방법을 사용한다. 이 소고에서는 때때로 풀링의 규칙에 관한 참고문헌의 내용을 정리하고, 블록효과가 오차항으로 풀링되었다는 사실이 알려 졌을 때에 독립표본에 의한 모평균의 차이에 대한 95% 신뢰구간의 길이가 쌍체비교에 의한 신뢰구간의 길이보다 짧을 확률을 다양한 예비검정의 유의수준 ${\alpha}_1$값과 충분한 검정력이 보장되지 않은 블록의 크기인 $2{\leq}n{\leq}13$ 범위에서 살펴보았는데, 그 결과는 풀링한 경우에 주효과에 대한 검정력이 높아진다는 사실을 뒷받침하고 있다. In engineering experiments, 'Sometimes Pooling Rules' to remove insignificant terms from the model has been implemented to increase the power of detecting the small size of main effects when the preliminary test of higher order interaction effects declare to be insignificant. In this note, we review the sometimes pooling rules in the literature and also study the probability of the length of 95% confidence interval of ${\mu}_1-{\mu}_2$ of the comparison of two independent samples being shorter than that of the paired comparison at the various level of significance ${\alpha}_1$ of the preliminary test and the insufficient number of blocks n in [2,13], given the block effects being pooled to the error term. This study supports that the sometimes pooling results in the power improvement of the main effects.
임용빈,Lim, Yong-Bin 한국통계학회 2007 응용통계연구 Vol.20 No.2
혼합물 성분들의 비율의 상한과 하한에 대한제한조건이 부과된 제한된 혼합물 실험 공간 R에서의 혼합물 실험을 위한 최적 설계를 찾는 데에 D-, G-, V- 최적기준 등과 같은 다양한 최적 설계 기준이 사용된다. 각각의 실험 설계는 선택된 최적 기준에 대해서는 최적이지만, 제한된 혼합물 실험 공간에서의 예측력에 대해서는 만족스럽지 못하다는 것은 잘 알려진 사실이다. (Vining 등, 1993; Khuri 등, 1999). 우리의 관심사는 2차 혼합물 반응표면모형을 가정한 경우에 제한된 혼합물 공간에서의 효율적인 실험 설계를 찾는 것이다. 이 논문에서는 꼭지점, 선중심점, 면중심점, 중앙점과 내부점으로 구성된 확장된 후보 실험점 그룹을 구성한 다음에, D-최적기준, G-최적기준, V-최적기준과 실험점들 간의 거리에 근거한 U-최적기준에 강건한 실험 설계를 제안한다. Khuri 등(1999)에서 분석된 비료 혼합물 실험과Vining과 Cornell(1993)이 분석한 조명탄 혼합물 실험의 사례에서 강건한 실험설계들과 두 논문에서 추천된 실험 설계들에 대한 예측치의 표준화된 분산의 분위수의 그림(SVPQP)을 비교한 결과 강건한 설계가 상대적으로 우월함이 판명되었다. Various single-valued design optimality criteria such as D-, G-, and V-optimality are used often in constructing optimal experimental designs for mixture experiments in a constrained region R where lower and upper bound constraints are imposed on the ingredients proportions. Even though they are optimal in the strict sense of particular optimality criterion used, it is known that their performance is unsatisfactory with respect to the prediction capability over a constrained region. (Vining et at., 1993; Khuri et at., 1999) We assume the quadratic polynomial model as the mixture response surface model and are interested in finding efficient designs in the constrained design space for a mixture. In this paper, we make an expanded list of candidate design points by adding interior points to the extreme vertices, edge midpoints, constrained face centroids and the overall centroid. Then, we want to propose a robust design with respect to D-optimality, G-optimality, V-optimality and distance-based U-optimality. Comparing scaled prediction variance quantile plots (SPVQP) of robust designs with that of recommended designs in Khuri et al. (1999) and Vining et al. (1993) in the well-known examples of a four-component fertilizer experiment as well as McLean and Anderson's Railroad Flare Experiment, robust designs turned out to be superior to those recommended designs.
품질경영학회 50주년 특별호: 통계적 기법 분야 연구 리뷰
임용빈 ( Yong Bin Lim ),김상익 ( Sang Ik Kim ),이상복 ( Sang Bok Lee ),장대흥 ( Dae Heung Jang ) 한국품질경영학회 2016 품질경영학회지 Vol.44 No.2
Purpose: This research reviews the papers, published in the Journal of the Korean Society for Quality Control (KSQC) and the Journal of the Korean Society for Quality Management (KSQM) since 1965, in the area of statistical methods. The literature review is performed in the four fields of the statistical methods and we categorize the published articles into the several sub-areas in each field. Methods: The reviewed articles are classified into the four main categories: probability model and estimation, Bayesian analysis and non-parametric analysis, regression and time series analysis, and application of data analysis. We examine the contents and relationships of the published articles of the several sub-areas in each category. Results: We summarize the reviewed papers in the chronological road-maps for each sub-area, and outline the relations of the connected papers. Some comments on the contents and the contributions of the reviewed papers are also provided in this paper. Conclusion: Various issues are employed and published on the research of the application statistical methods for past 50 years, and many worthy works are achieved in the theory and application areas of statistical methods for improving quality in the manufacturing and service industries. The future direction of the research in the statistical quality management methods also can be explored by the contents of this research.
임용빈 ( Yong Bin Lim ),조호 ( Ho Cho ),김영일 ( Yoing Ii Kim ) 한국품질경영학회 2011 품질경영학회지 Vol.39 No.4
Evolutionary operation (EVOP) proposed by Box(1957) is a method for continuous monitoring and improvement of a full-scale manufacturing process with the objective of moving the current operating conditions toward the better ones. EVOP in experiments with mixtures consists of screening vital few components and making small changes in the current operating condition by making small increments in the proportion of the screened component. In this paper, how to determine operating conditions in EVOP in experiments with mixtures around the current operating condition is proposed. The proposed methods are illustrated with the simulated data based on the well known flare experimental data described by McLean and Anderson(1966).