• Communications for Statistical Applications and Methods
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• v.12 no.1
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• pp.47-59
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• 2005

Expected mean square(EMS) is an important part of conducting the analysis of variance in the experimental design problem, especially in mixed or random models. We present a set of EMS rules for balanced factorial designs under no restriction on interaction. Also we point out how to use the variance component of SPSS or SAS procedure to obtain EMS.

• Journal of the Korean Statistical Society
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• v.15 no.1
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• pp.31-45
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• 1986

It is often necessary to obtain some run orders in factorial designs which have a small number of factor level changes and a small linear time trend. In this paper we propose an algorithm to find optimal or near-optimal run orders for $2^4, 2^5, 3^2$ and $2\cdot 3^2$ factorial designs under the criterion that the number of factor level changes and the linear time trend should be simultaneously small.

• Communications for Statistical Applications and Methods
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• v.15 no.4
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• pp.497-507
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• 2008

Confounding techniques have to be used repeatedly in the situations where it is necessary to perform only 2 runs under homogeneous conditions in $2^m$ factorial and fractional factorial experiment. Combinations of confounded $2^m$ factorial and fractional factorial designs enable the estimation of all main effects and all of or a part of 2 factor interaction effects. Defining contrast are used for our designs and treatment combinations of designs to be run are presented.

• Journal of the Korean Statistical Society
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• v.25 no.2
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• pp.277-288
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• 1996

The minimum aberration criterion is commonly used for selecting good fractional factorial designs. In this paper we give same necessary conditions for $3^{n-k}$ fractional factorial designs. We obtain minimum aberration $3^{n-k}$ designs for k = 2 and any n. For k > 2, minimum aberration designs have not found yet. As an alternative, we select a design with minimum aberration among minimum-variance designs.

• Communications for Statistical Applications and Methods
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• v.13 no.3
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• pp.777-786
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• 2006

Two factorial designs with quantitative factors are called geometrically equivalent if the design matrix of one can be transformed into the design matrix of the other by row and column permutations, and reversal of symbol order in one or more columns. Clark and Dean (2001) gave a sufficient and necessary condition (which we call the 'gCD condition') for two symmetric factorial designs with quantitative factors to be geometrically equivalent. This condition is based on the absolute value of the Euclidean(or Hamming) distance between pairs of design points. In this paper we extend the gCD condition to asymmetric designs. In addition, a modified algorithm is applied for checking the equivalence of two designs.

• Journal of Korean Institute of Industrial Engineers
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• v.27 no.4
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• pp.352-365
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• 2001

Two-level factorial designs are popular in industry due to their simplicity, efficiency, graphical interpretation, and flexibility in sequential experimentation. However, experimenters are often frustrated when they have factors with more than two levels. There have been some works on design of experiments with two- and four-level factors, which mostly deal with qualitative four-level factors. This paper discusses differences between qualitative and quantitative four-level factors. Optimal designs are provided for some designs with four-level quantitative and two-level factors.

• Journal of the Korean Data and Information Science Society
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• v.14 no.3
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• pp.707-714
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• 2003

Because of complex aliasing, nonregular designs have traditionally been used for screening only main effects. However, complex aliasing actually may allow some interactions entertained and estimated without making additional runs. According to hierarchical principle, the minimum aberration has been used as an important criterion for selecting regular fractional factorial designs. The criterion is not applicable to nonregular designs. In this paper, we give a criterion for choosing fractional factorial designs based on the fan theory. The criterion is focused on the partial ordering given by set inclusion on estimable sets which is called leaves.

• Journal of Korean Society for Quality Management
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• v.34 no.1
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• pp.27-33
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• 2006

In this paper, an effective method for identifying influential main effects and interactions in the 2-level factorial designs is suggested by exploiting the resolution V designs developed by Kim(1992). For analysis of such designs, we employ the Bayesian approach for easy and clear identification of influential effects in the half normal probability plot.

• Journal of Korean Society for Quality Management
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• v.49 no.1
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• pp.31-45
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• 2021

Purpose: A noncentral composite design method is to be developed to explore farther region for the first factorial design. A general guideline for sequential experimentation is provided. Methods: (1) A non-overlapping noncentral composite design (NNCD) is developed, in which the second factorial design shares one design point that indicates the best response value in the first factorial design. (2) Four composite designs are compared in terms of the four design evaluation criteria, which are D-, A, G, and I-optimality. (3) A follow-up design strategy is suggested based on the interaction effect, direction of improvement, number of factors. Results: (1) NNCD and model building method are presented, which is useful for exploring farther region from first factorial design block. (2) The performances of the four composite designs are compared. (3) A follow-up design strategy is suggested. Conclusion: (1) NNCD will be useful to explore farther region for the first factorial design. (2) A follow-up design strategy can be beneficial to the experimental practitioners for product and process design and improvement.

• Journal of Korean Society for Quality Management
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• v.32 no.3
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• pp.234-243
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• 2004

In this paper, we study the optimality of 2-level resolution V minimal fractional factorial designs which can be constructed by using a partially balanced array. Moreover the relative efficiencies of such designs are compared in the sense of three optimality criteria such as determinant(D)-optimality, trace(A)-optimality, and eigenvalue(E) -optimality criterion.