• 대한산업공학회지
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• 제27권4호
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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.

• Communications for Statistical Applications and Methods
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• 제14권3호
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• pp.483-495
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• 2007

In a general fractional factorial design, the n-levels of a factor are coded by the $n^{th}$ roots of the unity. Pistone and Rogantin (2007) gave a full generalization to mixed-level designs of the theory of the polynomial indicator function using this device. This article discusses the optimal blocking scheme for nonregular designs. According to hierarchical principle, the minimum aberration (MA) has been used as an important criterion for selecting blocked regular fractional factorial designs. MA criterion is mainly based on the defining contrast groups, which only exist for regular designs but not for nonregular designs. Recently, Cheng et al. (2004) adapted the generalized (G)-MA criterion discussed by Tang and Deng (1999) in studying $2^p$ optimal blocking scheme for nonregular factorial designs. The approach is based on the method of replacement by assigning $2^p$ blocks the distinct level combinations in the column with different blocks. However, when blocking level is not a power of two, we have no clue yet in any sense. As an example, suppose we experiment during 3 days for 12-run Plackett-Burman design. How can we arrange the 12-runs into the three blocks? To solve the problem, we apply G-MA criterion to nonregular mixed-level blocked scheme via the mixed-level indicator function and give an answer for the question.

• Communications for Statistical Applications and Methods
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• 제6권3호
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• pp.695-706
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• 1999

When fractional factorial experiments contain some infeasible treatment combinations called debarred combinations we should construct experimental designs so that those debarred combinations are to be excluded by selecting defining contrasts appropriately. By applying Franklin(1995)'s procedure for selecting defining contrasts to Cheng and Li(1993)'s method this paper presents a method of selecting defining contrasts to construct orthogonal 3-level fractional factorial experiments which exclude some debarred combinations.

• Communications for Statistical Applications and Methods
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• 제15권2호
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• pp.235-244
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• 2008

실험계획의 요인배치법에서 부분실험을 설계할 때, 직교배열을 이용한 실험설계방법이 널리 사용된다. 그러나 부분실험의 해상도(resolution)가 큰 경우, 직교배열을 일반화한 균형배열이 효과적으로 사용될 수 있다. 특히 2-수준 요인실험법에서는 강도(strength)가 4인 균형배 열은 resolution-V인 부분실험법과 동일하다는 것이 알려져 있다. 본 연구에서는 강도(strength)가 4인 균형배열의 직교성을 평가하는 측도를 제시하고자 한다. 그리고 본 연구에서 제시된 평가측도를 응용하여 실험횟수가 가장 적고 직교성에 가까운 최소 균형 resolution-V 부분실험법의 설계방법을 제시하고자 한다.

• 응용통계연구
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• 제5권1호
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• pp.19-28
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• 1992

본 논문에서는 부분균형배열을 이용하여 $2^t$ 요인 실험계획에서 최소의 실험횟수를 가지 고 2인자 교호작용까지 분석할 수 있고, 추정량의 분산-공분산행렬이 균형을 이루고 있는 실험계획법을 기술하였다. 그리고 제안된 실험계획법의 최적성을 검토하여 트레이스 최적실 험계획을 찾아보았다. 이러한 최소균형 Resolution V $2^t$요인 부분실험법은 직교배열을 이용하여 주효과만 분석하는 기존의 다구찌방법과는 달리 2인자 교호작용까지 분석하고자 할 때 효과적으로 사용될 수 있으며 그 응용방법을 검토하였다.

• Journal of the Korean Statistical Society
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• 제32권3호
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• pp.235-244
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• 2003

In unreplicated factorial or fractional factorial experiments, the presence of one or more outliers can seriously affect the analysis of variance. Using the normal plot of t residuals to identify outliers in factorial or fractional factorial is an easy method to find these dubious points. In some cases, the t residuals form the identical pairs. One can not tell from the plot which is doubtful. This phenomenon occurs for all minimal designs of resolution IV, which fits the model containing all main effects and some two-factor interactions, whether it is orthogonal or not. In these kinds of models, when we drop one point or two points (not foldover pair) from the fraction, the phenomenon of identical pairs of t residuals may still occur. In this paper, the theoretical background of the phenomenon and its sequences will be investigated in detail.

• 품질경영학회지
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• 제28권3호
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• pp.59-67
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• 2000

In analysis of resolution IV fractional factorial experiments, the main effects only are analyzed, even though we can get some useful information on the confounded 2-factor interactions. In this paper, we introduce an exploiting method of the confounded structure of interactions, especially for the near minimal resolution IV 3$^{t}$ fractional factorial designs developed by Anderson and Thomas (1979). Moreover, in this paper the application way of the proposed method is also discussed by analyzing some simulated data.

• 대한안전경영과학회지
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• 제7권5호
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• pp.69-84
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• 2005

This paper proposes statistically designed experiments which provide a proactive means to implement safety and environmental applications. Minimal experimental designs such as fractional factorial design, Plackett-Burman design, Box-Behnken design are economical and can be achieved tremendous savings with relatively few experiments. These experimental designs and analysis methods are illustrated with cases.

• 한국연초학회지
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• 제5권1호
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• pp.49-56
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• 1983

• Journal of the Korean Statistical Society
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• 제8권2호
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• pp.125-130
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• 1979

It is well known that $L_2(m)$ type PBIB designs have the Property A, so they are BNAS PBIB designs. However, $L_3(m)$ type PBIB designs are not of type of Property A but do have the factorial structure (Cotter, John, and Smith(1973)). In this paper, the properties of the $L_3(m)$ type PBIB designs are investigated. Extended Property A and fractional BNAS are defined and a solution formula for the treatment effects in the $L_32(m)$ type designs is obtained.